ABSTRACT 
 
 
 
 
Title of Dissertation: PASSIVE AND ACTIVE GRADED-INDEX 
ACOUSTIC METAMATERIALS: SPATIAL 
AND FREQUENCY DOMAIN 
MULTIPLEXING  
  
  
 Amirhossein Yazdkhasti, Ph.D., 2022 
 
  
Dissertation directed by: Professor Miao Yu, Department of Mechanical 
Engineering and Institute for Systems Research, 
University of Maryland, College Park, MD 
 
 
  
Acoustic metamaterials, similar to their electromagnetic counterparts, are artificial subwavelength 
materials designed to manipulate sound waves. By tailoring the material's effective properties such 
as bulk modulus, mass density, and reflective index, these materials can be designed to achieve 
unprecedented acoustic waves control and realize functional devices of novel properties. 
Specifically, high-refractive-index acoustic metamaterials have an effective refractive index much 
larger than air, enabling wave compression in space and a strong concentration of wave energy. 
Another type of acoustic metamaterials closely related to high-index acoustic metamaterials is 
graded-index metamaterials, which can be obtained by gradually varying material compositions or 
geometry over a volume of high-index acoustic metamaterials. 
  
The overall goal of this dissertation is to achieve a fundamental understanding of passive and active 
graded-index acoustic metamaterials for spatial and frequency domain multiplexing and explore 
their applications in far-field acoustic imaging and sonar systems. Three research thrusts have been 
pursued. In the first thrust, the spatial domain multiplexing of passive graded-index acoustic 
metamaterials has been investigated for enhancing far-field acoustic imaging. An array of passive 
graded-index acoustic metamaterials has been designed and developed to achieve a far-field 
acoustic imaging system. Parametric studies have been carried out to facilitate the performance 
optimization of the imaging system. The performance of the metamaterial-based imaging system 
has been investigated and compared to the scenario without the metamaterials. In the second thrust, 
frequency-domain multiplexing with active graded-index acoustic metamaterials has been 
investigated. An active graded-index metamaterial system with a number of active unit cells has 
been designed and fabricated. A fundamental understanding of the frequency multiplexing 
properties of the metamaterials has been developed through numerical and experimental studies. 
In the third thrust, the capabilities of an acoustic sensing system with active graded-index 
metamaterials as an emitter for shape, size, and surface classification have been explored.  
 
 
 
 
  
 
 
 
 
 
 
 
PASSIVE AND ACTIVE GRADED-INDEX ACOUSTIC METAMATERIALS: 
SPATIAL AND FREQUENCY DOMAIN MULTIPLEXING 
 
 
 
 
                                                                      by 
 
 
Amirhossein Yazdkhasti 
 
 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2022 
 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor Miao Yu, Chair 
Professor Amr Baz 
Professor Balakumar Balachandran 
Professor Nikhil Chopra 
Professor Timothy Horiuchi (Dean?s Representative) 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Amirhossein Yazdkhasti 
2022 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
Dedication 
To my Maman and Baba for always loving and supporting me. 
Actually, they don?t read my stuff, so if someone doesn?t tell them about this, they 
will never know. 
 
 
 
 
 
 
 
 
 
 
ii 
 
 
 
Acknowledgements 
 
First and foremost, I am extremely grateful to my advisor, Professor Miao Yu, for her 
invaluable advice, continuous support, and patience during my Ph.D. study. Her 
immense knowledge and plentiful experience have encouraged me in all the time of my 
academic research and daily life. 
I am also very grateful to my Ph.D. supervisory committee members, Professor Amr 
Baz, Professor Balakumar Balachandran, Professor Nikhil Chopra, and Professor 
Timothy Horiuchi. I am grateful for their willingness to serve on my committee, 
provide me with help whenever needed, and review this dissertation. 
I acknowledge the generous financial support from the AFOSR Centre of Excellence 
on Nature-Inspired Flight Technologies and Ideas and NSF (CMMI1436347). 
I gratefully recognize the help of all the members of Sensor and Actuator Lab for their 
support and friendship. Special thanks to my colleague Dr. Randy Ganye, Keshav 
Rajasekaran, Dr. Liuxian Zhao, and Dr. Hyuntae Kim for a cherished time spent 
together in the lab and in social settings. My appreciation also goes out to Mr. Majid 
Aroom for his personal and professional supports. 
I would also like to thank many of my friends who supported me during my study at 
the University of Maryland. Finally, I would like to express my gratitude to my parents. 
Without their tremendous understanding and encouragement in the past few years, it 
would be impossible for me to complete my study. 
 
iii 
 
 
 
Table of Contents 
 
Dedication ..................................................................................................................... ii 
Acknowledgements ....................................................................................................... ii 
Table of Contents ......................................................................................................... iv 
List of Tables ............................................................................................................... vi 
List of Figures ............................................................................................................. vii 
Chapter 1: Introduction and Background ...................................................................... 1 
1.1 Problem statement ............................................................................................... 1 
1.2 Literature review ................................................................................................. 3 
1.2.1 Airborne acoustic imaging ........................................................................ 3 
1.2.2 Passive acoustic metamaterials .................................................................... 7 
1.2.3 Active acoustic metamaterials ................................................................... 13 
1.2.4 Bioinspired acoustic sensing ...................................................................... 18 
1.2.5 Acoustic classification ............................................................................... 22 
1.3 Overview of the dissertation work .................................................................... 25 
Chapter 2: Spatial domain multiplexed passive graded-index acoustic metamaterials 
for far-field acoustic imaging ...................................................................................... 28 
2.1 Introduction ....................................................................................................... 28 
2.2 Design and performance characterization of a single graded-index acoustic 
metamaterial device ................................................................................................ 29 
2.3 Design and development of an acoustic imaging system based on spatial 
domain multiplexed graded index acoustic metamaterials ..................................... 34 
2.3.1 Imaging algorithm ...................................................................................... 35 
2.3.2 Array design ............................................................................................... 36 
2.3.3 Imaging system development .................................................................... 41 
2.4 Directivity pattern of imaging system ............................................................... 43 
2.5 Performance of the imaging system .................................................................. 44 
2.5.1 Single object experiments .......................................................................... 44 
2.5.2 Two object imaging experiment ................................................................ 48 
2.5.3 Three objects imaging experiment ............................................................. 50 
2.6 Summary ........................................................................................................... 52 
Chapter 3: Active graded-index acoustic metamaterials with frequency domain 
multiplexing: Design, modeling, and development .................................................... 54 
3.1 Introduction and motivation .............................................................................. 54 
3.2 Design and fabrication ...................................................................................... 56 
3.3 Active metamaterial with single active unit cell ............................................... 61 
3.4 Metamaterial with three active unit cells .......................................................... 65 
3.4.1 Emission investigation ............................................................................... 66 
3.4.2 Reception investigation .............................................................................. 70 
3.5 Metamaterial with ten active unit cells ............................................................. 72 
3.5.1 Emission Performance of each active unit cell .......................................... 74 
3.5.2. Phase manipulation ................................................................................... 75 
3.5.3 Directivity pattern ...................................................................................... 81 
iv 
 
 
 
3.5.4 Mimicking bat emission calls .................................................................... 82 
3.5.5 Reception performance of the active metamaterial receiver ...................... 84 
3.6 Summary ........................................................................................................... 85 
Chapter 4: Active graded-index acoustic metamaterials for sonar applications ......... 87 
4.1 Introduction ....................................................................................................... 87 
4.1.1 Object recognition ...................................................................................... 88 
4.1.2 Texture classification ................................................................................. 89 
4.2 Proposed sonar classification system ................................................................ 90 
4.3 Machine learning methods ................................................................................ 93 
4.3.1 K-Nearest Neighbors (KNN) ..................................................................... 94 
4.3.2 Support Vector Machine (SVM) ................................................................ 94 
4.3.3 Random Forest (RF) .................................................................................. 94 
4.3.4 Multilayer Perceptron (MLP) .................................................................... 95 
4.3.5 Convolutional Neural Network (CNN) ...................................................... 96 
4.4 Numerical simulation studies ............................................................................ 97 
4.5 Experiment ...................................................................................................... 101 
4.5.1 Performance optimization with time shifts in emission signal ................ 102 
4.5.2 Shape and size classification .................................................................... 104 
4.5.3 Surface roughness classification .............................................................. 107 
4.6 Summary ......................................................................................................... 111 
Chapter 5: Summary ................................................................................................. 114 
5.1 Summary of the dissertation work .................................................................. 114 
5.2 Suggested future work .................................................................................... 115 
Bibliography ............................................................................................................. 117 
 
v 
 
 
 
List of Tables 
 
Table 3-1: Material properties of PIC255. .................................................................. 60 
Table 3-2: Properties of piezoelectric discs. ............................................................... 61 
Table 4-1:MLP parameters ......................................................................................... 96 
Table 4-2: Simulated shape and size classification accuracy of different supervised 
learning methods for system with and without metamaterial. .................................. 100 
Table 4-3: Shape and size classification accuracy of CNN algorithm for different 
signals. ...................................................................................................................... 104 
Table 4-4: Shape classification accuracy of different supervised learning methods for 
system with and without metamaterial ..................................................................... 105 
Table 4-5: Shape and size classification accuracy of different supervised learning 
methods. .................................................................................................................... 107 
Table 4-6: Surface classification accuracy of different supervised learning methods 
for system with and without metamaterial ................................................................ 111 
vi 
 
 
 
List of Figures 
Figure 1-1: (a) Picture of the prototype assembly with 16 elements and picture of 
single element [28], (b) prototype system comprises a linear array of 16 speakers 
[18], (c) 8 by 8 microphone array [29]. ........................................................................ 5 
Figure 1-2 (a) Schematic top view of the 9 emission/reception panel [36]. (b) 
Overview of the experimental setup with 128 element array [33]. (c) The top view of 
the sound compass microphone array[35]. ................................................................... 7 
Figure 1-3: (a) Schematic of a tapered metamaterial slab comprised of an array of 
stainless plates spaced by air gaps [42]. (b) Schematic of photonic?acoustic 
metamaterial hybrid sensing system [42]. (c) Schematic illustrations of the sample 
planer acoustic superlens [44], (d) Schematic of experimental setup [44], (e) 
Illustration of the metamaterial consisting of a periodic array of five symmetrical 
resonators [45],(f) Experimental realization using 3D printing [45]. ........................... 9 
Figure 1-4: (a) A cylindrical helical-structured unit cell consists of four equally 
spaced wide blades spiraling around a slender shaft [16], (b) Photograph of the 
fabricated helical-structured metamaterial unit cell [16], (c) 40 helical-structured 
metamaterial unit cells were fabricated and utilized to construct acoustic meta-lens 
[16] (d) Schematic illustration of the cochlear-inspired structure [47], (e) The 
schematic diagram of the three-dimensional axisymmetric acoustic GRIN lens[15]. 11 
Figure 1-5: (a) Schematics of the system, composed of a transmitter and a receiver 
that are spatially symmetrical. Each part is composed of a filter layer (green) and a 
grating layer (blue) [49]. (b) Schematic holey-structured metamaterial for deep-
subwavelength acoustic imaging [50]. (c) Picture of holey-structured 
metamaterial [50], (d) The model of the holey-structured lens cell [51],(e) The model 
of unit cell [51]............................................................................................................ 13 
Figure 1-6: (a) Schematics of the helical cylinder with two spiraling blades connected 
through a slender central column[52], (b) The fabricated helical cylinder is based on 
the 3D printing technique. [52],(c) The sample of the tunable metasurface is 
composed of a perforated circular plate and helical cylinders [52], (d) Schematics of 
acoustic metamaterial comprising an array of DE [53], (e) acoustic metamaterial 
comprising an array of DE [53].. ................................................................................ 15 
Figure 1-7: (a) Sketch of the AEH system composed of a defected supercell with a 
piezoelectric patch and a load circuit [54]. (b) Computed band structure in the 
frequency range (1.8 to 2.5 kHz) [54]. (c) Illustration of the plate with the cylindrical 
stubs and the L-shaped waveguide [55]. (d) The amplitude of the measured pressure 
field inside the Bragg-type bandgap at 117 kHz [55]. (e) experimental sample of the 
subwavelength active tube array [56]. (f) The radiation acoustic intensity fields of the 
planar acoustic focusing model [56]. .......................................................................... 17 
Figure 1-8: (a) Construction of the proposed active acoustic metamaterial cell 
composed of water volume confined from both sides with piezoelectric bimorphs[57] 
(b)The unit cell consists of a piezoelectric membrane controlled by electronics, 
photograph of fabricated unit cell and Metamaterial slab consisting of ten unit 
cells[37]. (c)Time instances of the acoustic responses to each one of the three 
pulses[37]. ................................................................................................................... 18 
vii 
 
 
 
Figure 1-9: (a) Photo of flexible sonar sensing platform[75]. (b) Assembled system 
setup mounted on the P3DX robot[75]. (c) ERLE-COPTER drone with sonar sensor 
platform[75]. ............................................................................................................... 20 
Figure 1-10: (a,b) Image and laser-generated map for the guidance experiment. The 
trajectories of 3 runs are depicted in the laser range map in different colors [77]. 
(c) Image of the Robat. Insert shows the Robat?s sensory unit, including a speaker and 
two receivers[79]. ....................................................................................................... 22 
Figure 1-11:(a,b) Experimental set-up [82]. (c) Measurement setup with two 
translation stages (x and y) and a rotation stage. The speaker and the microphone are 
moved along the x-axis. Thereby, echoes can be recorded at relative positions, which 
correspond to those of a robot passing by a target[81]. .............................................. 24 
Figure 2-1: (a) Dispersion curve of the metamaterial and air [42]. (b) The pressure 
field of sound is spatially compressed and amplified inside the graded high-refractive-
index acoustic metamaterial. (c) Schematic of the design of graded-index acoustic 
metamaterial. ............................................................................................................... 30 
Figure 2-2: (a) Simulated pressure field distribution. Frequency response at the peak 
pressure location with and without the metamaterial: (b) simulation results and (c) 
experimental data. (d) Simulated and experimental pressure amplification gain. ...... 33 
Figure 2-3: Directivity paterns of MEMS microphone with and without the 
metamaterial: (a) simulation results and (b) experimental results. ............................. 34 
Figure 2-4: Schematic of the entire imaging system, including an ultrasound speaker, 
a receiver array with 32 metamaterial-based sensing elements, a data acquisition 
(DAQ) system. The DAQ system is used to generate a 25 kHz sinusoidal input signal 
with a duration of .001 s to drive the speaker (located at the center of the array) and 
obtain receiver output signals. .................................................................................... 36 
Figure 2-5: Investigation of array spacing: (a)simulated pressure along X direction for 
different spacing, (b)schematic of the array used in simulations, (c) experimental 
setup, and (d) simulated and experimental gain of an array with deferent element 
spacing. ....................................................................................................................... 39 
Figure 2-6: (a) Image of an object with 32 element array of 3 cm spacing and 93 cm 
aperture size, (b) a 16 element array with 6 cm spacing and 93 cm aperture size, (c) 
a16 element array with 3 cm spacing and 46 cm aperture size. (d,e) Image amplitude 
along a vertical and horizontal line that passes through object position using arrays 
with the same aperture size and different spacing (3 and 6 cm). (f,g) Image amplitude 
along a vertical and horizontal line that passes through object position using arrays 
with the same spacing and different aperture size (93 and 45 cm). ............................ 40 
Figure 2-7: (a) Frequency of 32 MEMS microphones, (b) Sensitivity of 32 MEMS 
microphones at 25 kHz. .............................................................................................. 41 
Figure 2-8: Schematic of metamaterial receiver array with 32 sensing elements. A 
MEMS microphone is embedded in each sensing element at the maximum pressure 
amplification location for 25 kHz to measure the amplified echo signal. (c) 
Photograph of the fabricated and fully assembled imaging system. The insets in (b) 
and (c) show the schematic and the photograph of a single metamaterial sensing 
element, respectively. .................................................................................................. 42 
Figure 2-9: Directivity patterns of the metamaterial-based imaging system and 
MEMS microphone-based imaging system. ............................................................... 44 
viii 
 
 
 
Figure 2-10: Averaged maximum image amplitude versus object distance obtained 
with the metamaterial array and the MEMS array. The object was a 9 cm diameter 
pipe. ............................................................................................................................. 45 
Figure 2-11: Averaged maximum image amplitude versus object diameter was 
obtained with the metamaterial array and the MEMS array. The object was placed 5 
m away from the imaging array. ................................................................................. 47 
Figure 2-12:(a-c) 2D image, image amplitude along Y axis, image amplitude along X-
axis of a 9 cm diameter pipe at a distance of 15 m, respectively. (d-j) 2D image, 
image amplitude along Y axis, image amplitude along X-axis of a 6 mm diameter 
pipe object at a distance of 5 m, respectively. The image amplitude along X (or Y) 
axis was obtained at the maximum amplitude along Y (or X) axis. ........................... 48 
Figure 2-13: Imaging of three objects of different sizes in three different positions. (a) 
Schematic of the experiment. (b) 2D image in XY plane obtained with the 
metamaterial array. (c) Image project along the line x=0 obtained with the 
metamaterial array. (d) 2D image in XY plane obtained with the MEMS array. (e) 
Image project along the line x=0 obtained with the MEMS array. The insets in (b) and 
(d) are the zoomed-in images of the three. The red boxes in (c) and (e) are represent 
objects with different diameters. ................................................................................. 51 
Figure 3-1: (a) Human cochlear and Basilar membrane displacement as a function of 
frequency[87]. (b) The frequency domain multiplexing behavior of a graded-index 
acoustic metamaterial [43]. ......................................................................................... 55 
Figure 3-2: Schematic of active graded-index metamaterial devices with (a) 0.56 gap 
size and (b) 1 mm gap size. The red elements are piezoelectric discs. (c) Simulated far 
field pressure field obtained with (a) and (b), when the metamaterials are used for 
acoustic emission of three different frequencies. ........................................................ 57 
Figure 3-3: (a) Schematic of a MEMS microphone integrated with a passive graded-
index acoustic metamaterial device. (b) Schematic of a piezoelectric disc serving as 
an active element in an active graded-index acoustic metamaterial device. ............... 58 
Figure 3-4: Different methods to attach piezoelectric disc to the metamaterial: (a) side 
glued. (b) two points glued. (c) base glued. ................................................................ 59 
Figure 3-5: Simulated air pressure field and piezoelectric displacement field at 20 
kHz in reception and emission phases. ....................................................................... 62 
Figure 3-6: (a) Simulated far-field pressure frequency sweep with and without 
metamaterial,(b) Experiment far-field pressure frequency sweep with and without 
metamaterial,(c)Simulated generated voltage frequency sweep with and without 
metamaterial,(d) Experiment generated voltage frequency sweep with and without 
metamaterial, ............................................................................................................... 64 
Figure 3-7: Directivity pattering of metamaterial and piezoelectric disc at 21200 Hz 65 
Figure 3-8: (a) Schematic of the active graded-index metamaterial and working 
frequency of different active unite cells. (b)Photograph of the active graded-index 
metamaterial. ............................................................................................................... 66 
Figure 3-9: (a) Schematic of the metamaterial device with an active unit cell in red.  
(b) Simulated and (c) experimental frequency spectra of far- field pressure when a 
single piezoelectic disc was activated. ........................................................................ 67 
ix 
 
 
 
Figure 3-10: (a) Schematic of metamaterial with three active unit cells (in red). 
Spectra of far-field pressure when all the piezoelectric discs were activated: (b) 
simulation results and (c) experimental results. .......................................................... 68 
Figure 3-11: Pressure distribution of active metamaterial at three frequencies (a) 33.9 
kHz, (b) 28 kHz, (c) 23.3 kHz. ................................................................................... 69 
Figure 3-12: Directivity pattern of active graded-index metamaterial used for acoustic 
emission: (a) simulation and (b) experiment. ............................................................. 70 
Figure 3-13: Pressure distribution of the graded-index metamaterial in sensing mode 
for (a) 23000 Hz, (b)28000Hz, and (c)32000 Hz. ....................................................... 71 
Figure 3-14: (a) Schematic of the metamaterial with an active unit cell (in red). 
Spectral behavior at the active unite cell obtained with and without the metamaterial: 
(b) simulations and (c) experiment. ............................................................................ 72 
Figure 3-15: (a)Schematic of the active graded-index metamaterial and working 
frequency of different active unite cells. (b)Photograph of the active graded-index 
metamaterial. ............................................................................................................... 74 
Figure 3-16: (a) Simulated far-field pressure frequency sweep of all the active 
unicells of metamaterial, (b) Experimental far-field pressure frequency sweep of all 
the active unicells of metamaterial, ............................................................................ 75 
Figure 3-17: (a) Far-field pressure when 25th and 27th activated invidiously 
and simultaneous with 0 and 170-degrees phase differences. (i) Far-field pressure 
phase when 25th and 27th are activated. (b) Experimental phase sweep for the 
metamaterial when 25th and 23rd elements are activated. ........................................... 77 
Figure 3-18:(a,e) Simulated and experimental phase sweep for two piezoelectric with 
distance of 2mm, (b.f) Simulated and experimental phase sweep for the metamaterial 
when 25th and 23rd elements are activated, (c,g) Simulated and experimental phase 
sweep for the metamaterial when 27th and 23rd elements are activated, (d,h) Simulated 
and experimental phase sweep for the metamaterial when 29th and 23rd elements are 
activated. ..................................................................................................................... 79 
Figure 3-19: (a,b) Manipulation of emission spectrum with phase difference applied 
to active elements in the metamaterial: (a) uniform phase to generate curved spectrum 
and (b) various phase differences to generate flat spectrum. ...................................... 80 
Figure 3-20: (a) Directivity pattern of piezoelectric at different frequencies, 
(b)Directivity pattern of metamaterial at different frequencies .................................. 82 
Figure 3-21: (a) Single harmonic bat signal (b) two harmonic bat signal, (c,d) 
Spectrogram of metamaterial to imitate bat signals with one harmonic and two 
harmonics trough simulation.(e,f) Spectrogram of metamaterial to imitate bat signal 
with one harmonic and two harmonics trough experiment ......................................... 84 
Figure 3-22: (a) Simulated generated voltage frequency sweep of all the active 
unicells of metamaterial, (b) Experimental generated voltage frequency sweep of all 
the active unicells of metamaterial. ............................................................................ 85 
Figure 4-1: Experiment setup. (i) expected frequency components of the signal 
generated by different active unit cells ....................................................................... 91 
Figure 4-2: Acoustic classification framework. .......................................................... 93 
Figure 4-3: schematic depiction of CNN algorithm. .................................................. 96 
Figure 4-4: schematic depiction of CNN algorithm. .................................................. 97 
x 
 
 
 
Figure 4-5: (a) Simulated pressure distribution of broadband gaussian signal reflected 
by concave signal. ....................................................................................................... 98 
Figure 4-6: (a) Simulated pressure at a distance of 20cm from the object (b) 
Spectrogram of simulated pressure. ............................................................................ 98 
Figure 4-7: Shape confusion matrixes of CNN for broadband and narrowband 
scenario. .................................................................................................................... 100 
Figure 4-8: Size confusion matrixes of CNN for broadband and narrowband scenario.
................................................................................................................................... 101 
Figure 4-9: (a-c) Generated signal when only one piezoelectric disc is activated with a 
time shift of 0ms, .85ms, and 1.7ms. (d-f) Generated signal when all piezoelectric 
discs are activated with a time shift of 0ms, .85ms, and 1.7ms. (g-l) Frequency 
response and Spectrogram of generated signal with a time shift of 0ms, .85ms, and 
1.7ms. ........................................................................................................................ 103 
Figure 4-10: Shape classification confusion matrix of CNN .................................... 105 
Figure 4-11: (a) Shape classification confusion matrix of CNN. (b) Size classification 
confusion matrix of CNN. (c) Size and shape classification confusion matrix of CNN
................................................................................................................................... 107 
Figure 4-12: (a) Structured targets which were discs covered with cubes with different 
diameters. (b,c) frequency components of echoes from different objects using 
metamaterial and 25kHz narrowband speaker. ......................................................... 109 
Figure 4-13: Principal components analysis scatterplot of different classes with and 
without metamaterial. ............................................................................................... 110 
Figure 4-14: Classification confusion matrix of MLP for system with and without 
metamaterial .............................................................................................................. 111 
 
xi 
 
 
 
1. Chapter 1: Introduction and Background 
 
1.1 Problem statement 
Metamaterials are artificially engineered materials exhibiting unique or unusual 
properties that cannot be found in natural materials. Metamaterials can help overcome 
the limitations encountered with using natural materials. In 1967, Veselago proposed 
the theoretical framework of metamaterials, based on the interaction between 
electromagnetic waves and structural constituents of natural materials, which initiated 
metamaterial research [1]. However, physical experimentation on metamaterials did 
not occur until thirty-three years later due to the lack of available materials and 
sufficient computing resources. Since then, metamaterials with unique 
electromagnetic, optical, or acoustic properties have been proposed for a variety of 
applications such as metamaterial antennas [2], absorbers [3], superlens [4], cloaking 
devices [5], radars [6], and seismic protection [7]. 
The focus of this dissertation is on acoustic metamaterials, which are artificially 
engineered subwavelength composites capable of controlling and manipulating 
acoustic waves in manners that are uncommon in natural materials. Recent research on 
acoustic metamaterials have led to significant advances in acoustic technologies and 
functional devices such as negative refraction materials [8], super-resolution imaging 
devices [9], acoustic sensing systems[10], acoustic filters [11], waveguides [12][13], 
clocking devices [14], sound isolators [15], and acoustic lenses [16][17]. Generally, 
natural materials are assumed to be homogeneous medium. The wave equation in non-
1 
 
 
 
viscous homogeneous gases and liquids medium (adiabatic process) can be written as 
the following [18]: 
2
                                        ?2?? ? ?? ?? ??2 = 0                                                    (1-1) ?? ????
where ?? is the pressure, ?? is the mass density, and B is the adiabatic bulk 
modulus. Here, the speed of the wave in the medium is ?? = ???/??  . Through designing 
subwavelength unit cells of acoustic metamaterials, the material effective bulk modulus 
and mass density can be tailored so that unprecedented control of acoustic waves can 
be realized and functional devices of novel properties can be developed.  
Note that the refractive index ?? of a medium is a dimensionless number that 
characterizes the wave propagation through the medium, and determines how waves 
can be refracted, when entering the medium from air. It is conventionally defined as 
?? = ??0/??, where ??0is the speed of wave in air. For acoustic waves, the speed of the 
wave in air (340 m/s) is slower than that in any other natural materials. Therefore, for 
all the natural materials, their refractive indices are considered to have positive values 
smaller than that of the air (nair=1).  
Recently, the concept of acoustic metamaterials has been extended far beyond 
the scope of negative refraction materials since these materials can be designed to 
respond sound waves with large values of positive or negative mass densities, bulk 
moduli, and refractive indices. There is growing interest in acoustic metamaterials 
based on strong anisotropic structures/compositions. This gives rise to the field of 
anisotropic metamaterials, which enable the realization of functional devices with 
various novel material properties. One notable example of anisotropic metamaterials is 
high-index metamaterials. Note that the refractive index can also be seen as a factor by 
2 
 
 
 
which the wavelength in the medium is scaled with respect to that in air (e.g., ? =?0 /n, 
where ?0 is the wavelength in air). For natural materials, this implies that an acoustic 
wave in air has the shortest wavelength. However, a high-refractive-index metamaterial 
can be designed to have an effective refractive index neff much larger than that of air, 
and thus it can compress the wave in space and induce a strong concentration of wave 
energy. 
Another types of metamaterials that are closely related to high-index metamaterials 
are graded-index metamaterials, which can be obtained by varying material 
compositions or geometric parameters gradually over a volume of high-index 
metamaterials, resulting in favorable material properties. In this dissertation work, 
graded-index acoustic metamaterials constructed with alternating subwavelength air?
solid material layers will be investigated to achieve spatial and frequency domain 
multiplexing, which can help realize novel acoustic imaging and sonar devices.  
1.2 Literature review 
In this section, literature review on the following topics will be provided: i) airborne 
acoustic imaging, ii) passive acoustic metamaterials, iii) active acoustic metamaterials, 
and iv) bioinspired echo-acoustic sensing. v) acoustic classification. 
1.2.1 Airborne acoustic imaging 
Acoustic imaging using an array of acoustic transducers have been widely studied. A 
wide variety of array arrangement has been used, including linear array [19], 
combination of linear arrays [20], planar square array[21], cross array [22] [23], 
3 
 
 
 
circular array[24], combination of circular and linear array[25], spiral array [26], sparse 
2D array [27], and spherical array [28]. 
Commercial microphones and speakers are often used to build acoustic imaging 
systems. However, when commercial devices couldn?t meet the characteristic 
requirement, development of an acoustic transducer would be necessary. Capineri et 
al. [29] presented an airborne ultrasonic imaging system with a new sensor design 
operating at 150 kHz, which can be used for both close-range and long-range imaging. 
An array of 16 transducers was used for imaging (Figure 1-1 (a)). Each transducer 
consists of a hemicylindrical polyvinylidene fluoride film mounted on a printed circuit 
board. The transducers have very narrow directivity, which is a desirable feature for 
synthetic aperture imaging. Ultrasonic signals and a window with envelope data were 
used for image reconstruction, which reduced the computational cost. 
Some research focused on redesigning a well- developed imaging system for a 
particular application. Lindell et al. [19] demonstrated an alternate modality for non-
line-of-sight acoustic imaging. A linear array of 16 pairs of collocated speakers and 
microphones was mounted vertically on a horizontally scanning translation stage to 
image and resolve 3D shapes of hidden around corners (Figure 1-1 (b)). The resolution 
and signal decay of this modality were characterized. In another study, Izquierdo et al. 
[30] used a planar array of MEMS microphones to generate an acoustic image for 
biometric identification applications. The hardware of the system was based on 
modules of 8 by 8 square array of MEMS microphones that are spaced uniformly 
(Figure 1-1 (c)). The results revealed the feasibility of the system to make an acoustic 
4 
 
 
 
image of a person. This imaging system was also used for fault diagnosis [31] and high 
resolution imaging [32].  
 
Figure 1-1: (a) Picture of the prototype assembly with 16 elements and picture of single element 
[29], (b) prototype system comprises a linear array of 16 speakers [19], (c) 8 by 8 microphone array 
[30]. 
Shirkovskiy et al. [33] proposed an airborne ultrasound surface motion camera 
for non-contact surface vibrometry of the chest to provide useful data to promote 
cardiovascular health. Their system consists of nine emission panels arranged in a 
square matrix and one reception panel positioned at the same location as the central 
emission panel. Each emission panel is composed of 32 piezoelectric transducers 
uniformly distributed over an area of 24 cm x 24 cm, and the reception panel is 
composed of 16 by16 square array of receivers (Figure 1-2 (a)). A fast 2D mapping 
was achieved by originally combining multi-element airborne ultrasound arrays, a 
synthetic aperture implementation, and pulsed-waves. 
Crake et al. [34] designed a 3D sparse array for active and passive ultrasound 
imaging within a clinical MRI. The array was constructed from 5 by 0.4 mm 
piezoceramic disc elements arranged in a pseudorandom array (Figure 1-2 (b)). By 
exploiting thickness and radial resonance modes of the piezo discs, the array was 
5 
 
 
 
capable of both B-mode imaging at 5 MHz for skull localization, as well as passive 
reception at the second harmonic of the therapy array for detection of cavitation and 
3D passive acoustic imaging. With the active mode, B-mode imaging and 3D 
localization of a human skull were demonstrated by using the array, which was in a 
good agreement with the MRI imaging.  
Fedorkoa et al. [35] examined the possibilities of using acoustic visualization 
techniques in identifying adverse parameters or locations of occurrence of undesired 
operational conditions. An acoustic camera with a star microphone array using a 
rectangular display plane was used to accurately calculate the delay of acoustic sound 
signals emitted from different sound sources to individual microphones and eventually 
identified sources of noise as an indicator of the occurrence of adverse operational 
situations. 
Tietethe et al. [36] developed a sound compass, which was capable of 
measuring local noise levels and sound field directionality. The compass was composed 
of a sensor array with 52 MEMS microphones, an inertial measuring unit, and a low-
power field-programmable gate array arranged in four concentric rings (Figure 1-2 (c)). 
A data fusion technique based on probability map was introduced to combine the 
measurement data of several compasses and accurately locate five sound sources. 
 
 
6 
 
 
 
 
Figure 1-2 (a) Schematic top view of the 9 emission/reception panel [37]. (b) Overview of the 
experimental setup with 128 element array [34]. (c) The top view of the sound compass microphone 
array[36]. 
1.2.2 Passive acoustic metamaterials 
Generally, metamaterials are artificial structures with periodically or non-periodically 
arranged subwavelength elements, which exhibit unusual properties beyond natural 
occurring media [38]. Acoustic metamaterials are subwavelength composites that 
manipulate and control sound waves in ways that are not possible in conventional 
materials [39]. Recent research on acoustic metamaterials have led to significant 
advances in acoustic technologies and functional devices such as negative refraction 
materials, super resolution imaging devices [9], acoustic sensing systems [40], acoustic 
filters [11], waveguides [41], invisible clocks [42], sound isolators, and acoustic lenses.  
Most of the reported acoustic metamaterials are passive materials, which do not 
include active elements or external control system to vary the performance of the 
materials. Many of the passive acoustic metamaterials are constructed by using periodic 
structures. For example, Chen et al. [43] demonstrated a metamaterial-enhanced 
acoustic sensing system that achieves more than 20 dB signal-to-noise enhancement by 
7 
 
 
 
using graded-index acoustic metamaterials. The metamaterials consist of alternating 
subwavelength air?metal layers. This design allows sound propagation with a large 
wave vector, rendering a high-refractive-index medium. The higher reflective index 
leads to shorter wavelengths, which enables a spatial concentration of wave energy and 
induces a strong pressure enhancement in the metamaterials. By using this 
metamaterial, weak acoustic pulse signals overwhelmed by the noise were successfully 
recovered. In a later study, a miniature fiber optic acoustic probe capable of 
omnidirectional detection was used to spatially map both internal and external acoustic 
fields of this type of metamaterials [44]. 
Jia et al. [45] proposed an acoustic metamaterial based superlens, which 
consists of a periodic array of rigid slabs. The metamaterial was based on the excitation 
of guided modes and the moderate amplification of the evanescent waves that carry the 
subwavelength details of the objects. Subwavelength imaging with this metamaterial 
superlens was demonstrated.  
Moleron and Daraio [46] also presented a layered acoustic metamaterial that 
could transmit components of the acoustic field that were approximately equal to or 
smaller than the operating wavelength. The metamaterial consists of a wave-guiding 
structure with an array of coupled symmetric resonators. Evanescent waves containing 
subwavelength information were converted into propagative waves, which excited 
trapped resonances, and the periodicity was used to attenuate the propagative 
components. The metamaterial was demonstrated to provide sharp images of the edge 
of an object, with a resolution much smaller than the wavelength. In another work, 
Moler?n theoretically and experimentally investigated visco?thermal effects on the 
8 
 
 
 
acoustic propagation through metamaterials consisting of rigid slabs with 
subwavelength slits embedded in air [15]. 
 
Figure 1-3: (a) Schematic of a tapered metamaterial slab comprised of an array of stainless plates 
spaced by air gaps [42]. (b) Schematic of photonic?acoustic metamaterial hybrid sensing system 
[42]. (c) Schematic illustrations of the sample planer acoustic superlens [44], (d) Schematic of 
experimental setup [44], (e) Illustration of the metamaterial consisting of a periodic array of five 
symmetrical resonators [45],(f) Experimental realization using 3D printing [45]. 
In addition to layered structures, there are other kinds of unit cells that have 
been used to construct acoustic metamaterials. For example, Zhu [17] proposed and 
demonstrated a helical-structured acoustic metamaterial with a non-dispersive high 
effective refractive index, which could be tunable through adjusting the helicity of 
structures. The helicity-dependent refractive index of the metamaterials provided a new 
way to engineer the phase of acoustic waves passively. An array of these metamaterials 
was used to turn a normally incident plane wave into a self-accelerating beam along 
the prescribed parabolic trajectory.  
9 
 
 
 
Jia et al. [47] designed and developed a two-way spiral-shaped metamaterial 
and its two-dimensional array, which is capable to enhance sound energy. Due to the 
impedance matching design, the meta-structure shows almost opposite transmission 
behaviors in orthogonal directions. In one direction, sound waves are compressed and 
amplified due to a high-refractive index, while near-zero transmittance occurs along 
the other direction. Experimental results and numerical simulations revealed that the 
emission wave's sound intensity can be increased more than fifteen-fold compared with 
the insulation condition in the range of 4.8?5.8 kHz when the anisotropic metamaterial 
array was applied.  
Zhao and Zhou [48] proposed an acoustic metamaterial-based artificial cochlea, 
which was based on acoustic rainbow trapping. The device consisted of Helmholtz 
resonators arranged at sub-wavelength intervals along a cochlear-inspired spiral tube. 
The Helmholtz resonators had linear variation in heights, leading to a systematic 
modulation of the acoustic bandgap. This device was a frequency selective structure 
with graded geometries and properties that could filter mechanical waves spectrally 
and spatially.  
Li et al. [16] designed an ultrathin planar acoustic lens capable of focusing low-
frequency acoustic waves in 3D space. A specified type of hybrid labyrinthine unit was 
formed by coupling a modified coiling structure with air channels as the basic building 
blocks of the lens. The theoretical and the experimental results demonstrated that the 
resulting lens could enhance the acoustic energy by 15 dB at the focal point with very 
high transmission efficiency when acoustic waves with wavelength nearly six times 
larger than its thickness passed through. 
10 
 
 
 
Jin et al. [49] reported a new class of acoustic gradient-index metasurface 
engineered from soft graded-porous silicone rubber with a high acoustic index for 
broadband ultrasonic three-dimensional wavefront shaping in water. The value of the 
acoustic index was controlled by controlling the porosity of the silicone rubber. Lenses 
with different applications were designed by changing their reflective indices in 
different parts. These acoustic lenses were shown to generate steered planar, focused 
spherical, and helical acoustic wavefronts. 
 
Figure 1-4: (a) A cylindrical helical-structured unit cell consists of four equally spaced wide blades 
spiraling around a slender shaft [17], (b) Photograph of the fabricated helical-structured 
metamaterial unit cell [17], (c) 40 helical-structured metamaterial unit cells were fabricated and 
utilized to construct acoustic meta-lens [17] (d) Schematic illustration of the cochlear-inspired 
structure [48], (e) The schematic diagram of the three-dimensional axisymmetric acoustic GRIN 
lens[16]. 
Up to now, a variety of passive acoustic metamaterials and their capabilities 
have been discussed. Using these capabilities to overcome the limitation of the imaging 
systems is the next step. Over the past few years, several research groups have focused 
11 
 
 
 
on developing and improving an acoustic imaging system using metamaterials. Ma et 
al. [50] designed and tested an acoustic far-field subwavelength imaging system based 
on wave vector conversion. The system was based on a combination of resonator arrays 
that could enhance the waves with specific wave vectors and binary phase gratings that 
could add or subtract wave vectors by the first-order diffraction. The resonator array of 
subwavelength unit cells was designed to amplify selected subwavelength spatial 
frequencies. Binary phase grating was designed to remove the incident propagating 
components and to convert the subwavelength incident components to propagating 
ones. After the propagating wave passed through a long waveguide with minor 
attenuation, it was converted back into the incident wave. The performance of the 
system was evaluated for the edge detection of acoustic scattering objects. 
Zhu et al. [51] reported a 3D holey-structured metamaterial that could achieve 
acoustic imaging of objects with a feature size far below the diffraction limit. The 
metamaterial was a rigid block perforated with a periodic array of deep-subwavelength 
square holes surrounded by air. Propagation of acoustic waves inside deep-
subwavelength-sized apertures was shown to lead to the formation of Fabry-P?rot 
transmission resonances. These Fabry-P?rot resonant modes could be excited 
by evanescent field components of a subwavelength object and used to form an image 
with a feature size far below the diffraction limit. Similarly, Su used a holey-structured 
metamaterial for near-field acoustic imaging beyond the diffraction limit, but their 
metamaterial consisted of a rigid slab perforated with an array of cylindrical holes with 
periodically modulated diameters [52]. These works are all for near field imaging, and 
studies on far-field imaging are still relatively lacking. 
12 
 
 
 
 
Figure 1-5: (a) Schematics of the system, composed of a transmitter and a receiver that are 
spatially symmetrical. Each part is composed of a filter layer (green) and a grating layer 
(blue) [49]. (b) Schematic holey-structured metamaterial for deep-subwavelength acoustic 
imaging [50]. (c) Picture of holey-structured metamaterial [50], (d) The model of the holey-
structured lens cell [51],(e) The model of unit cell [51]. 
1.2.3 Active acoustic metamaterials 
Properties of acoustic metamaterials are determined to a great extent by their structures 
instead of the properties of the materials. The acoustic properties of passive 
metamaterials are difficult to change once they are fabricated, so they have fixed 
capabilities to manipulate the sound. Tunable, reconfigurable, or active acoustic 
metamaterials are alternatives to address this limitation. Active capabilities can be 
achieved by using active components and reconfigurable structures in the 
metamaterials. In this case, the properties of the metamaterials can be actively tuned 
for enhanced functionalities (e.g., broadband capacities). Some examples of active 
acoustic metamaterials are reviewed as follows. 
Zhao et al. proposed an active acoustic metamaterial with active unit cells based 
on helical cylinders that were screwed into a plate. It was used as a continuously tunable 
13 
 
 
 
acoustic metasurface. By controlling the screwed depth, the spiral channel length and 
subsequently phase of the acoustic wave that passes through the spiral channel could 
be tuned continuously. Different distributions of the unit components could be designed 
to provide various applications. One of the applications that were extensively 
investigated with the metasurface was three-dimensional adjustable broadband acoustic 
focusing [53]. 
Various actuators can be used to actively control the geometry of unit cells of 
acoustic metamaterials. Active acoustic metamaterials can be constructed using smart 
materials such as piezoelectric. These materials can generate a mechanical strain under 
an applied electrical field. Research on utilizing smart materials in active acoustic 
metamaterial structures will be discussed next. 
Yu et al. [54] proposed active acoustic metamaterials with relatively broadband 
sound attenuation performance. The metamaterial was comprised of an array of 
resonators being attached to the sidewall of a rigid duct. Each unit cell of the 
metamaterial was a pre-stretched dielectric elastomer (DE) membrane used to tune the 
acoustic property of each resonator and subsequently control the property of 
metamaterial. 
14 
 
 
 
 
Figure 1-6: (a) Schematics of the helical cylinder with two spiraling blades connected through a 
slender central column[52], (b) The fabricated helical cylinder is based on the 3D printing 
technique. [52],(c) The sample of the tunable metasurface is composed of a perforated circular 
plate and helical cylinders [52], (d) Schematics of acoustic metamaterial comprising an array of 
DE [53], (e) acoustic metamaterial comprising an array of DE [53]. 
Qi proposed an acoustic energy harvester based on a defected acoustic 
metamaterial with piezoelectric material [55]. The strain energy was originated from 
an acoustic incidence by creating suitable resonant defects in the acoustic metamaterial. 
The metamaterial was based on an array of silicone rubber stubs that were periodically 
deposited on a thin homogenous aluminum plate. Piezoelectric discs replaced four 
stubs. Removing these stabs confined the strain energy that originated from the acoustic 
wave, and this confined energy was harvested using the piezoelectric discs. The 
harvester system was demonstrated to have high power efficiency, small dimensions at 
relatively low frequencies, easy fabrication, and good durability, which could achieve 
sound insulation and energy harvesting for various applications. 
15 
 
 
 
Casadei et al. [56] reported a tunable acoustic waveguide configuration, 
whereby Bragg scattering bandgaps were combined with piezoelectric resonators to 
confine and control the propagation of elastic waves in a photonic crystal plate. The 
waveguide consists of a periodic array of cylindrical stubs bonded to the plate surface. 
A large frequency bandgap was produced, which was used to confine the propagation 
to the waveguide. Moreover, the second array of piezoelectric resonators was added to 
the vertical portion of the waveguide for wave transmission control. The resonating 
characteristics of the shunted piezoelectric actuators resulted in strong wave attenuation 
at the tuning frequency and provided the waveguide with resonating mechanical 
properties, which led to negative group velocities. 
Li et al. [57] presented a broadband acoustic composite phased array consisting 
of the subwavelength active tube-array metasurface structure and piezoelectric 
transducer array to form a special acoustic beam and determine the acoustic source's 
directivity characteristics. The tube array was also redesigned to focus the sound wave 
in a particular position. 
16 
 
 
 
 
Figure 1-7: (a) Sketch of the AEH system composed of a defected supercell with a piezoelectric 
patch and a load circuit [54]. (b) Computed band structure in the frequency range (1.8 to 2.5 
kHz) [54]. (c) Illustration of the plate with the cylindrical stubs and the L-shaped waveguide [55]. 
(d) The amplitude of the measured pressure field inside the Bragg-type bandgap at 117 kHz [55]. 
(e) experimental sample of the subwavelength active tube array [56]. (f) The radiation acoustic 
intensity fields of the planar acoustic focusing model [56]. 
Akl and Baz [58] developed an active acoustic metamaterial to overcome 
passive acoustic metamaterials' limited frequency bandwidth. Their metamaterial was 
based on a cylindrical (1D) cell composed of a water domain in cylindrical Acrylic pipe 
confined from both ends with lead zirconate titanate (PZT) diaphragms. One PZT 
diaphragm acted as a sensor to detect the acoustic pressure passing through the 
composite cell. The other diaphragm functioned as an actuator to control the diaphragm 
stiffness. The composite cell possessed intrinsic self-sensing and actuating capabilities. 
Moreover, different feedback control gains were implemented to vary the effective 
material properties of the metamaterial and to control the dynamic density of the 
17 
 
 
 
material. Using these engineered cells in a cascading arrangement could produce a fluid 
domain system with controllable dynamic properties.  
Bogdan et al. [38] designed a metamaterial slab to act as a very thin acoustic 
lens that could manipulate incident pulses on the lens. The metamaterial consisted of 
10 unite cells, each of which was an electronically controlled piezoelectric membrane 
mounted between two identical Helmholtz cavities. The three-terminal piezoelectric 
membranes were used for both sensing and emitting. The acoustic lens was used to 
manipulate three modulated Gaussian pulses coming in quick succession differently. 
In addition, the slab was configured to play two different roles simultaneously. 
 
Figure 1-8: (a) Construction of the proposed active acoustic metamaterial cell composed of water 
volume confined from both sides with piezoelectric bimorphs[58] (b)The unit cell consists of a 
piezoelectric membrane controlled by electronics, photograph of fabricated unit cell and 
Metamaterial slab consisting of ten unit cells[38]. (c)Time instances of the acoustic responses to 
each one of the three pulses[38]. 
1.2.4 Bioinspired acoustic sensing 
Bats, whales, dolphins, a few birds like the nocturnal oilbird, some swiftlets, and some 
shrews are all known to echolocate. Their capability to extract information is not 
limited to the location of objects. Many animal species are known for unparalleled 
18 
 
 
 
abilities to encode sensory information that supports fast, reliable action in complex 
environments, but the mechanisms are often unclear. 
Bats use echolocation to sense their environment by broadcasting a sequence of 
ultrasonic sounds and listening to echoes. They are able to detect and localize objects 
surrounded by obstacles [59] [60], detect target movement such as fluttering insect 
wings [61],[62], [63], classify objects with different shapes [64] and surfaces [65], and 
navigate complex environment [66] [67] using their echolocation. This powerful 
echolocation system relies on an efficient sound generating system and a complex 
tunable sensing system. Bats create calls with adjustable repletion rate, sonar beam, 
and spectro-temporal profile [68]. At the same time, their deformable ears can measure 
the echo from different directions [69]. So, a bat can perceive two reflecting surfaces 
with a distance of half a millimeter[70]. This high resolution enables them to observe 
an object in great detail. Several studies investigated the capabilities of bats to classify 
objects' size [71] [72] [73] [74] and surface [75][70]. Inspired by these abilities, several 
research groups have attempted to model and mimic bats? abilities. We will discuss 
these research studies in the following. 
Inspired by the animals? biosonar systems, there have been many efforts on 
developing bio-inspired sonar systems. Laurijssen et al. [76] presented a flexible, low-
cost sonar sensor platform that can be used for a wide range of biomimetic sonar 
experiments and autonomous sonar navigation applications. The flexible sonar sensor 
platform consists of a combination of three printed circuits boards (a core board, an 
amplifier board, and a USB communication board), two small microphones, and an 
ultrasonic transducer. In order to validate the sonar platform, the hardware was 
19 
 
 
 
mounted on a P3DX robotics platform and an ERLE-COPTER drone, which was 
introduced in an unknown testing environment to perform autonomous navigation. The 
results of the autonomous navigation in cluttered unknown environments proved to be 
successful since no collisions occurred and the trajectory remained fairly stable. 
 
Figure 1-9: (a) Photo of flexible sonar sensing platform[76]. (b) Assembled system setup mounted 
on the P3DX robot[76]. (c) ERLE-COPTER drone with sonar sensor platform[76]. 
Sumiya et al. [77] used ultrasonic binaural echoes measured by a miniature 
dummy head (MDH) to evaluate the object discrimination ability of sighted 
echolocation novices with the help of 48 participants. The performance on the 
discrimination of shape, texture, and material was examined separately. Discrimination 
of objects with various features like a wooden board, acrylic board, artificial grass, and 
garden fence was also investigated. Furthermore, the possibility of effective acoustic 
signal design for human echolocation using ultrasound was explored.  
Simona et al.[78] showed that artificial sonar beacons inspired by floral shapes 
streamline the navigation efficacy of sonar-guided robot systems. They developed 
floral-inspired reflectors and demonstrated their functionality in two proof-of-principle 
experiments. First, they showed that the reflectors are easily recognized among dense 
20 
 
 
 
clutter. Second, they showed that it is possible to discern different reflector shapes and 
use this identification to guide a robot through an unfamiliar environment. 
Tanveer et al. [79] presented an approach for estimating the leaf density of trees 
while navigating in a forest. For that purpose, they used an Unmanned Aerial Vehicle 
(UAV) equipped with biosonar that mimic bats? echolocation. They used a Mel 
spectrogram and a Deep Convolutional Neural Network (CNN) to extract information 
about leaf density from sonar measurements as the UAV navigates in different 
environments. Their classification method achieves promising results with an accuracy 
of 98.7%. 
Eliakim et al. [80] presented the ?Robat?, which is a fully autonomous bat-like 
terrestrial robot that relies on echolocation to move through an environment while 
mapping it solely based on sound. Using the echoes reflected from the environment, 
the Robat delineates the borders of objects it encounters and classifies them using an 
artificial neural network, thus creating a rich map of its environment. The novelty of 
this research is a biologically plausible signal processing approach to extract 
information about objects? position and identity. 
 
21 
 
 
 
 
Figure 1-10: (a, b) Image and laser-generated map for the guidance experiment. The trajectories 
of 3 runs are depicted in the laser range map in different colors [78]. (c) Image of the Robat. Insert 
shows the Robat?s sensory unit, including a speaker and two receivers[80].  
1.2.5 Acoustic classification  
Acoustic sensing systems are important due to their advantages of high depth 
perception, robustness to lighting conditions, energy efficiency, and low cost. 
Currently, echolocation based on acoustic sensors have been widely used to measure 
the information about the shape, size, surface, and location of an object. Extracting this 
information helps perceive the environment more accurately [81]. Some acoustic 
classification methods are reviewed as follows. 
Kroh et al. [82] exploited Artificial Neural Networks (ANNs) with multiple 
hidden layers to identify and classify sound-reflecting objects. During the classification 
process, a signal was emitted by an ultrasonic speaker and reflected off three different 
target objects (disc, cylinder, and hollow hemisphere) in various orientations. The 
reflected signal was measured using a microphone and digitized using an ADC 
interface card. Pulse-compressed echo signals and their frequency spectra were used to 
22 
 
 
 
train multi-layer perceptron ANNs to estimate features of the different objects. As a 
result, different target geometries were distinguished with a high rate of success, and 
the capabilities for size discrimination of targets with the same geometric shape were 
demonstrated. Tanveer et al. [79] presented an approach for estimating the leaf density 
of trees while navigating in a forest. For that purpose, they used an Unmanned Aerial 
Vehicle (UAV) equipped with biosonar sensors that mimic bats? echolocation. They 
used a Mel spectrogram and a Deep Convolutional Neural Network (CNN) to extract 
information about leaf density from sonar measurements as the UAV navigates in 
different environments. Their classification method achieves promising results with an 
accuracy of 98.7%. 
Dmitrieva et al. [83] presented a classification of spherical objects with 
different physical properties. Their classification was based on the energy distribution 
in wideband pulses that have been scattered from objects. The echo was transferred in 
Time-Frequency Domain (TFD), using Short Time Fourier Transform (STFT) with 
different window lengths, and is fed into a Convolution Neural Network (CNN) for 
classification. Their system shows an accuracy of 98.44 % over five objects. They also 
compared the performance of CCN with Multilayer Perceptron classifier (MLP). 
23 
 
 
 
 
Figure 1-11: (a,b) Experimental set-up [83]. (c) Measurement setup with two translation stages (x 
and y) and a rotation stage. The speaker and the microphone are moved along the x-axis. Thereby, 
echoes can be recorded at relative positions, which correspond to those of a robot passing by a 
target [82]. 
Magistris et al.[84] utilized Neural Networks to classify underwater objects 
from active sonar system data collected for underwater surveillance. Data collected 
during two sea trials is transformed in the time-frequency domain and used to train 
CNN classifier. The performance of the classification system was evaluated using data 
from a third sea trial in different geographical locations and environmental conditions. 
They claimed that the CNN classifier significantly reduces false alarms and 
outperforms traditional feature-based classifiers. 
Kritly et al. [85] studied people?s ability to discriminate between different 2D 
textures of walls based on passive listening. In addition, the impact of artificial 
enhancement of the early reflection and removal of the direct component was 
investigated. Listening test results for different textures, ranging from a flat wall to a 
staircase, were assessed using a Two-Alternative-Forced-Choice (2AFC) method, in 
24 
 
 
 
which 14 sighted, untrained participants indicated two equally perceived stimuli out of 
three presented stimuli. The overall texture discriminability was more significant for 
the walls reflecting with a higher spectral coloration. 
Kang and Kim [86] proposed an end-to-end machine learning approach that 
uses convolutional neural networks (CNNs), which can translate spectral cues that are 
delivered by reflected echoes into meaningful information for the target object. They 
attempted to learn a set of predefined everyday surfaces using reflected acoustic signals 
that are emitted from a distance. They also investigated whether echo-acoustic signals 
can be used for the classification of an acoustically smooth surface (e.g., liquid 
solutions) through experiments. The experimental results showed that our system could 
recognize texture and density information. 
Valdenegro [87] performed a comprehensive evaluation on the use of Deep 
Neural Networks (DNN) for the problem of acoustic marine debris detection and 
related problems such as image classification, matching, and detection. They formed a 
dataset of 2069 acoustic images that were captured using an ARIS Explorer 3000 
sensor. The objects used to produce this dataset contain typical household marine debris 
and distractor marine objects (tires, hooks, valves, etc.), divided into ten classes plus a 
background class. Their result shows that DNNs is a superior technique for the 
evaluated tasks than the corresponding state-of-the-art.  
1.3 Overview of the dissertation work 
The overall goal of this dissertation is to achieve a fundamental understanding on 
passive and active graded-index acoustic metamaterials for spatial and frequency 
25 
 
 
 
domain multiplexing and explore their applications in imaging and sonar systems. The 
dissertation work will include the following three research thrusts: 
Research Thrust 1: Investigate spatial domain multiplexing with passive 
graded-index acoustic metamaterials for enhancing far-field imaging. In this 
research thrust, a spatial domain multiplexing array of passive graded-index acoustic 
metamaterials will be designed and developed to achieve an acoustic imaging platform. 
Parametric studies will be carried out to facilitate the performance optimization of the 
imaging system. The performance of the metamaterial-based imaging system will be 
investigated and compared to the scenario without the metamaterials. 
Research Thrust 2: Design and develop active graded-index acoustic 
metamaterials for achieving broadband capability through frequency-domain 
multiplexing. In this research thrust, an active graded-index metamaterial system will 
be designed by adding a number of active unit cells to the metamaterial structure. The 
frequency multiplexing property of the metamaterials will be investigated through 
analytical, numerical, and experimental studies.  
Research Thrust 3: Investigate the applications of the active graded-index 
metamaterials with frequency multiplexing. Based on the understanding to be 
obtained about the active graded-index metamaterials in Thrust 2, the frequency 
multiplexing property of the metamaterial will be explored in an acoustic sensing 
system to classify objects with different. 
The rest of this dissertation is organized as follows: in Chapter 2, the 
performance of passive graded-index metamaterial for spatial domain multiplexing will 
26 
 
 
 
be investigated through numerical simulations and experimental studies. In Chapter 3, 
the design and development of an active graded-index acoustic metamaterial system 
for frequency-domain multiplexing will be discussed. The performance of the active 
acoustic metamaterials for the enhancement of multi-frequency band acoustic reception 
and emission will also be investigated. In Chapter 4, the capabilities of the frequency 
multiplexed acoustic metamaterials to improve the performance of a sonar sensing 
system for shape and surface roughness classification will be explored. Finally, in 
Chapter 5, a summary of the dissertation work will be provided. 
27 
 
 
 
2. Chapter 2: Spatial domain multiplexed passive graded-
index acoustic metamaterials for far-field acoustic imaging 
 
 
2.1 Introduction 
Currently, optical imaging systems are wildly used in autonomous systems (e.g., 
autonomous vehicles and drones). However, these systems have limited functions in 
dark environments and inclement weather conditions and often face serious constraints 
due to memory limitations, computational resources, and battery power. On the other 
hand, acoustic imaging systems can potentially overcome these limitations.  
Generally, the resolution of an acoustic imaging system is determined by the 
frequency of the sound wave used for imaging. A lot of research has been focused on 
ultrasound imaging with high frequencies. On the other hand, the attenuation of 
acoustic waves is directly related to frequency. Higher frequency waves have higher 
attenuation and cannot propagate long distances. Therefore, using high-frequency 
ultrasound for far-field imaging is quite challenging. Most research on ultrasound 
imaging systems focused on near-field imaging, and studies on far-field ultrasound 
acoustic imaging are still relatively limited. 
To address the challenge of far-field ultrasound imaging, this dissertation will 
explore the use of spatially multiplexed graded-index acoustic metamaterials for 
acoustic pressure wave amplification, which will be used in far-field ultrasound 
imaging to overcome the range limitation due to the attenuation of high-frequency 
28 
 
 
 
acoustic wave propagation. In this chapter, wave physics of graded-index acoustic 
metamaterials will be reviewed, and their spatial and spectral properties will be 
discussed. Furthermore, the design of the array parameters that affect the imaging 
system's performance will be discussed. Finally, the performance of the acoustic 
imaging system will be characterized in different environments. 
2.2 Design and performance characterization of a single graded-
index acoustic metamaterial device 
The graded-index metamaterial is constructed of a subwavelength sequence of air-solid 
layers. Previous studies on this material has demonstrated that it is a high-refractive-
index metamaterial with an effective refractive index neff much larger than that of air. 
For this reason, the dispersion of the metamaterial is shown to deviate from that of the 
air (Figure 2-1 (a)). The non-uniform geometry renders a gradually increased refractive 
index from nair to neff, thus efficiently overcoming the wave impedance mismatch at the 
air-metamaterial interface. Owing to the graded-index profile, the pressure wave can 
be spatially compressed along the propagation direction, exhibiting a gradual decrease 
of the wavelength in the metamaterial, and wave pressure field is progressively growing 
along the propagation direction (Figure 2-1 (b)). It is evident that the spatial periodicity 
of the pressure wave is axially decreased, therefore indicating an obvious wave 
compression effect in the metamaterial region. This leads to significantly amplified 
pressure field along the wave propagation direction. 
29 
 
 
 
 
Figure 2-1: (a) Dispersion curve of the metamaterial and air [43]. (b) The pressure field of sound 
is spatially compressed and amplified inside the graded high-refractive-index acoustic 
metamaterial. (c) Schematic of the design of graded-index acoustic metamaterial. 
In this dissertation work, a 2D graded-index metamaterial device is a tapered 
array of air-solid plates (Figure 2-1 (c)). The metamaterial properties such as special 
and spectral distributions of the effective reflective index are functions of metamaterial 
geometric parameters, including the metamaterial periodicity (??), dimension of the last 
unit cell (????????),  and filling ratio of material plates  ?
?????? . By tailoring these 
??
parameters, the graded-index acoustic metamaterials can be designed to achieve desired 
amplification of the pressure field, which could help overcome the limitations of a 
conventional acoustic sensing systems. Numerical simulations (by using commercial 
software COMSOL Multiphysics-Thermoacoustics Module) were performed to 
investigate the effects of these parameters on sound propagation and subsequently on 
the performance of the metamaterial.  
In this dissertation, simulations were conducted to facilitate the optimization of 
design parameters of the metamaterial at a selected working frequency of 25 kHz. 
Generally, the metamaterial unit cell in which the pressure amplification happens 
should be half a wavelength of the input sound. For this reason, the width of the last 
30 
 
 
 
unit cell ????????  was chosen to be 8.6 mm. The periodicity (??) and gap size (??) were 
determined through parametric studies so that the highest amplification at the working 
frequency can be achieved in the last unit cell. The obtained metamaterial design 
includes a sequence of 25 plates with a thickness of 2 mm. The diameter of plates 
increases from 2 to 9 mm with a 0.34 mm step, and the air gap between each plate is 
1.6 mm. The total length of the metamaterial is 8.5 cm. 
To detect the amplified acoustic pressure, a MEMS microphone was used to 
measure the highest sound pressure in the metamaterial device. The simulated 2D 
pressure field distribution of the metamaterial is shown in Figure 2?2 (a). It can be seen 
that the highest pressure happens in Gap 21 from the tip. Therefore, the middle point 
of this gap was determined as the location of the MEMS microphone. 
The designed metamaterial device was manufactured by using 3D printing 
(Stratasys Objet500, accuracy of 200 microns). The MEMS microphone 
(SPU0410LR5H-QB) with a sensitivity of 10.53 dB/Pa at 25 kHz was placed at the 
midpoint of the Gap 21 along the centerline of the metamaterial. Since the MEMS 
sensor has small dimensions (3.76 mm ? 3 mm ? 1.1 mm), its effects on the pressure 
field can be neglected.  
The graded-index metamaterial can not only be used to manipulate acoustic 
energy in the spatial domain, but it can also redistribute energy in the spectral domain. 
The spectral behavior of the metamaterial was investigated through both numerical 
simulations and experimental studies.  
31 
 
 
 
A frequency sweep experiment was performed. In the experiment, sinusoidal 
waves with different frequencies were broadcasted by using a speaker (Pettersson L400 
Ultrasound speaker), which was located at a distance of 1 m from the tip of the 
metamaterial. Although the speaker is broadband, it does not have the same 
performance at all the frequencies. To eliminate this effect, a B&K microphone (Br?el 
and Kj?r type-4958 14 inch) was used as a reference sensor in air and the measured 
signal from the MEMS microphone was normalized by sound pressure measured by 
the B&K microphone. A data acquisition device (NI 6363 DAQ) was used to record 
the sensor measurement and generate the input signals to the speaker. Each experiment 
was repeated three times and the results were averaged to reduce the random errors. 
The spectral behavior of the metamaterial sensing element was investigated 
through both numerical simulations and experimental studies. The obtained pressure 
responses at the location of the microphone (peak pressure location) are compared with 
those obtained with the same microphone without the metamaterial (Figure 2-2 (b),(c)). 
These results demonstrate the pressure amplification of the metamaterial device at the 
designed working frequency of 25 kHz. The experimental results are in good agreement 
with the simulation results. The pressure gain spectra are shown in Figure 2-2 (d). The 
maximum pressure gain obtained in the experiment is 13.45 at 25.6kHz, which is 
slightly lower than that (16.6 at 25.7kHz) from the simulations. One reason was 
believed to be the effects of the embedded MEMS microphone on the pressure field in 
the experiment. Moreover, the imperfections in the metamaterial fabrication process 
(e.g., surface roughness) could reduce the amplification because of the increased 
thermoacoustic loss.  
32 
 
 
 
 
Figure 2-2: (a) Simulated pressure field distribution. Frequency response at the peak pressure 
location with and without the metamaterial: (b) simulation results and (c) experimental data. (d) 
Simulated and experimental pressure amplification gain. 
MEMS microphones are omnidirectional, which means that they have the same 
sensitivity to sound from different directions. On the other hand, the graded-index 
acoustic metamaterial could control the wave directional patterns. When using the 
metamaterial device as an acoustic receiver, it will exhibit directional response. The 
effects of the metamaterial on the directivity of the embedded MEMS microphone were 
investigated in both numerical simulations and experimental studies. The simulation 
results are shown in Figure 2-3 (a), which clearly shows directional response of the 
metamaterial. In the experiment, a rotational stage (from Newport) located within a 
meter of the speaker was used to rotate the metamaterial from 0 to 360 degree with a 
step of 1 degree. Similar to the frequent sweep experiments, these experiments were 
repeated three times and the result were averaged to ensure repeatability and reduce the 
33 
 
 
 
random noise. The experimental directivity patterns are shown in Figure 2-3 (b), which 
are in good agreement with the simulation results. 
 
Figure 2-3: Directivity paterns of MEMS microphone with and without the metamaterial: (a) 
simulation results and (b) experimental results. 
Both the simulation and experiment results show that metamaterial amplifies 
incident acoustic wave and manipulates the receiver directivity pattern from being 
omnidirectional to highly directional.  
2.3 Design and development of an acoustic imaging system based on 
spatial domain multiplexed graded index acoustic metamaterials 
In this subsection, spatial domain multiplexing of the graded index acoustic 
metamaterials is investigated for achieving a far-field acoustic imaging system. This 
system consists of two parts. A hardware part consisting of a speaker and a spatial 
domain multiplexing array of graded-index acoustic metamaterials as the sensing 
34 
 
 
 
elements, and a software part consisting of signal processing and imaging algorithm. 
Both parts will be designed and developed in this work.  
2.3.1 Imaging algorithm 
In an acoustic imaging system, a sound wave is emitted and the reflection of this sound 
from different surfaces is measured by a number of sensors. Based on the time delay 
of the echoes measured by different sensors, an image can be obtained. Image 
processing of an acoustic array is challenging since the large number of sensors 
generate a large amount of data to be processed. Furthermore, imaging algorithms 
required to properly process the raw data are often complex. There are several 
algorithms that can be used to reconstruct an image. The most well-known algorithm 
is Delay-and-sum (DAS) beamforming. This algorithm has the advantages of being 
simple and having robustness to noise and short computation time [66]. DAS 
beamforming is used here in multiple firings to obtain an image of the reflecting objects 
located in a wide region. On each firing, at each location (focal point), the time delays 
from all of the sensing elements are calculated. This delay is the flight time of an 
acoustic wave transmitted from the speaker, reflected from the focal point, and received 
by a particular sensor. By applying these time delays to all of the signals obtained from 
different sensing elements, and coherently summing and integrating them, the acoustic 
amplitude of that focal point can be calculated, and a map or image of acoustic 
amplitude can be produced by scanning all of the focal points over the region. During 
the imaging process, all incoming signals are combined to amplify the echo signal and 
suppress the environmental noise. As a result, the signal to noise ratio is increased. The 
final image is formed after passing the signal through a band-pass filter to eliminate 
35 
 
 
 
undesired signals of other frequencies. The schematic of the imaging system is shown 
in Figure 2-4. 
 
Figure 2-4: Schematic of the entire imaging system, including an ultrasound speaker, a receiver 
array with 32 metamaterial-based sensing elements, a data acquisition (DAQ) system. The DAQ 
system is used to generate a 25 kHz sinusoidal input signal with a duration of .001 s to drive the 
speaker (located at the center of the array) and obtain receiver output signals.  
2.3.2 Array design 
The performance of an acoustic imaging array is related to the number of sensing 
elements and their geometrical arrangement. Here, the acoustic imaging system based 
on an array of graded index acoustic metamaterial receiver devices is considered. The 
performance of this imaging system in terms of directivity and range is characterized. 
To have a long-range imaging system, the sensing elements should have enough 
sensitivity. Since the metamaterial helps increase the pressure sensitivity of the sensing 
elements, using metamaterials is expected to improve the performance of the imaging 
system.  
36 
 
 
 
Reflections from undesired directions like the ground are inevitable for acoustic 
imaging systems. These reflections could interfere with the main reflection 
constructively or destructively. Sensing elements with directional response may help 
reduce the interference. Since the metamaterial can serve as a beam controller to enable 
highly directional response of the sensing element, using metamaterial may help 
enhance the performance of the imaging system by reducing the noise due to 
interference.  
Although a variety of arrays using commercial microphones have been 
proposed for far-field airborne acoustic imaging, using acoustic metamaterials for 
enhancing far-field imaging has not been attempted. For proof-of-concept, real-time 2-
D imaging with graded index acoustic metamaterial array is investigated. A Uniform 
Linear Array (ULA) consists of acoustic metamaterial-based sensing elements 
distributed uniformly along a line is used in this research. The performance of the linear 
array is related to the number of elements, element spacing, and frequency of the signal. 
Theoretically, for a fix number of elements, increasing the spacing will increase the 
aperture size of the array and thus increase the imaging resolution. However, if the 
spacing of the array is larger than the wavelength of the transmitted signal, sidelobes 
will appear in addition to the main lobes in the directivity pattern. These side lobes 
other than the main lobe are called grating lobes or fringes. The existence of the grating 
lobe is an indicator of poor performance of the array [67]. 
For a spatial multiplexed graded-index metamaterial array, the pressure field 
around each metamaterial element affects its performance. If the spacing between the 
metamaterial elements is reduced, the pressure fields from adjacent metamaterial 
37 
 
 
 
elements may have interference that could affect the performance of the imaging array. 
If the spacing is increased to avoid metamaterial interference, the resulting grating 
lobes may affect the imaging quality. Therefore, a tradeoff must be considered in the 
design of the spacing of the metamaterial imaging array.  
An array consisting of three graded-index metamaterial elements was used to 
investigate how to obtain the optimal spacing in both numerical simulations and 
experimental studies. First, the effect of the array spacing on the pressure gain of each 
metamaterial element in the array was studied. The obtained pressure amplitude along 
the x direction is shown in Figure 2-5 (a). It can be seen that a decrease in the spacing 
will reduce the signal amplitude of all of the metamaterial elements, and the one located 
in the middle suffers the most. It also shows that when the spacing is 3 cm, the signal 
amplitudes from all the metamaterial elements reach the maximum, and increasing the 
spacing beyond 2.5 cm offers very little benefit. To verify these simulation results, an 
experiment was conducted on an array of three metamaterial elements with variable 
spacing (Figure 2-5 (c)). The amplification gains of metamaterials for the array with 
different spacing was measured. As illustrated in Figure 2-5 (d), both experiments and 
simulated results confirmed that the spacing does not affect the performance of 
metamaterials if the spacing is more than 2.5 cm. 
38 
 
 
 
 
Figure 2-5: Investigation of array spacing: (a)simulated pressure along X direction for different 
spacing, (b)schematic of the array used in simulations, (c) experimental setup, and (d) simulated 
and experimental gain of an array with deferent element spacing. 
Next, experimental studies were carried out to investigate the imaging 
performance of arrays with different spacings and aperture sizes. A pipe of 9 cm 
diameter was placed at a distance of 7.8 m from the receiver array. Here, the maximum 
array aperture was limited to be 93 cm. In Figure 2-6 (a-c), the obtained images with 
arrays of different spacing and apertures sizes are plotted. In Figure 2-6 (d-g), the image 
intensities along the vertical (x) and horizontal (y) directions are plotted for different 
spacings and aperture sizes. With a constant aperture size (90 cm), increasing the 
spacing from 3 cm to 6 cm (total number of elements reducing from 31 to 16) will 
reduce the image intensity, resulting in a decreased signal-to-noise ratio (SNR) (Figure 
39 
 
 
 
2-6 (d-e)). With a constant spacing (3 cm), reducing the aperture size from 93 cm (32 
elements) to 45 cm (16 elements) will result in a decrease in SNR (Figure 2-6 (f-g)). 
Low SNR will result in low imaging resolution.  
 
Figure 2-6: (a) Image of an object with 32 element array of 3 cm spacing and 93 cm aperture size, 
(b) a 16 element array with 6 cm spacing and 93 cm aperture size, (c) a16 element array with 3 cm 
spacing and 46 cm aperture size. (d,e) Image amplitude along a vertical and horizontal line that 
passes through object position using arrays with the same aperture size and different spacing (3 
and 6 cm). (f,g) Image amplitude along a vertical and horizontal line that passes through object 
position using arrays with the same spacing and different aperture size (93 and 45 cm).  
40 
 
 
 
Another factor that affects the performance of the imaging system is the 
performance of each single sensing element [30]. Inconsistency in the sensitivities of 
the elements leads to higher grading lobes. Since the sensing element was constructed 
by integration of a MEMS microphone with a graded-index acoustic metamaterial, the 
sensitivity frequency responses of all the 32 MEMS sensors were measured, as shown 
in Figure 2-7. Cleary, different MEMS microphones exhibited different sensitivities. 
For this reason, the imaging array could have large grading lobes. 
 
Figure 2-7: (a) Frequency of 32 MEMS microphones, (b) Sensitivity of 32 MEMS microphones at 
25 kHz. 
2.3.3 Imaging system development 
After carefully designing the array parameters and choosing the imaging algorithm, the 
metamaterial-based acoustic imaging system was developed, as shown in Figure 2?8. 
Thirty-two metamaterial-based sensing elements were assembled into a linear array 
41 
 
 
 
with a spacing of 3 cm and an aperture size of 96 cm. Each of the 3D printed 
metamaterials was integrated with a MEMS microphone to receive echoes. 
A 25 kHz Ultrasonic speaker (MA40S4R, manufacture) was used as the emitter 
to generate outgoing ultrasound waves. The speaker has an aperture size of 1.1 cm, and 
it can generate a wide directivity pattern (80 degrees). The speaker requires an input 
voltage of 30 V. To drive the speaker, a 25 kHz sinusoidal signal with a duration of 
.001 s was generated by 32-Channel DAQ (NI PXle-1082), and the signal was sent to 
an amplifier to increase the voltage to 30 V. The speaker was located in the middle of 
the array and above the sensing elements at a distance of 5cm. All 32 signals from the 
sensing elements were sent to the same DAQ (NI PXle-1082) through a customized 
print circuit board for signal processing.  
 
Figure 2-8: Schematic of metamaterial receiver array with 32 sensing elements. A MEMS 
microphone is embedded in each sensing element at the maximum pressure amplification location 
for 25 kHz to measure the amplified echo signal. (c) Photograph of the fabricated and fully 
assembled imaging system. The insets in (b) and (c) show the schematic and the photograph of a 
single metamaterial sensing element, respectively. 
42 
 
 
 
2.4 Directivity pattern of imaging system 
Experimental studies were carried out to investigate the range and the directivity of the 
proposed imaging system. In the experiment, a pipe with 6 cm diameter was used as 
the imaging object. The object was moved to various positions along the horizontal 
direction (x axis) to determine the farthest observable points by the array. The 
observable point is assumed to be a point that the amplitude of the image is twice the 
noise floor. By doing this procedure at different distances along the y direction, the 
directivity pattern of the imaging system can be obtained. To compare the performance 
of the metamaterial-based imaging system with a conventional array, a similar 
experiment was performed by using an array of MEMS microphones with the same 
spacing and aperture size. The obtained the directivity patterns of the metamaterial-
based imaging system and the MEMS array are compared in Figure 2?9. Clearly, the 
metamaterial array had a much longer range, and the MEMS array exhibited a much 
significant grating lobe problem. 
43 
 
 
 
 
Figure 2-9: Directivity patterns of the metamaterial-based imaging system and MEMS 
microphone-based imaging system. 
2.5 Performance of the imaging system 
2.5.1 Single object experiments  
Experimental studies were performed to characterize the imaging performance of the 
metamaterial-based imaging system. First, the effect of the object distance on the 
amplitude of the image was studied. Since the acoustic wave attenuates as it propagates 
in the air, the image amplitude of a particular object will decrease as the distance of the 
object to the imaging array increases. This attenuation is the sum of the attenuation due 
to geometric spreading and attenuation due to atmospheric absorption. While the 
acoustic wave propagates in the air, the reduction in sound intensity due the acoustic 
energy spreading is known as geometric spreading attenuation. This loss dependents 
on the pressure, relative humidity, and frequency of sound. During the experiment, as 
the humidity and frequency were assumed to be constant, the distance was considered 
44 
 
 
 
to the factor affecting the image amplitude. To investigate the influence of the distance 
on the attenuation of the image amplitude, a pipe object with a diameter of 9 cm was 
placed at deferent distances along the middle line of the imaging array. Once an image 
of the object was obtained by using the array at a specific distance, the maximum 
amplitude of the image was determined. At each distance, the measurements were 
performed ten times. For comparison, the experiments were repeated using an array of 
MEMS microphones of the same array parameters. Figure 2?10 shows the averaged 
maximum image amplitude as a function of the object distance for both the 
metamaterial array and the MEMS array. The error bars in this figure indicate the 
maximum deviations from the averaged values, which are relatively small. 
 
Figure 2-10: Averaged maximum image amplitude versus object distance obtained with the 
metamaterial array and the MEMS array. The object was a 9 cm diameter pipe.  
  The MEMS array was not capable of producing an image of the 9 cm object 
when the object distance was more than 6 m, while the metamaterial array could still 
produce an image of the obstacle at a distance of 15 m. The image amplitude obtained 
for the object at 15 m was three times larger than the noise floor. Note that the distance 
45 
 
 
 
of 15 m was not the limitation of the metamaterial imaging system, but it was due to 
the space limitation of the indoor experimental environment. The relationship between 
attenuation and distance can be approximated by using curve fitting of the results 
presented in Figure 2-10. 
The existence of an object on the propagation path influences the wave 
propagation in four ways: reflection, scattering, diffraction, and refraction. The 
imaging system can only measure the reflection of transmitted sound, and only a 
portion of the transmitted sound is reflected by the object. The reflection depends on 
object features such as diameter, shape, and texture, the distance of the object to the 
imaging array. As a result, the object diameter can be interpreted from the image by 
eliminating the effects of other factors (e.g., shape and distance of the object).  
In this work, the performance of the metamaterial imaging system was 
investigated in terms of detectability of objects with deferent diameters ranging from 6 
mm to 115 mm, which were placed at a distance of 5 m from the array. In Figure 2?11, 
the performance of the metamaterial array and the MEMS array were compared for 
their abilities to detect objects of different diameters. Similar to the previous 
experiments, the experiment was repeated ten times, and the averaged measurement 
was obtained. Here, the noise floor was defined as the image amplitude at the location 
of the object in the absence of any object, which is shown as the dashed line in Figure 
2-11. 
46 
 
 
 
 
Figure 2-11: Averaged maximum image amplitude versus object diameter was obtained with the 
metamaterial array and the MEMS array. The object was placed 5 m away from the imaging 
array. 
As illustrated in Figure 2-11, the imaging system using the MEMS array was 
not capable of detecting an object with a diameter smaller than 60 mm while the 
metamaterial-based imaging system could easily detect a 6 mm object.  
To compare the objects of various sizes at different positions, the attention of 
sound due to propagation over different distances was taken into account. For this 
reason, the image amplitude was normalized by curve fitting function obtained from 
Figure 2-10. The images of an object place at the maximum distance of the 
experimental environment (15 m) and an object with the minimum detectable size 
(6mm diameter) are shown in Figure 2?12. Note that the output of the imaging system 
is a 3D image in which X and Y are two axes of the Cartesian coordinate system, and 
Z is the amplitude of the image. These results are obtained from the top, front, and end 
view of the 3D projection of the image. From these results, it can be seen clearly that 
47 
 
 
 
even at the maximum distance and with the minimum detectable size, the obtained 
image amplitudes are still much above the noise floor.  
 
Figure 2-12:(a-c) 2D image, image amplitude along Y axis, image amplitude along X-axis of a 9 cm 
diameter pipe at a distance of 15 m, respectively. (d-j) 2D image, image amplitude along Y axis, 
image amplitude along X-axis of a 6 mm diameter pipe object at a distance of 5 m, respectively. 
The image amplitude along X (or Y) axis was obtained at the maximum amplitude along Y (or X) 
axis. 
2.5.2 Two object imaging experiment 
We first characterized the lateral resolution for imaging of two closely placed, identical 
objects experimentally. Both the metamaterial receiver array and the MEMS 
microphone array were used to obtain images of two identical 6 cm diameter pipes 
placed at a distance of 3.5 m from the arrays. One object was aligned with the array 
center (X=0). The separation distance between the two objects was gradually reduced 
from a large value to determine the lateral resolutions (see Figure 2?13 (a)). Here, the 
lateral resolution is defined as the smallest distance between two identical objects in 
the lateral direction (along X-axis) at which the system can detect the objects at correct 
48 
 
 
 
locations and at least 20 % lower image amplitude (compared with the peak image 
amplitude) can be obtained at the center of the images of two objects.  
In Figure 2?13, the images obtained by using the metamaterial receiver array and the 
MEMS microphone array are shown when the distance between the two objects was 
reduced to 0.08 m (lateral resolution of the metamaterial receiver array). In the image 
obtained by using the metamaterial receiver array (Figure 2?13 (b)), the two objects 
were at the correct positions and can be clearly distinguished. However, the image 
obtained with the MEMS microphone array (Figure 2?13 (c)) suffered from position 
errors and low image amplitude, and our experiments show that it cannot produce an 
accurate image of two identical objects if their distance is smaller than 0.21 m. 
 
49 
 
 
 
 
Figure 2-13: Experimental results of imaging of two objects for lateral resolution determination. 
(a) schematic depiction of the experiment. (b) the MEMS array (c) the metamaterial array. The 
insets (i) in (b) and (c) show the 2D images. The insets (ii) in (b) and (c) show the image 
amplitude profile along the X-axis for Y=3.5 m. The two objects are 6 cm diameter pipes placed 
at a distance of 3.5 m from the imaging array. The images shown in (b) and (c) are at the lateral 
resolution (0.08 m) of the metamaterial receiver array. 
2.5.3 Three objects imaging experiment 
In this experimental study, the capability of the metamaterial array and MEMS array 
to obtain image of a more complex environment consisting of three objects of different 
diameters is investigated. The goal is to investigate these acoustic imaging systems 
capable of obtaining the correct position and size for each object. Three pipes of 
different diameters (3 cm, 9 cm, and 6 cm) were placed at three positions ((-0.475 m, 
50 
 
 
 
3 m), (0, 5.5 m), and (0.5 m, 8m)) in the XY plane, respectively. The obtained images 
are shown in Figure 2-13. 
 
Figure 2-13: Imaging of three objects of different sizes in three different positions. (a) Schematic 
of the experiment. (b) 2D image in XY plane obtained with the metamaterial array. (c) Image 
project along the line x=0 obtained with the metamaterial array. (d) 2D image in XY plane 
obtained with the MEMS array. (e) Image project along the line x=0 obtained with the MEMS 
array. The insets in (b) and (d) are the zoomed-in images of the three. The red boxes in (c) and (e) 
are represent objects with different diameters. 
The images obtained with the metamaterial array and the MEMS array are 
shown in Figure 2?14. It can be seen that that image (Figure 2?14 (b), Figure 2?14 (c)) 
51 
 
 
 
obtained by using the metamaterial array shows qualitatively the correct sizes and 
positions of the three objects. The larger object exhibited a larger image amplitude, 
which was not affected by the distance. On the other hand, the image obtained with the 
MEMS array suffered from large side lobe effect (e.g., the image of 9 cm object) and 
failed to indicate the correct object sizes (e.g., the image amplitude of the 6 cm object 
was smaller than that of the 3 cm object).  
2.6 Summary 
In this chapter, the development of an airborne far-field acoustic imaging system based 
on graded-index acoustic metamaterials in a spatial domain multiplexing array was 
carried out. First, the spatial and spectral behaviors of a graded-index metamaterial 
device were investigated. Second, an imaging system constructed with a graded-index 
acoustic metamaterial array was designed for achieving high resolution and range for 
far-field imaging. Finally, the performance of the imaging system was characterized 
and compared with another imaging array constructed with MEMS microphones. The 
results can be summarized as follows. 
? The metamaterial-based imaging system was capable of obtaining images of an 
object placed at a distance of at least 15 m while the MEMS array failed to 
obtain an image of the same object at a distance farther than 6 m. 
? The metamaterial-based imaging system was capable of imaging of 6 mm 
object while with the MEMS array, any object smaller than 6 cm was not 
observable. 
? The lateral resolution was 8 mm for the metamaterial-based imaging system 
and 21 mm for the MEMS system. 
52 
 
 
 
? The metamaterial-based imaging system was capable of producing qualitatively 
correct images in the condition with multiple objects of various sizes and 
positions, which demonstrates its better imaging capabilities in more 
complicated environments, in comparison with the MEMS array. 
Although graded-index metamaterial improves the imaging system's 
performance, the imaging system still has limitations that can be improved. The 
directivity pattern of the imaging system is relatively sharp, which makes it inefficient 
for imaging a complex broad environment which can be addressed by redesigning the 
array and reducing the spacing of the elements and increasing the working frequency 
of the imaging system. 
3.  
53 
 
 
 
4. Chapter 3: Active graded-index acoustic metamaterials 
with frequency domain multiplexing: Design, modeling, 
and development 
 
 
3.1 Introduction and motivation 
The human basilar membrane (BM) within the cochlea of the inner ear is a resonant 
structure that varies in width and stiffness and appears as a large trapezoidal vibrating 
structure. External sound waves can excite mechanical waves traveling along the BM, 
and different frequency components of the sound waves activate different positions 
along the BM (Figure 3?1(a)). Low-frequency waves cause maximum vibration near 
the apex of the membrane, while high-frequency sound waves cause maximum 
vibration of the membrane near the base of the cochlear. Subsequently, the BM 
amplifies and demultiplexes a complex sound wave and transmits it to the auditory 
system for signal processing. The cochlea offers great advantages for detecting 
transient weak signals and processing a large amount of complex audio information at 
extremely fast rates, with high accuracy and low energy consumption, mainly because 
of its ability to perform direct signal amplification and frequency decomposition. 
Previous studies showed that as the sound with a particular frequency 
propagates through a graded-index metamaterial, the sound wave is compressed and 
the sound pressure is amplified in a particular location. This behavior is due to the 
54 
 
 
 
gradually changed high reflective index of the metamaterial. This reflective index 
variation leads to sound amplification with different frequencies in different locations. 
This closely resembles the amplification of mechanical waves traveling through the 
BM of the cochlea.  
 
Figure 3-1: (a) Human cochlear and Basilar membrane displacement as a function of 
frequency[88]. (b) The frequency domain multiplexing behavior of a graded-index acoustic 
metamaterial [44]. 
In this chapter, the design, development, and characterization an active grade-
index metamaterial is carried out. Similar to the last chapter, the metamaterial is a cone-
shaped layered structure. By embedding sensors at different locations inside the 
metamaterial, different frequency components of a complex acoustic signal can be 
amplified and measured separately. The amplification behavior of the metamaterial is 
reversible. If a broadband speaker is placed in a particular location inside the 
metamaterial, the metamaterial amplifies a narrow band of the generated signal. By 
placing several narrow-band speakers with different working frequencies, the 
metamaterial acts a multiplexer and amplifier simultaneously, and complex high-
amplitude broadband sound can be broadcasted. In this work, the capability of active 
55 
 
 
 
graded-index metamaterial for broadband acoustic emission and reception are 
investigated through numerical and experimental studies. 
3.2 Design and fabrication 
In order to design the structure of active graded-index metamaterial, several parameters 
should be tailored to achieve desired multi-frequency enhancement in acoustic 
emission and reception, such as periodicity, filing ratio, and geometry of unit cells. 
Preliminary simulations were carried out to study these design parameters.  
The thickness of layers was chosen to be 1 mm based on the available 
thicknesses of existing commercial piezoelectric discs and the precision of fabrication 
process. Numerical simulations were carried out to investigate the effect of gap size. In 
Figure 3-2 (a) and Figure 3-2 (b), two different designs of the metamaterial with 
different gap sizes (1mm and 0.56mm) are shown. Both designs have three active unit 
cells (i.e., three plates are replaced by using piezoelectric discs), which are capable of 
acoustic wave emission and reception at three different frequencies. When sinusoidal 
waves with different frequencies are applied to all of the piezoelectric discs, far-field 
pressures for different frequencies between 15 to 40 kHz are shown in Figure 3-2. 
Based on these simulation results, a reduction in gap size results in higher peak 
amplification frequencies, but the amplification gains have very little change. 
56 
 
 
 
 
Figure 3-2: Schematic of active graded-index metamaterial devices with (a) 0.56 gap size and (b) 1 
mm gap size. The red elements are piezoelectric discs. (c) Simulated far field pressure field 
obtained with (a) and (b), when the metamaterials are used for acoustic emission of three different 
frequencies. 
The active metamaterial device was constructed by replacing some of the solid 
plates of a passive graded index acoustic metamaterial with piezoelectric discs (see 
Figure 3-3 (b)). Using these piezoelectric discs, the active metamaterial can be used as 
a speaker and a sensor simultaneously. Note that although there are other commercial 
speakers and sensors that have better sensitivity and efficiency such as MEMS 
microphone (see Figure 3-3 (a)). The geometries of these devices are not usually 
compatible with the metamaterial structure, leading to undesired pressure field 
distortions. 
57 
 
 
 
 
Figure 3-3: (a) Schematic of a MEMS microphone integrated with a passive graded-index 
acoustic metamaterial device. (b) Schematic of a piezoelectric disc serving as an active element in 
an active graded-index acoustic metamaterial device. 
Although it is possible to use piezoelectric discs with a thickness smaller than 
the designed metamaterial layer thickness, it makes the process of integrating the 
piezoelectric discs more complex. Furthermore, the boundary conditions of 
piezoelectric discs affect their capabilities of sound emission and reception. With these 
considerations in mind, three methods were investigated to embed the piezoelectric 
elements in the metamaterial and each of them represents a different boundary 
condition for the vibration of the piezoelectric disc.  
58 
 
 
 
 
 
Figure 3-4: Different methods to attach piezoelectric disc to the metamaterial: (a) side glued. (b) 
two points glued. (c) base glued. 
The performance of the devices with the three different boundary conditions 
was investigated through experimental studies. It was found that the device with a two-
point glued piezoelectric disc was able to generate acoustic waves with the highest 
amplitude. It was determined in the experiment that replacing a whole solid layer of a 
passive device with a two-point glued piezoelectric disc was the most feasible method. 
In the subsequent studies, this method was used to construct active metamaterials. 
The piezoelectric discs used in the experiments were made of ferroelectric soft 
piezo manufactured by Physik Instrument (PIC255), which are suitable for airborne 
ultrasound sensors and actuators and are made to have several different sizes 
(diameters). The material properties of the piezoelectric disc are listed in Table 3?1. 
The polarization direction of these discs is along the thickness. 
 
 
59 
 
 
 
                  Table 3-1: Material properties of PIC255. 
Property  Amount Unit 
Density ?? 7.8 ??/????3 
??
Relative permittivity ??33/??0 1450  
????11/??0 1400 
???? 0.62  
Coupling factor ???? 0.48 
 ??31 0.35 
 ??33 .69 
Elastic stiffness 2????  11.1 ? 1010 ?? /?? coefficient 33  
?? ?12
Compliance coefficient ??11 15.6 ? 10  ??/??2 
???? ?1233 19.7 ? 10   
 
Generally, the working frequency of a graded-index acoustic metamaterial 
device is related to its unit cell width. The graded-index acoustic metamaterials are 
designed to have unit cells of different width, each of which renders different reflective-
index, cutoff frequency, and spectral behavior. The unit cells that are closer to the tip 
of the metamaterial have a smaller width and thus offer pressure amplification of high-
frequency sound, while the unit cells that are further from the tip provide pressure 
amplification of low-frequency sound.  
As the thickness of the metamaterial layer was designed to be 1mm, the 
thickness of the piezoelectric disc was chosen to be 1 mm. In each unit cell, the 
wavelength of the sound with the highest amplification gain is approximately twice the 
width of that unit cell. The width of the layers varies from 2 mm to 14 mm. Since 
controlling the orientation of the piezoelectric discs with a diameter smaller than 5 mm 
is challenging, the active discs were placed in the region in which the unit cells have a 
width between 5 mm to 14 mm. This renders a metamaterial that covers the frequency 
range from 12000 Hz to 34000 Hz. Three piezoelectric discs with thickness and 
60 
 
 
 
diameter compatible with the designed structure were chosen and their properties are 
shown in Table 3-2. 
  Table 3-2: Properties of piezoelectric discs. 
Resonant Resonant Electrical 
Property Diameter Thickness frequency frequency capacitance 
(thickness) (radial) 
Small piezo 6.5 mm 1 mm 2110 kHz 349 kHz 0.346 nf 
Medium piezo 8 mm 1 mm 2110 kHz 284 kHz 0.524 nf 
Big piezo 10 mm 1 mm 2110 kHz 227 kHz 0.837 nf 
 
3.3 Active metamaterial with single active unit cell 
In graded-index metamaterials, depending on the diameter of the unit cell, the 
amplification occurred at a particulate frequency. When the sound with other 
frequencies propagates through the metamaterial, it passes the unit cell without 
amplification. It either will be amplified in other unit cells or haven't coupled into the 
metamaterial. So, each metamaterial unit cell plays the role of narrowband amplifiers 
with different frequency ranges. As an illustrative example, we investigate the 
performance of the metamaterial when only one unit cell is activated. 
In this work, the performance of the designed active graded-index metamaterial 
is investigated through numerical simulations and experimental studies. The 
commercial software COMSOL Multiphysics 5 was used to obtain 3D pressure 
distribution around the metamaterial when a sinusoid signal with different frequencies 
was applied to the piezoelectric disc mounted in the 16th unit cell of the metamaterial. 
In the simulations, the metamaterial was immersed in air and modeled as a rigid body, 
and the active layers were modeled as piezoelectric materials. In the emission phase, a 
20 kHz sinusoidal voltage was applied to the piezoelectric element. Piezoelectric discs 
61 
 
 
 
converted this electrical energy to mechanical energy and deformed the structure of the 
metamaterial. This structural vibration generated an acoustic wave which was 
amplified as it propagated through the metamaterial. In the reception phase, a 20 kHz 
plane wave as generated in front of the metamaterial. The amplified pressure wave was 
measured at the 45th unit cell. The piezoelectric layer converted this acoustic energy 
to electrical energy. By measuring the voltage generated by piezoelectric, the far-field 
pressure was determined. Figure 3-5 shows the air pressure field and piezoelectric 
displacement field in the emission and reception phase. 
 
Figure 3-5: Simulated air pressure field and piezoelectric displacement field at 20 kHz in reception 
and emission phases. 
As mentioned previously, the metamaterial can not only serve a sound amplifier 
but also a filter with a narrow frequency band. The filtering properties were 
investigated in both experiments and numerical simulations. For emission, we 
compared the far-field acoustic pressure amplitude generated by the single 
piezoelectric element in the metamaterial and without the metamaterial in the 
simulations (Figure 3-6 (a)) and experiment (Figure 3-6 (b)). In the experiment, 20 V 
sinusoidal signals of different frequencies were applied to the piezoelectric disc, and 
an ultrasound reference microphone (Br?el and Kj?r type-4958 14 inch) was used to 
62 
 
 
 
measure sound pressure at a distance of 1 m from the emitter. The experiment was 
conducted in an anechoic chamber to prevent undesirable reflection from the 
environment. The measurements were repeated three times and averaged to reduce 
random noise. The experimental results exhibit a significant emission gain of 8.1 at 
19.8 kHz with a 2 kHz bandwidth. The simulation results show a higher-pressure 
amplitude (emission gain of 19.2) at a larger frequency (21.3kHz). This discrepancy 
may be because of minor surface defects and structural deformation of the metamaterial 
device, which were not considered in the simulations, as well as inconstant boundary 
conditions of the piezoelectric layer between experiments and simulations. 
For reception, the sound pressure received by the single piezoelectric disc when 
input plane waves propagated through the metamaterial was measured and compared 
with the scenario without metamaterial in both simulations (Figure 3-6 (c)) and 
experiment (Figure 3-6 (d)). In the experiment, an ultrasound speaker (Pettersson L400) 
placed at a distance of 1 m from the piezoelectric disc was used to generate sinusoidal 
plane waves of different frequencies. The sound pressure induced voltage change of 
the piezoelectric disc was measured. Both simulation and experimental results show 
that metamaterial receiver rendered enhanced sensing capability. Similar to the 
emission results, the experimental results show lower pressure amplitude (18.1) at a 
lower peak frequency (19.6 kHz) compared with those (amplitude of 19.4 at frequency 
of 21.3 kHz) of the simulation results.  
63 
 
 
 
 
Figure 3-6: (a) Simulated far-field pressure frequency sweep with and without metamaterial, (b) 
Experiment far-field pressure frequency sweep with and without metamaterial, (c)Simulated 
generated voltage frequency sweep with and without metamaterial, (d) Experiment generated 
voltage frequency sweep with and without metamaterial,  
Furthermore, we characterized the directivity of the metamaterial emitter and 
receiver, which is particularly important characteristic for speakers and acoustic 
sensors[89]. The directivity of the metamaterial emitter with a single active layer was 
measured in the experiment and compared with the case without metamaterial. A 
motorized rotational stage (Newport URS50BCC) was used to rotate the emitter 360 
degrees with a step of 0.5 degree. A 20 kHz sinusoidal signal was applied to 
piezoelectric disc, and the far-field sound pressure was measured by using the reference 
microphone. We also investigated the reception directivity pattern of the metamaterial 
by broadcasting a 20 kHz plane wave using the ultrasound reference speaker and 
measuring the voltage generated by the largest piezoelectric while changing the angular 
passion of the metamaterial using the rotational stage. As shown in Figure 3-7 (a) and 
Figure 3-7 (b), the metamaterial exhibits highly directional emission and reception 
patterns that can concentrate the acoustic energy in a small range of directions, while 
64 
 
 
 
the piezoelectric disc without metamaterial shows a bi-directional response with much 
smaller emission power. 
 
Figure 3-7: Directivity patterns of the active metamaterial and a single piezoelectric disc without 
metamaterial at 21200 Hz 
3.4 Metamaterial with three active unit cells  
In the previous section, an active graded-index metamaterial device with a 
single active component was studied. The next step is to increase the number of active 
components to achieve multi-frequency emission. The proposed active metamaterial is 
composed of three 1mm thick active layers, and the width of unit cells ranging from 
2mm to 13 mm (see Figure 3-8 (a) and Figure 3-8 (b)). The predicted frequency 
response of system is shown in Figure 3-8 (c). 
65 
 
 
 
 
Figure 3-8: (a) Schematic of the active graded-index metamaterial and working frequency of 
different active unit cells. (b) Photograph of the active graded-index metamaterial. 
3.4.1 Emission investigation 
Frequency sweep experiments were conducted to verify the simulation results. Similar 
to simulations, an amplified sinusoid pure-tone signal of different frequencies was 
applied to one of the piezoelectric elements. The piezoelectric disc generated a sound 
wave that propagated through the metamaterial medium. A B&K microphone was used 
to measure the pressure amplitude of the propagated sound at a distance of half a meter 
from the tip of the metamaterial device. In Figure 3-9, the simulated and experimental 
frequency responses of piezoelectric discs with and without the metamaterial are 
plotted when only one of the piezoelectric discs was activated at a time. Both the 
simulation and experimental results show that the active acoustic metamaterial device 
enhances the acoustic emission of the embedded piezoelectric discs at the designed 
66 
 
 
 
working frequencies. The experimental results are in good agreement with the 
simulation results. 
 
Figure 3-9: (a) Schematic of the metamaterial device with an active unit cell in red. (b) Simulated 
and (c) experimental frequency spectra of far-field pressure when a single piezoelectic disc was 
activated. 
 The next step is activating all of the piezoelectric discs simultaneously. In 
Figure 3-10 (b) and (c), the calculated and measured far-field pressure are shown when 
all three piezoelectric discs were activated. These results show that the metamaterial 
amplifies the pressure produced by different piezoelectric discs at the designated 
working frequencies, rendering an enhanced acoustic emission over a relatively broad 
frequency range. However, the sound waves generated from different piezoelectric 
67 
 
 
 
discs could have constructive or destructive interference, and therefore the spectral 
response of the system when all of the piezoelectric discs were activated is different 
from the simple combination of the responses obtained with each one of the 
piezoelectric discs activated. Further investigation is needed to understand how to 
design the active acoustic metamaterial to achieve optimal performance of the device 
when all the active elements are activated simultaneously. 
 
Figure 3-10: (a) Schematic of metamaterial with three active unit cells (in red). Spectra of far-field 
pressure when all the piezoelectric discs were activated: (b) simulation results and (c) experimental 
results.  
To understand the wave manipulation property of the metamaterial, simulations 
were conducted to obtain the pressure field distribution when all three piezoelectric 
discs were activated. In Figure 3-11, pressure distributions of the emitted acoustic field 
at the three frequencies of 23.3, 28, and 33.9 kHz are shown. Each active element was 
found to produce a strong emission at its designed working frequency.  
68 
 
 
 
 
Figure 3-11: Pressure distribution of active metamaterial at three frequencies (a) 33.9 kHz, (b) 28 
kHz, (c) 23.3 kHz. 
When the graded-index metamaterial device is used for emission enhancement, 
one characteristic is its high directivity in comparison to a regular speaker. This makes 
the metamaterial useful in applications that require focused sound in a small region. 
Here, the directivity of the active acoustic metamaterial was investigated through 
simulations and experimental studies (Figure 3-12). The results demonstrates that the 
emitted sound waves are highly directional at all three emitted frequencies. The 
experimental results exhibited much larger side lobes compared with the simulations. 
The reason can be explained as follows. The defects during the fabrication may cause 
inconsistency in the fabrication process and boundary conditions of piezoelectric discs. 
As a result, the pressure distribution and directivity of an active metamaterial-based 
emitter may be affected. 
69 
 
 
 
 
Figure 3-12: Directivity pattern of active graded-index metamaterial used for acoustic emission: 
(a) simulation results and (b) experimental results. 
3.4.2 Reception investigation 
Similar to emission enhancement, as the sound wave propagates from free space into 
the active metamaterial, the pressure field is amplified in a specific region of the 
metamaterial depending on the frequency. As the piezoelectric effect of the active 
element is reversible, the amplified pressure field can cause deformation in 
piezoelectric discs that will generate electrical charges. Measuring this electrical signal 
allows us to determine the sound pressure. Therefore, the active acoustic metamaterial 
can serve as a multifrequency receiver. 
In this dissertation work, simulations were first carried out to study the 
performance of the active graded-index metamaterial as a multifrequency receiver. 
Consider a sound wave emitting by a point source located at a distance of 0.5 m from 
the metamaterial and a perfectly matched layer (PML) at the backside boundaries of 
the metamaterial. The pressure field distributions obtained for three frequencies at 
which the highest amplification occurred are shown in Figure 3-13. 
70 
 
 
 
 
Figure 3-13: Pressure distribution of the graded-index metamaterial in sensing mode for (a) 23000 
Hz, (b) 28000 Hz, and (c) 32000 Hz. 
 Next, experimental studies were performed to validate the simulation results. A 
sinusoidal wave with different frequencies was broadcasted by using an ultrasound 
speaker (Pettersson L400), which was located at a distance of 0.5 m from the 
metamaterial. The sound wave of the selected frequencies was trapped and amplified 
by metamaterial and the acoustic energy was converted to electrical energy by the 
piezoelectric discs. A data acquisition system (National Instruments, NI 6363) was used 
to supply the input signal to the speaker and acquire the measured voltage generated by 
the piezoelectric discs in the metamaterial. For comparison, experiments were 
conducted by using only the three piezoelectric discs in a holder without the 
metamaterial. All the experiments were repeated three times, and the data were 
averaged to reduce random errors. The obtained spectral of generated voltage by 
different piezoelectric discs are shown in Figure 3-14. 
71 
 
 
 
 
Figure 3-14: (a) Schematic of the metamaterial with an active unit cell (in red). Spectral behavior 
at the active unit cell obtained with and without the metamaterial: (b) simulations and (c) 
experiment. 
Based on Figure 3-14, the frequencies of peak amplitudes in simulations and 
experiments are in fair agreement. However, the experimentally obtained peak 
frequencies are slightly lower than the simulated values, which may be due to the 
fabrication errors of the device. There are also discrepancies in the shapes of the 
frequency response curves. This is believed to be due to the relatively low voltage 
output of the piezoelectric elements, resulting in undesired noise in the signal.  
3.5 Metamaterial with ten active unit cells 
Here, graded-index metamaterial device is a linearly tapered structure consisting of 
periodic solid circular discs spaced with uniform air gaps (Figure 3-15 (a)). This 
structure renders a graded refractive index profile, from air (tapered end) to a relatively 
72 
 
 
 
high index value (in the metamaterial), overcoming the impedance mismatch. When an 
incoming broadband plane wave interact with the structure, this structure enables wave 
compression in space and energy localization (pressure amplification) of different 
frequency signals (different frequency components will be trapped in different regions 
of the metamaterial). This concept has been explored as a passive acoustic receiver 
system to enhance acoustic sensing. Owing to the reciprocal properties, this 
metamaterial will have the capability for enhancing multi-frequency sound emission 
and reception. Here, we combine two different types of discs in one device: passive 
discs (gray discs) and active piezoelectric discs (colored discs). The active discs will 
be used as both speakers for sound emission and sensors for receiving echoes.  
We fabricated a metamaterial device (with a total of 45 discs) with 10 active 
elements (odd number discs from 23 to 41). There was a passive disc in between two 
active discs. Based on the performance of the metamaterial with a single active element, 
this multi-active element device will serve as an emitter and a receiver with a 
combination of ten narrow working frequency bands (~1.5 kHz frequency spacing). 
Unlike our previous design, the active unit cells are close enough to cover all the 
frequencies between 20 to 30 kHz (~1 kHz frequency difference in peak frequencies of 
adjacent active unicells). 
 
73 
 
 
 
 
Figure 3-15: (a) Schematic of the active graded-index metamaterial and working frequency of 
different active unite cells. (b)Photograph of the active graded-index metamaterial. 
3.5.1 Emission Performance of each active unit cell 
Numerical simulations and experiments were performed to characterize the 
performance of each of these ten active unit cells for both emission and reception. 
Figure 3 (a) is simulated normalized far-field pressure when electrical sinusoidal 
signals with frequencies between 15 kHz to 40 kHz. The performance of the largest 
unit cell is shown with a red line which has the lowest peak frequency. By reducing the 
diameter of the active unit cell, the peak frequency is increased, and the frequency 
response of the smallest piezoelectric is shown with a purple line. Although the 
diameters of unit cells linearly increase, the peak frequencies are not reduced linearly. 
This nonlinearity of peak frequencies does not affect the inference of different unit cells 
since it is associated with an increase in bandwidths. We also measured the far-field 
pressure generated by each of the piezoelectric discs at the same frequency range using 
a reference microphone. The order, general pattern, and bandwidth of frequency 
responses are in agreement with simulation; however, experiment studies determined 
74 
 
 
 
lower working frequency (19.8kHz to 30.7kHz) compared with those (21.3kHz to 
32.9kHz) of the simulation results. 
.  
Figure 3-16: (a) Simulated far-field pressure frequency sweep of all the active unicells of 
metamaterial, (b) Experimental far-field pressure frequency sweep of all the active unicells of 
metamaterial,  
3.5.2. Phase manipulation 
Using active elements in the metamaterial enables various emission control 
capabilities. By introducing an appropriate phase difference between two active 
elements, constructive or destructive interference can be obtained to manipulate the 
output emission pattern of the metamaterial emitter. 
To investigate how these interferences depend on the phase difference of unit 
cells, the amplitude and phase of far-field sound were obtained in simulations when the 
25th and 23rd unit cells were activated individually and simultaneously with various 
75 
 
 
 
phase differences. As shown in Figure 3-15, the pressure spectral can be clearly 
manipulated when both layers are activated with a 0 and 170-degree phase difference.  
Furthermore, sinusoidal signals with the same frequency were applied to two 
adjacent unit cells (the 25th and 23rd unit cells). The signal applied to the first unit cell 
has a constant phase, while the phase of the signal applied to the second one is changed 
from 0 to 360 degrees with an interval of a degree. 
 
76 
 
 
 
 
Figure 3-17: (a) The experimental far-field pressure when the 25th and 27th elements are activated 
individually and simultaneous with 0 and 170-degrees phase differences. (b) Phase sweep for 
pressure spectra when the 25th and 23rd elements are activated. 
Figure 3-17 (b) shows the measured far-field pressure when the input signal 
frequency changes from 25 kHz to 35 kHz. The frequency response of metamaterial 
has one peak when the phase difference is 0 or 180 degrees, which indicates that 
destructive interference happens at these two phase differences. While constructive 
interference happens at a phase difference of 170 degrees, and the frequency response 
of the system has two peaks (see Figure 3-17 (b) dotted line). 
Numerical simulations were carried out to gain an understanding of the 
dependence of interference patterns on the input phase difference of active elements. 
77 
 
 
 
Sinusoidal signals of the same frequency were applied to a pair of active elements (23rd 
and 25th discs, 23rd and 27th discs, and 23rd and 29th discs). The signal applied to the 
23rd disc had a constant phase, while the phase of the signal applied to the other disc 
was changed from 0 to 360 degrees with a one-degree interval. Figure 3-18 (b-d) shows 
the obtained far-field pressure response (frequency range from 25 kHz to 35 kHz) as a 
function of applied phase difference. The results show that phase manipulation can only 
be used for two adjacent active elements (Figure 3-18 (b)), while for active layers with 
larger distances (Figure 3-18 (c), (d)) there was no interference and frequency response. 
As shown in. Figure 3-18 (b), the emission frequency response of metamaterial 
can be manipulated by introducing phase differences to the adjacent active elements. 
For example, one frequency band can be obtained when the input phase difference is 
0, while two frequency bands can be obtained when the input phase difference is 100 
degrees. Simulations were also performed for an emitter with only two piezoelectric 
discs separated by a distance of 2 mm to investigate the role of the metamaterial (. 
Figure 3-18 (a)). No interference was observed in this case.  
Experimental studies have been conducted to verify the simulation results. 
Sinusoidal signals with the same amplitude and frequency but different phased were 
applied to the pair of active unite cells inside the metamaterial (23rd and 25th discs, 23rd 
and 27th discs, and 23rd and 29th discs) and two piezoelectric discs without 
metamaterial. Pressure distributions measured by the ultrasound reference microphone 
located at a distance of 1 m when the frequency of signals applied to both piezoelectric 
(25kHz to 35kHz) and phase difference between two signals (0 to 360 Degrees) varied 
are shown in Figure 3-18(e-h). The experimental results are in good agreement with 
78 
 
 
 
the simulations. The minor differences are believed to be due to the inconsistency of 
performance and boundary conditions of piezoelectric discs. 
 
Figure 3-18: Simulations (a-d) and experimental results (e-h) of far-field pressure responses of an 
emitter with two piezoelectric discs as a function of phase differences applied to the two discs: (a, 
e) two piezoelectric discs separated by a distance of 2mm without metamaterial, (b, f) metamaterial 
emitter with 25th and 23rd elements activated, (c, g) metamaterial emitter with 27th and 23rd 
elements activated, (d, h) metamaterial emitter with 29th and 23rd elements activated. The top inset 
shows that arrangement of the two discs. The top insets show the arrangements of the two discs 
for cases without metamaterial (a, e) and in the metamaterials (b-d and f-h). 
79 
 
 
 
By adjusting the phase difference applied to active elements of the metamaterial emitter 
and obtaining appropriate interference, the emission characteristics of the metamaterial 
emitter can be controlled. Representative emission pattern control scenarios were 
studied in experiment. In Figure 3-19 (a), the measured far-field pressures exhibit 
different amplitudes at different frequencies when all of the elements activated by 
signals with same frequency and phase. In Figure 3-19 (b), by apply appropriate phase 
differences, a flat frequency response between 20 kHz to 32 kHz can be obtained with 
the metamaterial emitter.  
 
Figure 3-19: Manipulation of emission spectrum with phase difference applied to active elements 
in the metamaterial: (a) uniform phase to generate curved spectrum and (b) various phase 
differences to generate flat spectrum. 
80 
 
 
 
As it was mentioned before, the experimental frequency response has larger 
bandwidth and side lobs compared to simulation results. The existence of measurement 
noise reduces the signal-to-noise ratio of active metamaterial compared to simulation 
results. These differences prevent us from using simulated optimized phase differences 
to tune the generated signal. Although we choose the phase differences through trial 
and error, there are more accurate ways to solve this optimization problem using 
machine learning algorithms. 
3.5.3 Directivity pattern 
Here, the directivity characteristics of the graded-index acoustic metamaterial emitter 
are investigated. In general, a speaker working at a higher frequency will be more 
directional and generate a narrower beam. In nature, bats have the capability of 
generating highly directional ultrasound beams. The directivity of the sound generated 
by bats is also related to the frequency of the emitted signal: a higher frequency leads 
to a more directional sound beam. Experiments were performed to compare the 
directivity spectrum of our metamaterial emitter to that of a single piezoelectric disc. 
In the experiment, the phase differences applied to the active elements were the same 
as those used to obtain Figure 3-19 (b) to generate a uniform output sound pressure at 
different frequencies. As shown in Figure 3-20 (a), the single piezoelectric disc speaker 
exhibits omnidirectional emission pattern for all frequencies. As illustrated in Figure 
3-20 (b), the metamaterial emitter shows highly directional response in the frequencies 
between 18 to 31 kHz and the emitted beam becomes narrower as the frequency 
increases. 
81 
 
 
 
 
Figure 3-20: Directivity spectral pattern obtained by using (a) a single piezoelectric disc without 
the metamaterial and (b) the active metamaterial emitter.  
3.5.4 Mimicking bat emission calls  
Big brown bats can generate frequency-modulated signals for echolocation. Research 
has shown that the signal consists of either one downward harmonic sweep from 10 
kHz to 90 kHz (see Figure 3-21(a)) or two harmonic sweeps (the first sweep from 10 
kHz to 40 kHz, and the second from 40 kHz to 100 kHz, both with the same duration, 
see Figure 3-21 (b)). The abilities of generating calls with a broad frequency band or 
different frequency bands allow the bats to extract a variety of information about their 
environment from received echoes (e.g., object shape and surface roughness, object 
location). The frequency modulated harmonics have been shown to improve 
echolocation performance [63]. 
Here, we show that the metamaterial emitter is capable of mimicking the bat 
echolocation calls. Bat calls sweep through broadband of frequencies within a few 
milliseconds. The duration and separation rate of these calls limit their temporal 
resolution. Despite the smaller bandwidth of metamaterial (11.5 kHz) compared to 
bats(more than 100), we want to use the metamaterial emitter to generate two signals 
with spectrums similar to bats call shown in Figure 3-21 (a-b). 
82 
 
 
 
Gaussian signals with the same bandwidth (1.2kHz) but different central 
frequencies and time delays are applied to different active unit cells. The center 
frequency of the signal applied to each unit cell is equal to the peak frequency of that 
unit cell. For a single-harmonic call (Figure 3-21 (a)), the signals applied to adjacent 
unit cells have a time delay of 0.9ms. The activation process started with the smallest 
unicell and finished with the biggest unit cell to achieve a downward chirp. The sound 
generated by the metamaterial using these signals is calculated and measured through 
simulation and experiment. We used a short-time Fourier transform (STFT) with a 
window length of 0.05 ms to have time-frequency transformations of the signals[83]. 
The spectrograms of simulated and experimental results are shown in Figure 3-21 (c, 
e). For the two-harmonic call, we only change the activation order of unit cells to 
1,6,2,7,3,8,4,9,5, and 10. This call's simulated and experimental spectrums are shown 
in Figure 3-21 (d, f). The experimentally obtained spectrograms exhibit slightly lower 
frequencies and thicker bandwidths than the simulated spectrograms in both calls, since 
the measured emission frequency responses of the metamaterial have lower peak 
frequencies and wider bandwidths compared to the simulation results. 
83 
 
 
 
 
Figure 3-21: (a) Single harmonic bat signal (b) two harmonic bat signal, (c,d) Spectrogram of 
metamaterial to imitate bat signals with one harmonic and two harmonics trough simulation.(e,f) 
Spectrogram of metamaterial to imitate bat signal with one harmonic and two harmonics trough 
experiment 
3.5.5 Reception performance of the active metamaterial receiver  
The active metamaterial with ten piezoelectric discs can be used as a multi-frequency 
receiver. The voltage generated by each piezoelectric is not equal because of 
differences in piezoelectric performance and unicell geometry which can be 
compensated by adjusting the amplifiers. To compare the sensing performances of 
different unit cells, we normalized the frequency response of each unit cell with its 
maximum amplitude. In Figure 3?22 (a, b), both simulation and experimental results 
on normalized far-field frequency responses are shown. Similar to the results obtained 
from the active metamaterial as an emitter, the experimentally obtained bandwidth and 
separation of different frequency bands in the receiver spectrum are consistent with 
84 
 
 
 
those of the simulations. However, a slight frequency shift is observed between 
experimental and simulation results. 
 
Figure 3-22: Receiver frequency response when all the active unit cells of metamaterial are used 
in reception mode: (a) Simulations and (b) Experimental results.  
3.6 Summary  
In this Chapter, two active graded-index metamaterial devices have been designed and 
developed. The first device has three active unit cells that are widely separated to avoid 
interference between the active elements. The second device has ten active unit cells 
and the interference between adjacent unit cells can be manipulated to achieve emission 
control. The performance of these two devices for both emission and reception has been 
investigated through experimental and numerical studies. The results can be 
summarized as follows.  
85 
 
 
 
? In the emission mode, the active graded-index acoustic metamaterial can be 
used to generate broadband sound waves with different time durations and 
frequency components. Both experiments and simulations demonstrated that 
the amplitude of sound wave generated by the active metamaterial is at least ten 
times larger than that generated by the piezoelectric disc without the 
metamaterial. The effect of phase and amplitude of the piezoelectric signal on 
the directivity and frequency response of generated sound wave has been 
investigated. By introducing an appropriate phase difference between active 
elements, emission control capabilities of the active metamaterial emitter have 
been demonstrated.  
?  In the reception mode, although the piezoelectric discs can only generate weak 
voltage signals when receiving sound from a far field speaker, at each active 
unit cell, the metamaterial can amplify sound pressure at the selected frequency 
band.  
Although the broadband emission and reception were achieved, active graded 
index metamaterial has limitations that can be addressed in future works. The 
piezoelectric with diameter compatible with metamaterial structure doesn't provide 
high sensitivity in reception mode while it shows good emission performance. The 
sensing performance can be enhanced by changing the active component's material or 
redesigning the structure based on high-sensitivity piezoelectric discs.  
86 
 
 
 
Chapter 4: Active graded-index acoustic metamaterials for sonar 
applications 
 
 
4.1 Introduction  
Echolocation, also called biosonar, is used by a number of animal species. Echolocating 
animals emit calls out to the environment and listen to the echoes of those calls, which 
return from various objects near them. Among many echolocating animals, bats have 
received much attention. Behavioral studies show that bats can classify complex echoes 
reflected by their food (e.g., insects, fruit, etc.) and objects in the environment (e.g., 
water surfaces, meadows, walls, vegetation, etc.). This powerful echolocation system 
relies on efficient sound generation and sensing systems. Bats create calls with 
adjustable repletion rate, sonar beam, and spectro-temporal profiles [68]. Furthermore, 
their deformable ears can measure echoes from different directions [69]. Bats can detect 
the variations in features of echolocation signals such as frequency content, intensity, 
and duration and delay of calls. Based on these features, bats can accurately perceive 
the environment, such as two reflecting surfaces with a distance of half a millimeter 
[70]. This high-resolution detection capability enables them to observe an object in 
great detail. 
An import part of bats echolocation is calls generation. Some bats use frequency 
modulated (FM) sweeps ranging from as low as 1 kHz to as high as 100 kHz. This 
broadband FM approach offers the advantages of precise range discrimination and 
providing information about the features of the reflecting object. FM tones also render 
87 
 
 
 
a short call duration compared to a single-frequency tone, which help bats emit many 
extremely rapid calls without overlapping.  
Inspired by bats' echolocation, it is desirable to develop an efficient sound 
emission and sensing system that can be used to extract information about the location, 
size, shape, and surface features of an object based on echolocation. As discussed in 
Chapter 3, the active graded-index metamaterials enable the control of spectral and 
spatial properties of sound generation. Here, this feature is used to generate a sound 
wave similar to bats FM tones. A sonar system based on the active metamaterial emitter 
will be developed and the application of this system in echolocation for extracting 
object features such as shape and surface pattern information will be investigated. 
4.1.1 Object recognition 
When sound waves interact with an object, the acoustic energy is either reflected or 
scattered in different directions depending on the object's size and geometry. 
Depending on the object's physical properties, the reflected wave may contain only 
particular frequencies. Bats use the rates of reflection and scattering from an object to 
recognize its features [65]. Research on bat echolocation has shown that bats could 
discriminate simple object characteristics such as size, shape, and texture. 
When an object reflects a broadband signal such as the FM bat call, the reflected 
signal with wavelengths within the range of the object diameter will be attenuated. In 
contrast, signals with longer wavelengths do not experience this extenuation. This 
frequency-related attenuation pattern is sometimes referred to as the acoustic color of 
the object. According to the radar equation, echo intensity linearly depends on the 
cross-section of the reflecting object [66]. Therefore, for an object larger than the sound 
88 
 
 
 
wavelength, the object size can be inferred from the intensity of the echo, while the 
subwavelength features of the object can be inferred from the frequency components 
of the echo. 
4.1.2 Texture classification 
The object's surface structure is one of an object's features that can be recognized by 
using the frequency components of the echo. As discussed in Chapter 1, research has 
been carried out to investigate the texture classification of bats. Theoretically, the echo 
intensity variation due to the object size could be determined by the ratio between the 
object size and the sound wavelength. This behavior can be classified in the following 
three domains: 
? Rayleigh domain: If the object size is smaller than the wavelength, the echo 
intensity decreases as the sound wavelength increases. The intensity decrease 
is inversely proportional to the fourth power of the wavelength. 
? Resonance domain: If the object size is of the same order as the sound 
wavelength, the echo intensity depends on the ratio of the object size to 
wavelength. 
? Optics domain: If the object size is an order of magnitude larger than the 
wavelength, the echo intensity is equal for all frequencies. This intensity is a 
function of the object size. 
If the sound frequency range in a wave that reflects from an object is in the optics 
domain and reflection due to the object texture is in the Rayleigh domain, the effect of 
texture on the frequency response of the object echo can be determined. In this case, 
89 
 
 
 
the object texture is a Rayleigh scatter, and the sound with a wavelength four times the 
texture structural depth (??) is canceled [65]; that is, 
                                             ?????????????????? = 4??                                                         (4-1) 
Based on this principle, the capability of the metamaterial sonar system is limited by 
its bandwidth. 
The metamaterial emitter is used to generate acoustic calls with controlled 
spectro-temporal properties. The calls are reflected from an object. The echoes, which 
contain information about different features of the object, are recorded to form a 
dataset. This dataset is used to train and test different machine learning algorithms. 
Based on the accuracy of supervised learning methods, the performance of sonar 
system for object classification is evaluated. First, the performance of the sonar 
classification system is investigated through numerical simulations. Second, the system 
is experimentally optimized by tuning the spectrogram of the generated signal. The 
performance of the metamaterial sonar system is compared with another system 
without the metamaterial. Finally, the capabilities of the optimized system for 
classification of objects with different sizes, shapes, and surface roughness are 
investigated. 
4.2 Proposed sonar classification system 
The sonar classification system consists of a sound emitter, an acoustic sensor, and a 
classification algorithm. An active graded-index metamaterial with ten active unit cells 
(piezoelectric discs) is used as the sound emitter. By adjusting the sound intensity and 
duration of each frequency band generated by the piezoelectric discs, the frequency 
component and temporal behavior of generated signal can be controlled.  
90 
 
 
 
In principle, the piezoelectric discs can be used to sense and generate sound 
simultaneously. Although the metamaterial has an excellent performance for emission 
and reception enhancement, simultaneous sound generation and reception is practically 
challenging. In a cycle of generating a sound pulse and sensing the echo, the potential 
difference between the piezoelectric electrodes rapidly changes from a high voltage 
input signal which causes the piezoelectric to vibrate to a weak output signal induced 
by the echo. Differentiating these two signals without increasing the measurement 
noise are challenging. As a result, in this dissertation work, only a metamaterial emitter 
is used and another ultrasound microphone (Br?el and Kj?r type-4958 14 inch) is used 
to record the echo (see Figure 4-1).  
 
Figure 4-23: Experiment setup for a sonar system with a metamaterial emitter. The inset in (i) 
illustrates the expected frequency components of the signal generated by the metamaterial 
emitter. 
91 
 
 
 
Different parts of an object reflect sound in a particular direction and phase. 
Interference of these echoes changes the frequency components of echo measured far 
from the object. Therefore, the measured frequency-domain signal contains shape-
related information. On the other hand, the measured time-domain signal includes 
location-related information Short-time Fourier transform (STFT) is used to combine 
these two pieces of information and obtain time-frequency transformations of the 
measured signal [90]. 
It is important to have a frequency-time domain transformation of the received 
signal to extract information related to shape and textures since this transformation 
contains both time-domain and frequency-domain information. Although STFT is one 
of the simplest methods, there are more complex transformations with higher 
concentration of information, such as Wavelet transformation[91]. For the sake of 
simplicity, we use STFT, but implementing Wavelet transformation will improve the 
performance of the acoustic sensing system.  
 In experiment, the sound pressure is measured along the emitted wave direction 
at a distance from the object. This measurement contains the emitted sound and the 
echo. After obtaining the spectrogram of the measured signal, a part of the spectrogram 
containing echo information is used to form a dataset. This dataset is used to train and 
test a verity of machine learning algorithms for classification of object shape, size, and 
surface roughness (see Figure 4-2). 
92 
 
 
 
 
Figure 4-24: Acoustic classification framework. 
4.3 Machine learning methods 
In this study, for training the machine learning models, 10% of data was 
randomly selected first as the test set to be used for tuning the models? hyperparameters. 
The remaining 90% of the data was then used for training and validating the models. 
The K-fold cross-validation technique was used to ensure the models? robustness, 
where K was set to be equal to ten. In this technique, the dataset was divided into ten 
equal splits. Each time, the model was trained by using nine of these splits and was 
tested by using the remaining one. In this way, each data point was used in the 
validation set once to ensure the model performance consistency. Additionally, input 
features were normalized by using a standard scaler to equalize the effects of different 
features of a hyperparameter. 
Several well-known machine learning algorithms were used in the sonar 
classification system. Machine learning has been widely used in signal processing and 
proved to yield promising results[92] In this dissertation work, five algorithms were 
used, including K-Nearest Neighbors (KNN), Support Vector Machine (SVM), 
93 
 
 
 
Random Forest (RF), Multi-Layer Perceptron (MLP), and Convolutional Neural 
Network (CNN) for classification. These algorithms will be briefly discussed next [93]. 
4.3.1 K-Nearest Neighbors (KNN) 
The KNN is one of the most famous non-parametric classification algorithms [94] [95]. 
The simplicity of the idea behind KNN and its applicability to input features without 
any required preprocessing are among the reasons behind its popularity. KNN classifies 
each data point by finding similar data points in the training data. Given a new record, 
KNN computes the distance of this record to all data points in the training set to find 
the nearest K points. The label for the new record is then the most frequent label among 
these K nearest neighbors. In this study, distances are calculated by the Euclidean 
metric. Number K is set to be equal to 20, which gives the minimum error rate on the 
test set. 
4.3.2 Support Vector Machine (SVM) 
The SVM is a linear model for classification [96]. The basic idea behind this algorithm 
is to find the hyperplane that separates two classes of data by maximizing their margin 
to the plane. SVM can also be used for nonlinear classification by mapping the input 
data into high-dimensional feature spaces using a kernel function. The SVM model 
trained for this study utilizes a sigmoid Kernel function. 
4.3.3 Random Forest (RF) 
The RF is an ensemble supervised machine learning method that make use of Decision 
Trees (DTs) to classify objects. DTs aim to divide data into branches in a way that the 
94 
 
 
 
impurity of each branch is minimized. One of the most common measurements for 
impurity is Gini Index that is calculated according to the following equation [94]: 
???????? ?????????? = 1 ? ?????=1(?? 2??) .                                                                    (4-2) 
where ???? is the probability of class ?? being classified for a distinct class. The variable 
that yields minimum Gini index goes to the tree?s root and splits the data into two 
branches. The tree grows with the same rule until the stopping condition is met. This 
stopping condition can be the maximum depth of the tree or minimum number of 
samples in one branch. RF model iteratively selects random sets of samples with 
replacement from the training dataset. These random sets will then be used to build a 
forest of DTs. RF runs a new record through all the DTs and gets the associated labels 
[97]. The final prediction for this new record is the majority class selected by the DTs. 
In this dissertation work, 100 DTs with maximum depth of 12, as stopping condition, 
are used in the forest.  
4.3.4 Multilayer Perceptron (MLP) 
The MLP is a feed-forward Artificial Neural Network (ANN) model. The MLP is 
constructed from three types of layers of nodes: the input layer, the hidden layers, and 
the output layer. The input layer's nodes are the input features of the data. In the hidden 
layers and the output layer, each node is a neuron that uses a nonlinear activation 
function that defines the node's output given its input [98]. Each layer is connected to 
its following layer with a weight vector. MLP uses a supervised learning technique 
called backpropagation to find these weights by minimizing the model's objective 
function [99]. In this work, the parameters and configuration that are used in MLP 
algorithm are shown in Table 4-1 and Figure 4-3. 
95 
 
 
 
 
 
Figure 4-25: Schematic of PLM algorithm. 
 
 
Table 4-3:MLP parameters 
Parameters  Parameters 
Number of hidden layers 3  Drop out layer 25% 
Number of nodes 128,128,64  Learning rate 0.0005 
Activation faction ReLu  Epochs 100 
Last layer activation Softmax  Batch size 8 
function 
Loss function cross entropy    
 
4.3.5 Convolutional Neural Network (CNN) 
CNN is a class of ANN commonly used to analyze 2D data like images. CNNs are 
regularized MLP. The hidden layers of CNN include layers that perform convolution, 
which typically means performing a dot product of the convolution kernel with the 
layer's input matrix. This generates a feature map of the layer's inputs that contribute 
to the input of the next layer. This operation extracts hierarchical patterns from the 
original input features [100]. The low calculation cost and efficiency of this algorithm 
96 
 
 
 
encourage researchers to use it for optic and acoustic object classification [86][101]. 
The architect of CNN algorithm used in this work is shown in Figure 4-4. 
 
Figure 4-26: Schematic of CNN algorithm. 
4.4  Numerical simulation studies 
Simulation studies are necessary to check the feasibility of object classification in the 
operating frequency range of the metamaterial and investigate the effects of various 
parameters. 3D time explicit numerical simulations were carried out by using the finite 
element solver in COMSOL Multiphysics 5. In the simulations, different objects were 
modeled as rigid bodies immersed in the air and surrounded by perfectly matched layers 
(PML). A broadband gaussian plane wave with a center frequency of 25 kHz was 
generated in front of the object. A 3 cm-diameter hollow hemisphere (concave surface) 
was used as a far field object. The obtained pressure distributions of the propagating 
wave and the reflected wave at four different times are shown in Figure 4-5.  
97 
 
 
 
 
Figure 4-27: Simulated pressure distribution of a broadband plane wave reflected by a concave 
object. 
The time response of acoustic pressure obtained at a distance of 20 cm from the 
object along the propagation direction of the sound wave is shown in Figure 4-6 (a). 
STFT transform was performed to the time domain pressure response to obtain the 
time-frequency spectrogram, which is shown in Figure 4-6 (b).  
 
Figure 4-28: (a) Simulated pressure at a distance of 20 cm from the object. (b) Spectrogram of 
simulated pressure. 
98 
 
 
 
In the simulations, five object shapes, sphere, hollow hemisphere, disc, 
ellipsoid, and equilateral triangular prism, were used. An empty class was added to 
these shapes to form six classes of shapes. In addition to shape, parameters such as size, 
distance, and orientation, also change the received echo in both time and frequency 
domains. The data set of each class should contain echoes of different sizes at different 
distances and orientations. We define the diameter of the sphere, hollow hemisphere, 
and disc, the largest diameter of the ellipsoid, and the side of an equilateral triangular 
prism as the size feature for objects. Ten sizes changing from 1 cm to 10 cm, 15 angular 
positions between -15 degrees to +15 degrees, and three axial distances between 16cm 
to 24 cm were considered. As a result, there are 450 scenarios in each class. To 
investigate the effect of the broadband input sound on the classification performance, 
the simulations were also performed for another system with 25 kHz pure tone sound 
waves as a comparison without metamaterial. 
The performance of the sonar classification system with different machine 
learning methods was characterized in terms of the classification accuracy, which is 
defined as the percentage of correct predictions in the total dataset. Table 4-2 shows 
the shape and size classification accuracy of the broadband and narrowband systems. 
CNN was found to have the best performance among all the tested algorithms, which 
was used in the following studies.  
 
 
99 
 
 
 
Table 4-4: Simulated shape and size classification accuracy of different machine learning 
algorithms for systems with (broadband) and without metamaterial (narrowband).  
Shape accuracy with Shape accuracy without Size accuracy with Size accuracy without 
Algorithm  MM MM MM MM 
KNN 97.3 ? 1.6% 60.1 ? 3% 65.7 ?8.2% 45.4 ? 7.5% 
RF 98.8 ? 1.1% 67.5 ? 4.1% 81.5 ? 15.9% 50.9 ? 13.3% 
SVM 98.1 ?1.4% 68.04 ? 2.8% 65.6 ? 9.9% 43.5 ? 5.5% 
 train test train test train test train test 
MLP 96.3 ? .1% 93.2 ? 3.4% 73.6 ? 2.5% 72.3 ? 3.8% 78.1 ? 8.8% 75.3 ? 4.1% 42.9 ? 2.9% 36.4 ? 4.4% 
CNN 98.4 ? .2% 96.3 ? 2.5% 75.6 ? 2% 75.5 ? 1.1% 81.6 ? 7% 79.3 ? 13.1% 49.8 ? 1.9% 43.2?2.9% 
 
A way to visualize the performance of an algorithm to classify different classes 
is using the confusion matrix. The main diagonal elements of the matrix are true 
predictions of the system, and off-diagonal elements are false negatives or false 
positives for each class. As illustrated in Figure 4-7, the broadband system accurately 
classifies different shapes, while the narrowband system confuses the hollow 
hemisphere with ellipsoid and the empty environment with the prism. In Figure 4-8, 
confusion matrices for size classification using broadband and narrowband emitters are 
shown. Again, the broadband system exhibits better performance.  
 
Figure 4-29: Shape confusion matrices of using CNN in broadband (a) and narrowband (b) 
scenarios. 
100 
 
 
 
 
 
Figure 4-30: Size confusion matrices of using CNN for broadband (a) and narrowband (b) 
scenarios. 
 
4.5  Experiment 
The metamaterial structure was fabricated by using 3D printing (Stratasys Objet30 Pro) 
with the Vero blue material. Ten layers of metamaterial were replaced by piezoelectric 
discs made of ferroelectric soft piezo material. These piezoelectric discs can be used to 
generate sound with different waveforms based on the electrical signals applied to their 
electrodes. Objects with diffident features were used in the experiment. The echo 
signals were recorded by using an ultrasound microphone (Br?el and Kj?r, type-4958 
14 inch). 
Three object shapes (sphere, hollow hemisphere, and disc) were tested in the 
experiment. Each of these shapes was 3D printed using PLA material in four sizes. 
Similar to the simulations, the dataset of each class was obtained, which contains 
101 
 
 
 
echoes of objects of different sizes at different distances and orientations. The 
diameters change from 2 cm to 8 cm, 20 angular positions change between -10 degrees 
to +10 degrees, and three axial distances change between 60 cm to 80 cm. A motorized 
rotational stage was used to control the angular position of an object. To minimize the 
undesired reflection from the stage, the object was fixed to the rotational stage by using 
a long thin rod (see Figure 4-1) All the experiments were performed in an anechoic 
chamber (2.4 ? 1.8 ? 3 m) to eliminate reflection from undesired surfaces and objects 
in the environment. Each experiment was repeated five times. 
4.5.1 Performance optimization with time shifts in emission signal 
Bats modify their echolocation system depending on the environmental complexity and 
sensorimotor challenges by tuning the echolocation call [102]. Frequency and duration 
of calls are two parameters that bats can control. Like bats, the metamaterial emitter 
can be used to adjust the duration and frequency components of emitted sound to 
achieve better performance in acoustic classification. Based on the simulation results, 
the broadband signal is required for high accuracy classification. In this work, the 
metamaterial emitter was used to adjust the time duration of the emitted ultrasound 
pulses to optimize the classification performance.  
Since the metamaterial emitter is a graded-index metamaterial, each active unit 
cell can emit a narrowband signal of a particular frequency. A gaussian waveform with 
a center frequency equal to the working frequency of the unit cell and bandwidth of 1.2 
kHz was applied to each piezoelectric disc. The time shift between signals of different 
piezoelectric discs determines the call duration. For simplicity, time shifts of adjacent 
piezoelectric discs were kept the same. The effect of time shift on the performance of 
102 
 
 
 
the classification system was investigated. In Figure 4-9 (a)-(c), the far-field pressure 
was obtained when each piezoelectric disc was activated one at a time. In Figure 4-9 
(d)-(i), measured far-field pressure and their FFT when all of the piezoelectric discs 
were activated with different time shifts are shown. In Figure 4-9 (j)-(l), the 
spectrograms of the measured pressure are shown. 
 
Figure 4-31: (a-c) Measured far-field pressure when each piezoelectric disc is activated 
individually (a) with a time shift of 0.85 ms (b) and 1.7 ms (c). (d-f) Measured far-field pressure 
when all piezoelectric discs are activated with a time shift of 0 ms (d), 0.85ms (e), and 1.7 ms (f). 
(g-i) Frequency response and (j-l) spectrogram of the measured pressure with a time shift of 0 ms 
(g, j), 0.85 ms (h, k), and 1.7 ms (i, l). 
It can be seen from the results that the frequency bands of sound generated by 
two adjacent piezoelectric discs have enough overlap to induce interfere. When all the 
piezoelectric discs are activated simultaneously, generated sound waves at these 
103 
 
 
 
common frequency regions will have constructive interference (Figure 4-9 (g)). 
Increasing the time shift separates the generated signals in the time domain. This will 
reduce the interference and frequency response shows multiple frequency bands. The 
performance of the sonar classification system with different time shifts was 
investigated. Table 4-3 shows the accuracy when using the CNN algorithm to classify 
the shape of objects with a diameter of 3.5 cm for three different time shift scenarios.  
Table 4-5: Shape and size classification accuracy of CNN algorithm for different time shifts. 
Algorithm 0 ms shift 0.85 ms shift 1.7 ms shift  
 train test train test train test 
CNN 71.1 ? .2% 69.3 ? 3.5% 94.1 ? 2.2% 89.5 ? 5.1% 95.3 ? 1.1% 90.3 ? 8.1% 
 
Compared to synchronized signals, 0.85 ms and 1.7 ms shifted signals provide 
higher accuracy. A longer time shift makes the entire emission signal to have a longer 
duration. If the duration of the emitted sound is increased, the distance between the 
object and the sensing system needs to be increased to prevent the interference of the 
generated sound and the echo. Since the accuracy of 1.7 ms shifted signals is only 
slightly higher than 0.85 ms shifted signals, given the size limitation of the anechoic 
chamber, 0.85 ms shifted signals were chosen for the following the experiments. 
4.5.2 Shape and size classification 
In this subsection, the sonar classification system using a metamaterial emitter was 
investigated to explore its capability for improving the acoustic classification system. 
Two sets of experiments were conducted to classify objects of three different shapes 
with the same diameter of 4 cm. Five machine learning algorithms were used for 
classification. The sonar system with the metamaterial was compared with another 
104 
 
 
 
sonar system using a 25 kHz ultrasound speaker. The experimental conditions, the 
number of measurements for each class, and the parameters of machine learning 
algorithms were kept the same for both systems. The obtained classification accuracy 
for different supervised learning methods by using these two systems are summarized 
and compared in Table 4-4. The obtained confusion matrices of using the CNN 
algorithm for the two systems are shown in Figure 4-10.  
 Table 4-6: Shape classification accuracy of different supervised learning methods for system with 
and without metamaterial 
Algorithm accuracy with MM accuracy without MM 
KNN 98.77 ? 1.77% 84.4 ? 5.5% 
RF 99.22 ? 0.7% 85.4 ? 7.4% 
SVM 94.44 ? 5.5% 83 ? 5% 
 training testing training testing 
MLP 95.15 ? 5.8% 87.93 ? 8.07% 94.72 ? 2.4% 79.48? 10.49% 
CNN 94.1 ? 2.2% 89.5 ? 5.1% 85.35 ? 4.1% 83.75 ? 2.94% 
 
 
 
Figure 4-32: Shape classification confusion matrices of using CNN for the system with 
metamaterial emitter (a) and that with a 25 kHz ultrasound speaker (b).  
105 
 
 
 
Furthermore, experimental studies were conducted to expand the dataset for 
objects of different sizes. For each shape, four samples with diameters ranging from 2 
to 8 were fabricated by using 3D printing. For each object, 1200 echo points were 
collected by changing locations and orientations of the object and the repeating the 
measurements. The goal is to be able to classify shape, size, and both shape and size 
simultaneously.  
In the experiment, three different shapes were used for shape classification and 
each object space had 4800 data points. The shape classifier dataset was formed by 
adding 600 measurements of the empty environment. The accuracies obtained with 
different supervised learning methods for shape only, size only, and shape and size 
together are provided in Table 4-5. The confusion matrices of using CCN algorithm are 
shown in Figure 4-11. Compared to the results shown in Figure 4-10, the shape 
classification accuracy using all the machine learning methods is higher since a larger 
dataset was used. For size classification, four different size classes were used, each of 
which had 3600 data points. The size classifier dataset was formed by adding 600 
measurements of the empty environment. As illustrated in Table 4-5, for all machine 
learning methods, the size classification accuracy is much lower than that of the shape 
classification. The reasons could be the following: i) The data used for size 
classification was not enough, ii) Size feature may not be accurately extracted from 
echoes of objects with a variety of shapes. Simultaneous shape and size classification 
was also explored. In this case, there were 12 classes (each with 1200 data points) and 
an empty class with 600 data points. Although the system shows good accuracy to 
classify the shape and size of hollow hemispheres and discs, it has difficulties in 
106 
 
 
 
classifying spherical objects. Since spherical objects reflect sound in different 
directions, only a small portion of the echo can be recorded by the microphone. 
Therefore, extracting size-related information for spherical objects is challenging.  
Table 4-7: Shape and size classification accuracy of different supervised learning methods. 
Algorithm Shape accuracy Size accuracy Size and shape accuracy 
KNN 97.1 ? 0.6% 65.7 ?5.2% 55.5 ?2.1% 
RF 97.1 ? 1.2% 53.5 ? 2.5% 57.1 ? 1.9% 
SV M 96.44 ? 0.5% 45.8 ? 5.1% 44.4 ? 3.8% 
training testing training testing training testing 
MLP 98.15 ? 95.8 ? 4. 72.1 ? 60.8? 65.8? 68.2? 7.8% 
1.7% 7% 2.4% 9.01% 4.3% 
CNN 99.21 ? 98.5 ? 1.1% 74.5 ? 65.75 ? 70? 5.9% 61.1? 
0.5% 4.1% 7.3% 6.01% 
 
 
 
Figure 4-33: Confusion matric of using the CNN algorithm: (a) Shape classification. (b) Size 
classification. (c) Size and shape classification. 
4.5.3 Surface roughness classification 
When a sound wave interacts with an object, both scattering and reflection can happen. 
The contribution of these two effects depends on the object size relative to the 
107 
 
 
 
wavelength of the sound. If the object is much larger than the wavelength, it reflects all 
of the received sound waves. If the object is smaller than the wavelength, the scenario 
is considered in the Rayleigh domain [64]. For large objects with small ragged edges, 
the subwavelength roughness plays the role of Rayleigh chatterers. If a broadband 
acoustic signal interacts with this object, high frequency components are reflected and 
low frequency components are scattered. The threshold between reflection and 
scattering can be determined when the roughness structural depth is a fourth of the 
wavelength [65]. 
Since the texture-related information can be extracted based on scattering 
properties of the object, the sonar classification system was investigated for surface 
roughness classification. Five discs with different surface textures were fabricated by 
using 3D printing. To change the surface texture, uniform squared patches with 
different dimensions were used (see Figure 4-12 (a)) on each disc. The patches size and 
spacing of patches were changed from 2.8 mm to 4.25 mm. These surface patterns were 
chosen based on the working wavelengths of the sonar system. The frequency 
components of measured echoes from these objects of different surface patterns and a 
flat object are shown in Figure 4-12 (b). Each measurement was repeated 20 times. For 
comparison, the same experiments were performed by using the sonar system with the 
25 kHz speaker (Figure 4-12 (c)). 
108 
 
 
 
 
Figure 4-34: (a) Objects used for surface pattern classification with different pattern sizes. (b,c) 
frequency components of echoes from different objects using the metamaterial sonar system and 
the sonar with a 25 kHz speaker.  
The results show that surface pattern classification is expected to be more 
challenging with the sonar system using a narrowband speaker since the differences of 
echoes in frequency-domain are not obvious. Instead of the spectrogram, the FFT of 
echo was used for surface classification. Moreover, visual differences in FFT of echoes 
encourage us to use Principal Component Analysis (PCA) as the first method of 
classification. PCA is a well-known dimension reduction technique. PCA reduces the 
dimension by projecting each data point onto the first few principal components while 
preserving the data's variation as much as possible [103]. PCA allows visualization of 
the dataset and provides some insight into the next step decision making on machine 
learning models. The PCA scatterplots of the dataset with and without metamaterial are 
shown in Figure 4-13. 
109 
 
 
 
 
 
Figure 4-35: Principal component analysis results: (a) metamaterial sonar and (b) sonar with 25 
kHz speaker. a is the length of squared patch.  
It is unable to separate each class in the scenario with the 25 kHz speaker since 
the scatterplot of the first two principal components divides the data into three clusters, 
one of which contains data from five different classes (empty, a=0, a=2.83 mm, a=3.09 
mm, and a=4.25 mm). In the scenario with the metamaterial speaker, the PCA separates 
the data into five clusters and only the classification of two classes (a=3.09 mm and 
a=3.7 mm) may be challenging. Although these two classes form one cluster, they are 
not distributed evenly and can be distinguished in most cases. These results show that 
the sonar using a metamaterial emitter may increases the possibility of correct 
classification by using the FFT of echoes instead of the spectrogram.  
Surface classification using different machine learning algorithms were carried 
out with these two sonar systems. Since the spectrogram of echoes were not used, the 
datapoints were vectors not compatible with the structure of the CNN algorithm. The 
surface classification accuracies of different supervised learning methods are provided 
in Table 4-6. The confusion matrices of using the MLP algorithm for scenarios with 
the metamaterial sonar and without metamaterial are shown in Figure 4-14. 
110 
 
 
 
Table 4-8: Surface classification accuracy of using different supervised learning methods with a 
metamaterial sonar and a sonar using 25 kHz speaker. 
Algorithm Accuracy with MM Accuracy without MM 
KNN 97.1 ? 1.2% 64.7 ?4.2% 
RF 99.1 ? 2.2% 63.5 ? 5.5% 
SVM 99.3 ? 1.4% 55.8 ? 9.1% 
MLP 99.4 ? 1.2% 72.1 ? 4.4% 
 
 
 
Figure 4-36: Classification confusion matrices of using MLP algorithm: (a) metamaterial sonar 
and (b) sonar with a 25 kHz speaker without the metamaterial. 
As expected, surface pattern classification accuracy using the metamaterial 
sonar is higher than that without the metamaterial for all the tested machine learning 
algorithms.  
4.6 Summary  
Inspired by the echolocation capabilities of bats, a sonar system equipped with a 
metamaterial emitter was developed and the performance of this system for acoustic 
object classification was investigated. The metamaterial emitter is capable of 
generating sound with different spectral and temporal characteristics. Acoustic 
111 
 
 
 
classification of shape, size, and surface patterns based on echoes of different objects 
was carried by using different machine learning algorithms including RF, KNN, SVM, 
MLP, and CNN. The experimental and simulation results can be summarized as 
follows.  
? The simulation results confirmed the feasibility of shape classification from an 
object pool containing objects with six different shapes and fourteen different 
sizes. The results also showed that size classification can be more challenging. 
Moreover, the effect of the frequency bandwidth of generated signals on the 
shape classification accuracy was investigated. The system using broadband 
emission signals demonstrated better classification accuracy compared to that 
using a narrowband speaker. 
? Experiments were conducted to investigate the effect of temporal 
characteristics of emission signals on the accuracy of the classification system. 
An appropriate emission signal was determined for achieving a high accuracy. 
? The shape classification accuracy of the metamaterial sonar system was 
characterized experimentally and compared with that of another sonar system 
using a 25 kHz ultrasound speaker. The metamaterial sonar was found to 
provide better classification accuracy for all tested machine learning algorithms 
for the shape classification of objects with four different shapes and the same 
size. The sample size was extended to include four different sizes for each 
object shape. The experimental results showed that the metamaterial sonar 
system can provide satisfactory shape classification performance, but size 
classification may be challenging. 
112 
 
 
 
? The surface classification capabilities of the metamaterial sonar classification 
system were investigated experimentally for objects with different surface 
pattern sizes. The metamaterial sonar demonstrated good accuracy in surface 
classification, which was proven to have better performance than that of the 
sonar system using a 25 kHz speaker.  
Although shape and surface classification was achieved by the metamaterial-
based sensing system, there are some limits that addressing them improve the system's 
capabilities. Firstly, we couldn't use the metamaterial for simultaneous emotion and 
reception due to practical difficulties, so we didn't use the full potential of the active 
graded-index acoustic metamaterial. We also can improve the classification accuracy 
by increasing the number of the objects' shapes and surfaces. 
113 
 
 
 
5. Chapter 5: Summary 
5.1 Summary of the dissertation work 
Acoustic imaging and sensing systems are important for many applications. Currently, 
acoustic sensors have been widely used in single sensor element applications such as 
distance sensing or multi-sensor applications such as near-field imaging. In single 
sensor applications, other than distance, information about the shape, size, surface 
features, and location of an object can be extracted from acoustic clues. Extracting this 
information requires broadband sound emitters and sensors. In imaging applications 
with multiple acoustic sensors, the tradeoff between the range and resolution of an 
imaging system needs to be addressed.  
In this dissertation, graded-index acoustic metamaterials are proposed to 
address the abovementioned needs and challenges. In this dissertation work, our 
understanding of passive and active graded-index acoustic metamaterials for acoustic 
wave manipulation is enhanced. This understanding leads to novel applications and 
improvements of acoustic imaging and sensing systems by using graded-index acoustic 
metamaterials. The main contributions of this dissertation work are summarized as 
follows. 
Contribution 1: Enhanced understanding on spatial domain multiplexing 
with passive graded-index acoustic metamaterials for far-field acoustic imaging 
has been developed.  
114 
 
 
 
A far-field imaging system is developed by using a linear uniform array of 32 
graded-index acoustic metamaterial-based sensing elements for the first time. Owing 
to the wave compression and pressure amplification properties of the graded-index 
acoustic metamaterials, the performance (e.g., range and resolution) of the 
metamaterial-based imaging system is greatly enhanced compared with a similar array 
constructed without the metamaterials. 
Contribution 2: Fundamental understanding on active graded-index 
acoustic metamaterials with frequency-domain multiplexing capabilities for 
enhanced broadband acoustic emission and reception has be developed.  
Active graded-index metamaterials with a number of active unite cells are 
designed and developed for the first time, which enable enhanced acoustic emission 
and reception over multiple frequency bands. The parameters that govern the spatial 
and spectral characteristics of the metamaterial are also investigated. 
Contribution 3: An acoustic classification system based on the active 
graded-index metamaterial has been developed to classify objects with different 
shapes and surface patterns. 
A novel metamaterial-based sonar system has been developed for shape and surface 
classification. Owing to the enhanced broadband emission and reception capacities of 
the active graded-index metamaterials, this system has much-improved performance 
than a conventional narrowband sonar system. 
5.2 Suggested future work 
As an extension of this desertion work, future work is suggested as follows. 
115 
 
 
 
1) Active acoustic metamaterials for simultaneous reception and emission. As 
mentioned in Chapter 4, although the active metamaterial has the capability of 
providing enhanced emission and reception, simultaneous emission and 
reception is practically challenging. This challenge can be potentially addressed 
by designing control electronics to separate these two signals without increasing 
the measurement noise.  
2) Broadband acoustic imaging system using an array of graded-index 
acoustic metamaterial. In this dissertation work, a linear array of acoustic 
metamaterial sensing elements was developed and used for two-dimensional 
acoustic imaging. As the broadband active graded-index metamaterial has been 
demonstrated to have better performance for shape and surface classification, by 
using the broadband active acoustic metamaterial, a two-dimensional broadband 
acoustic imaging system can be developed to extract information about the size, 
shape, location, and surfaces of multiple objects in a complex environment. 
3) Graded-index acoustic metamaterial for underwater sensing and imaging 
applications. In this dissertation, an airborne active graded-index acoustic 
metamaterial device was developed, which is capable of sensing and emitting in 
a frequency range between 20 kHz to 30 kHz. Future work is suggested to 
explore the graded-index acoustic metamaterials for underwater applications. 
The main challenge to extend the airborne metamaterial to waterborne is the 
shear loss in water. Thorough theoretical, numerical, and experimental studies 
are needed to design impedance matching acoustic metamaterials for underwater 
applications.  
116 
 
 
 
Bibliography 
[1] V. G. Veselago, ?Electrodynamics of substances with simultaneously negative 
and.,? Usp. Fiz. Nauk, vol. 92, p. 517, 1967. 
 
[2] K. B. Alici and E. ?zbay, ?Radiation properties of a split ring resonator and 
monopole composite,? Phys. Status Solidi Basic Res., vol. 244, no. 4, pp. 1192?
1196, 2007. 
 
[3] W. Li and J. Valentine, ?Metamaterial perfect absorber based hot electron 
photodetection,? Nano Lett., vol. 14, no. 6, pp. 3510?3514, 2014. 
 
[4] J. B. Pendry, ?Negative refraction makes a perfect lens,? Phys. Rev. Lett., vol. 
85, no. 18, pp. 3966?3969, 2000. 
 
[5] D. Schurig et al., ?Metamaterial electromagnetic cloak at microwave 
frequencies,? Science (80-. )., vol. 314, no. 5801, pp. 977?980, 2006. 
 
[6] A. Y. Modi, M. A. Alyahya, C. A. Balanis, and C. R. Birtcher, ?Metasurface-
Based Method for Broadband RCS Reduction of Dihedral Corner Reflectors 
with Multiple Bounces,? IEEE Trans. Antennas Propag., vol. X, no. c, pp. 1?
12, 2019. 
 
[7] M. Brun, S. Guenneau, and A. B. Movchan, ?Achieving control of in-plane 
elastic waves,? Appl. Phys. Lett., vol. 94, no. 6, pp. 10?13, 2009. 
 
[8] S. A. Cummer, J. Christensen, and A. Al?, ?Controlling sound with acoustic 
metamaterials,? Nature Reviews Materials. 2016. 
 
[9] M. Moler?n and C. Daraio, ?Acoustic metamaterial for subwavelength edge 
detection,? Nat. Commun., 2015. 
 
[10] Y. Xie, T. H. Tsai, A. Konneker, B. I. Popa, D. J. Brady, and S. A. Cummer, 
?Single-sensor multispeaker listening with acoustic metamaterials,? Proc. Natl. 
Acad. Sci. U. S. A., vol. 112, no. 34, pp. 10595?10598, 2015. 
 
[11] G. Ma, M. Yang, Z. Yang, and P. Sheng, ?Low-frequency narrow-band acoustic 
filter with large orifice,? Appl. Phys. Lett., vol. 103, no. 1, 2013. 
 
[12] F. Casadei, T. Delpero, A. Bergamini, P. Ermanni, and M. Ruzzene, 
?Piezoelectric resonator arrays for tunable acoustic waveguides and 
metamaterials,? J. Appl. Phys., vol. 112, no. 6, 2012. 
 
[13] C. Liu, B. Xia, and D. Yu, ?The spiral-labyrinthine acoustic metamaterial by 
coiling up space,? Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 381, no. 36, 
117 
 
 
 
pp. 3112?3118, 2017. 
 
[14] L. Zigoneanu, B. I. Popa, and S. A. Cummer, ?Three-dimensional broadband 
omnidirectional acoustic ground cloak,? Nat. Mater., 2014. 
 
[15] M. Moler?n, M. Serra-Garcia, and C. Daraio, ?Visco-thermal effects in acoustic 
metamaterials: From total transmission to total reflection and high absorption,? 
New J. Phys., vol. 18, no. 3, 2016. 
 
[16] Y. Li et al., ?Three-dimensional ultrathin planar lenses by acoustic 
metamaterials,? Sci. Rep., vol. 4, 2014. 
 
[17] X. Zhu et al., ?Implementation of dispersion-free slow acoustic wave 
propagation and phase engineering with helical-structured metamaterials,? Nat. 
Commun., vol. 7, no. May, 2016. 
 
[18] Heinrich Kuttruff, Acoustics An Introduction, 1st Editio. London, 2006. 
 
[19] D. B. Lindell and G. Wetzstein, ?Acoustic Non-Line-of-Sight Imaging,? Proc. 
IEEE Conf. Comput. Vis. Pattern Recognit., 2019. 
 
[20] X. Lin, J. Yu, N. Feng, and M. Sun, ?Synthetic aperture-based linear-array 
photoacoustic tomography considering the aperture orientation effect,? J. Innov. 
Opt. Health Sci., vol. 11, no. 04, p. 1850015, 2018. 
 
[21] Y. Han, X. Tian, F. Zhou, R. Jiang, and Y. Chen, ?A real-time 3-D underwater 
acoustical imaging system,? IEEE J. Ocean. Eng., vol. 39, no. 4, pp. 620?629, 
2014. 
 
[22] K. S. Kim and T. K. Song, ?High volume rate 3-D ultrasound imaging using 
cross array based on synthetic transmit focusing,? Proc. - IEEE Ultrason. Symp., 
vol. 2, no. c, pp. 1409?1412, 2004. 
 
[23] X. Liu, F. Zhou, H. Zhou, X. Tian, R. Jiang, and Y. Chen, ?A Low-Complexity 
Real-Time 3-D Sonar Imaging System with a Cross Array,? IEEE J. Ocean. 
Eng., vol. 41, no. 2, pp. 262?273, 2016. 
 
[24] S. Kagami, ?Circular microphone array for robot?s audition,? Proc. IEEE 
Sensors, 2004., pp. 565?570, 2006. 
 
[25] M. R. Bai, C.-S. Lai, and P.-C. Wu, ?Localization and separation of acoustic 
sources by using a 2.5-dimensional circular microphone array,? J. Acoust. Soc. 
Am., 2017. 
 
[26] Z. Prime and C. Doolan, ?A comparison of popular beamforming arrays,? Annu. 
Conf. Aust. Acoust. Soc. 2013, Acoust. 2013 Sci. Technol. Amenity, no. 
118 
 
 
 
November, pp. 151?157, 2013. 
 
[27] H. Yoon and T. K. Song, ?Sparse rectangular and spiral array designs for 3D 
medical ultrasound imaging,? Sensors (Switzerland), vol. 20, no. 1, 2020. 
 
[28] M. Legg and S. Bradley, ?Comparison of Clean-Sc for 2D and 3D Scanning 
Surfaces 4 Th Berlin Beamforming Conference,? pp. 1?11, 2012. 
 
[29] L. Capineri, A. Bulletti, M. Calzolai, and P. Giannelli, ?An Airborne Ultrasonic 
Imaging System Based on 16 Elements: 150 kHz Piezopolymer Transducer 
Arrays?Preliminary Simulated and Experimental Results for Cylindrical 
Targets Detection,? Sens. Imaging, vol. 17, no. 1, pp. 1?23, 2016. 
 
[30] A. Izquierdo, J. J. Villacorta, L. del Val Puente, and L. Su?rez, ?Design and 
evaluation of a scalable and reconfigurable multi-platform system for acoustic 
imaging,? Sensors (Switzerland), 2016. 
 
[31] L. del Val, A. Izquierdo, J. J. Villacorta, L. Su?rez, and M. Herr?ez, ?First steps 
on fan matrix condition monitoring and fault diagnosis using an array of digital 
mems microphones,? Proc. Meet. Acoust., vol. 30, no. 1, 2017. 
 
[32] A. Izquierdo, J. J. Villacorta, L. Del Val, L. Su?rez, and D. Su?rez, 
?Implementation of a virtual microphone array to obtain high resolution acoustic 
images,? Sensors (Switzerland), vol. 18, no. 1, 2018. 
 
[33] P. Shirkovskiy, A. Laurin, N. Jeger-Madiot, D. Chapelle, M. Fink, and R. K. 
Ing, ?Airborne ultrasound surface motion camera: Application to 
seismocardiography,? Appl. Phys. Lett., vol. 112, no. 21, 2018. 
 
[34] C. Crake, S. T. Brinker, C. M. Coviello, M. S. Livingstone, and N. J. 
McDannold, ?A dual-mode hemispherical sparse array for 3D passive acoustic 
mapping and skull localization within a clinical MRI guided focused ultrasound 
device,? Phys. Med. Biol., vol. 63, no. 6, 2018. 
 
[35] G. Fedorko, P. Liptai, and V. Moln?r, ?Proposal of the methodology for noise 
sources identification and analysis of continuous transport systems using an 
acoustic camera,? Eng. Fail. Anal., vol. 83, no. September 2017, pp. 30?46, 
2018. 
 
[36] J. Tiete, F. Dom?nguez, B. da Silva, L. Segers, K. Steenhaut, and A. Touhafi, 
?SoundCompass: A distributed MEMS microphone array-based sensor for 
sound source localization,? Sensors (Switzerland), vol. 14, no. 2, pp. 1918?1949, 
2014. 
 
[37] P. Shirkovskiy, A. Laurin, N. Jeger-Madiot, D. Chapelle, M. Fink, and R. K. 
Ing, ?Airborne ultrasound surface motion camera: Application to 
119 
 
 
 
seismocardiography,? Appl. Phys. Lett., vol. 112, no. 21, 2018. 
 
[38] B. I. Popa, D. Shinde, A. Konneker, and S. A. Cummer, ?Active acoustic 
metamaterials reconfigurable in real time,? Phys. Rev. B - Condens. Matter 
Mater. Phys., 2015. 
 
[39] S. A. Cummer, J. Christensen, and A. Al?, ?Controlling sound with acoustic 
metamaterials,? Nat. Rev. Mater., vol. 1, no. 16001, 2016. 
 
[40] T. Jiang, Q. He, and Z. K. Peng, ?Proposal for the Realization of a Single-
Detector Acoustic Camera Using a Space-Coiling Anisotropic Metamaterial,? 
Phys. Rev. Appl., vol. 11, no. 3, p. 1, 2019. 
 
[41] F. Casadei, T. Delpero, A. Bergamini, P. Ermanni, and M. Ruzzene, 
?Piezoelectric resonator arrays for tunable acoustic waveguides and 
metamaterials,? J. Appl. Phys., vol. 112, no. 6, 2012. 
 
[42] L. Zigoneanu, B. I. Popa, and S. A. Cummer, ?Three-dimensional broadband 
omnidirectional acoustic ground cloak,? Nat. Mater., vol. 13, no. 4, pp. 352?
355, 2014. 
 
[43] Y. Chen, H. Liu, M. Reilly, H. Bae, and M. Yu, ?Enhanced acoustic sensing 
through wave compression and pressure amplification in anisotropic 
metamaterials,? Nat. Commun., 2014. 
 
[44] R. Ganye, Y. Chen, and M. Yu, ?On-chip acoustic metamaterial with active 
tunable properties,? Adv. Mater. J., 2020. 
 
[45] H. Jia, M. Ke, R. Hao, Y. Ye, F. Liu, and Z. Liu, ?Subwavelength imaging by a 
simple planar acoustic superlens,? Appl. Phys. Lett., vol. 97, no. 17, 2010. 
 
[46] M. Moler?n and C. Daraio, ?Acoustic metamaterial for subwavelength edge 
detection,? Nat. Commun., vol. 6, pp. 2?7, 2015. 
 
[47] X. Jia, M. Yan, and M. Hong, ?Sound energy enhancement via impedance-
matched anisotropic metamaterial,? Mater. Des., vol. 197, p. 109254, 2021. 
 
[48] L. Zhao and S. Zhou, ?Compact acoustic rainbow trapping in a bioinspired spiral 
array of graded locally resonant metamaterials,? Sensors (Switzerland), vol. 19, 
no. 4, pp. 1?11, 2019. 
 
[49] Y. Jin, R. Kumar, O. Poncelet, O. Mondain-Monval, and T. Brunet, ?Flat 
acoustics with soft gradient-index metasurfaces,? Nat. Commun., vol. 10, no. 1, 
pp. 1?6, 2019. 
 
[50] S. Kim and N. X. Fang, ?Far-field acoustic subwavelength imaging and edge 
120 
 
 
 
detection based on spatial filtering and wave vector conversion,? Nat. Commun., 
no. 2019, pp. 1?10. 
 
[51] J. Zhu, J. Christensen, J. Jung, X. Yin, L. Fok, and X. Zhang, ?A holey-
structured metamaterial for acoustic deep-subwavelength imaging,? Nat. Phys., 
vol. 7, no. November 2010, 2011. 
 
[52] H. Su, X. Zhou, X. Xu, and G. Hu, ?Experimental study on acoustic 
subwavelength imaging of holey-structured metamaterials by resonant 
tunneling,? J. Acoust. Soc. Am., vol. 135, no. 4, pp. 1686?1691, 2014. 
 
[53] S. D. Zhao, A. L. Chen, Y. S. Wang, and C. Zhang, ?Continuously Tunable 
Acoustic Metasurface for Transmitted Wavefront Modulation,? Phys. Rev. 
Appl., vol. 10, no. 5, p. 1, 2018. 
 
[54] X. Yu, Z. Lu, F. Cui, L. Cheng, and Y. Cui, ?Tunable acoustic metamaterial with 
an array of resonators actuated by dielectric elastomer,? Extrem. Mech. Lett., 
2017. 
 
[55] S. Qi, M. Oudich, Y. Li, and B. Assouar, ?Acoustic energy harvesting based on 
a planar acoustic metamaterial,? Appl. Phys. Lett., vol. 108, no. 26, 2016. 
 
[56] F. Casadei, T. Delpero, A. Bergamini, P. Ermanni, and M. Ruzzene, 
?Piezoelectric resonator arrays for tunable acoustic waveguides and 
metamaterials,? J. Appl. Phys., 2012. 
 
[57] X. Y. Li, Z. Z. Yang, Y. F. Zhu, X. Y. Zou, and J. C. Cheng, ?Broadband acoustic 
phased array with subwavelength active tube array,? Appl. Phys. Lett., vol. 112, 
no. 9, 2018. 
 
 
[58] W. Akl and A. Baz, ?Analysis and experimental demonstration of an active 
acoustic metamaterial cell,? J. Appl. Phys., vol. 111, no. 4, 2012. 
 
[59] J. A. Simmons, ?Big brown bats and June beetles: Multiple pursuit strategies in 
a seasonal acoustic predator-prey system,? Acoust. Res. Lett. Online, vol. 6, no. 
4, pp. 238?242, 2005. 
 
[60] C. F. Moss, K. Bohn, H. Gilkenson, and A. Surlykke, ?Active listening for 
spatial orientation in a complex auditory scene,? PLoS Biol., vol. 4, no. 4, pp. 
615?626, 2006. 
 
[61] S. Mantani, S. Hiryu, E. Fujioka, N. Matsuta, H. Riquimaroux, and Y. Watanabe, 
?Echolocation behavior of the Japanese horseshoe bat in pursuit of fluttering 
prey,? J. Comp. Physiol. A Neuroethol. Sensory, Neural, Behav. Physiol., vol. 
198, no. 10, pp. 741?751, 2012. 
121 
 
 
 
 
[62] A. L. Baier and L. Wiegrebe, ?Flutter sensitivity in FM bats. Part I: delay 
modulation,? J. Comp. Physiol. A Neuroethol. Sensory, Neural, Behav. Physiol., 
vol. 204, no. 11, pp. 929?939, 2018. 
 
[63] J. A. Simmons, ?Temporal binding of neural responses for focused attention in 
biosonar,? J. Exp. Biol., vol. 217, no. 16, pp. 2834?2843, 2014. 
 
[64] Y. Yovel, M. O. Franz, P. Stilz, and H. U. Schnitzler, ?Complex echo 
classification by echo-locating bats: A review,? J. Comp. Physiol. A Neuroethol. 
Sensory, Neural, Behav. Physiol., vol. 197, no. 5, pp. 475?490, 2011. 
 
[65] R. Simon et al., ?Biosonar resolving power: Echo-acoustic perception of surface 
structures in the submillimeter range,? Front. Physiol., vol. 5 FEB, no. February, 
pp. 1?9, 2014. 
 
[66] Y. Yamada, Y. Mibe, Y. Yamamoto, K. Ito, O. Heim, and S. Hiryu, ?Modulation 
of acoustic navigation behaviour by spatial learning in the echolocating bat 
Rhinolophus ferrumequinum nippon,? Sci. Rep., vol. 10, no. 1, pp. 1?15, 2020. 
 
[67] M. J. Wohlgemuth, J. Luo, and C. F. Moss, ?Three-dimensional auditory 
localization in the echolocating bat,? Curr. Opin. Neurobiol., vol. 41, pp. 78?86, 
2016. 
 
[68] G. A. Wright, ?To feed or not to feed: circuits involved in the control of feeding 
in insects,? Curr. Opin. Neurobiol., vol. 41, pp. 87?91, 2016. 
 
[69] L. Gao, S. Balakrishnan, W. He, Z. Yan, and R. M?ller, ?Ear deformations give 
bats a physical mechanism for fast adaptation of ultrasonic beam patterns,? Phys. 
Rev. Lett., vol. 107, no. 21, pp. 1?5, 2011. 
 
[70] R. Simon et al., ?Biosonar resolving power: Echo-acoustic perception of surface 
structures in the submillimeter range,? Front. Physiol., vol. 5 FEB, no. February, 
pp. 1?9, 2014. 
 
[71] D. Von Helversen and O. Von Helversen, ?Object classification by echolocation 
in nectar feeding bats: Size-independent generalization of shape,? J. Comp. 
Physiol. A Neuroethol. Sensory, Neural, Behav. Physiol., vol. 190, no. 7, pp. 
515?521, 2004. 
 
[72] J. A. Simmons, ?Bats use a neuronally implemented computational acoustic 
model to form sonar images,? Curr. Opin. Neurobiol., vol. 22, no. 2, pp. 311?
319, 2012. 
 
[73] R. Simon, M. W. Holderied, and O. Von Helversen, ?Size discrimination of 
hollow hemispheres by echolocation in a nectar feeding bat,? J. Exp. Biol., vol. 
122 
 
 
 
209, no. 18, pp. 3599?3609, 2006. 
 
[74] P. Weissenbacher and L. Wiegrebe, ?Classification of virtual objects in the 
echolocating bat, Megaderma lyra,? Behav. Neurosci., pp. 833?839, 2003. 
 
[75] B. Falk, T. Williams, M. Aytekin, and C. F. Moss, ?Adaptive behavior for 
texture discrimination by the free-flying big brown bat, Eptesicus fuscus,? J. 
Comp. Physiol. A Neuroethol., vol. 197, no. 5, pp. 491?503, 2011. 
 
[76] D. Laurijssen, R. Kerstens, G. Schouten, W. Daems, and J. Steckel, ?A flexible 
low-cost biologically inspired sonar sensor platform for robotic applications,? 
Proc. - IEEE Int. Conf. Robot. Autom., vol. 2019-May, pp. 9617?9623, 2019. 
 
[77] M. Sumiya et al., ?Bat-inspired signal design for target discrimination in human 
echolocation,? J. Acoust. Soc. Am., vol. 145, no. 4, pp. 2221?2236, 2019. 
 
[78] R. Simon, S. Rupitsch, M. Baumann, H. Wu, H. Peremans, and J. Steckel, 
?Bioinspired sonar reflectors as guiding beacons for autonomous navigation,? 
Proc. Natl. Acad. Sci. U. S. A., vol. 117, no. 3, pp. 1367?1374, 2020. 
 
[79] M. H. Tanveer, H. Zhu, W. Ahmed, A. Thomas, B. M. Imran, and M. Salman, 
?Mel-spectrogram and Deep CNN Based Representation Learning from Bio-
Sonar Implementation on UAVs,? 2021 Int. Conf. Comput. Control Robot. 
ICCCR 2021, pp. 220?224, 2021. 
 
[80] I. Eliakim, Z. Cohen, G. Kosa, and Y. Yovel, ?A fully autonomous terrestrial 
bat-like acoustic robot,? PLoS Comput. Biol., vol. 14, no. 9, pp. 1?13, 2018. 
 
[81] P. K. Kroh, R. Simon, and S. J. Rupitsch, ?Neural Network-Based Detection of 
Ultrasonic Targets with Respect to Noise and Number of Sampling Positions,? 
IEEE Int. Ultrason. Symp. IUS, vol. 2019-Octob, pp. 1870?1873, 2019. 
 
[82] P. K. Kroh, R. Simon, and S. J. Rupitsch, ?Classification of sonar targets in air: 
A neural network approach,? Sensors (Switzerland), vol. 19, no. 5, pp. 1?17, 
2019. 
 
[83] I. International, W. On, M. Learning, and F. O. R. Signal, ?Object classification 
with convolution nueral network based on the time-frequency representation of 
their echo,? pp. 4?9, 2017. 
 
[84] G. De Magistris et al., ?Automatic object classification for low-frequency active 
sonar using convolutional neural networks,? Ocean. 2019 MTS/IEEE Seattle, 
Ocean. 2019, 2019. 
 
[85] L. Kritly, Y. Sluyts, D. Pelegr?n-Garc?a, C. Glorieux, and M. Rycht?rikov?, 
?Discrimination of 2D wall textures by passive echolocation for different 
123 
 
 
 
reflected-to-direct level difference configurations,? PLoS One, vol. 16, no. 5 
May, pp. 1?27, 2021. 
 
[86] G. Kang and S. C. Kim, ?DeepEcho: Echoacoustic Recognition of Materials 
using Returning Echoes with Deep Neural Networks,? IEEE Trans. Emerg. Top. 
Comput., vol. 0, no. 0, pp. 1?13, 2020. 
 
[87] M. Valdenegro-Toro, ?Deep Neural Networks for Marine Debris Detection in 
Sonar Images,? no. April, 2019. 
 
[88] M. Rupin, G. Lerosey, J. De Rosny, and F. Lemoult, ?Mimicking the cochlea 
with an active acoustic metamaterial Mimicking the cochlea with an active 
acoustic metamaterial,? 2019. 
 
[89] L. L. Beranek and T. J. Mellow, Acoustic components. 2012. 
 
[90] J. Abe?er, ?A review of deep learning based methods for acoustic scene 
classification,? Appl. Sci., vol. 10, no. 6, 2020. 
 
[91] V. Hajihashemi, A. A. Gharahbagh, P. M. Cruz, M. C. Ferreira, J. J. M. 
Machado, and J. M. R. S. Tavares, ?Binaural Acoustic Scene Classification 
Using Wavelet Scattering, Parallel Ensemble Classifiers and Nonlinear Fusion,? 
Sensors, vol. 22, no. 4, pp. 1?19, 2022. 
 
[92] H. Knutsson, M. Borga, and T. Landelius, Learning multidimensional signal 
processing, no. 531. 2002. 
 
[93] J. Han, M. Kamber, and J. Pei, ?Data Mining?: Concepts and Techniques?: 
Concepts and Techniques (3rd Edition),? Data Min., pp. 1?38, 2012. 
 
[94] T. K. Ho, ?Random decision forests,? Proc. Int. Conf. Doc. Anal. Recognition, 
ICDAR, vol. 1, pp. 278?282, 1995. 
 
[95] Naomi S. Altman, ?An Introduction to Kernel and Nearest-Neighbor 
Nonparametric Regression,? Am. Stat., vol. 4, no. 11, pp. 175?185, 1994. 
 
[96] C. Corinna and V. Vladimir, ?Support-Vector Networks,? Mach. Leaming, vol. 
20, no. 3, pp. 273?291, 1995. 
 
[97] L. Breiman, ?Random Forests,? Mach. Learn., vol. 45, no. 1, pp. 5?32, 2001. 
[98] J. J. Hopfield, ?Artificial Neural Networks,? IEEE Circuits Devices Mag., vol. 
4, no. 5, pp. 3?10, 1988. 
 
[99] J. Schmidhuber, ?Deep Learning in neural networks: An overview,? Neural 
Networks, vol. 61, pp. 85?117, 2015. 
 
124 
 
 
 
[100] S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back, ?Face recognition: A 
convolutional neural-network approach,? IEEE Trans. Neural Networks, vol. 8, 
no. 1, pp. 98?113, 1997. 
 
[101] S. Mun, S. Shon, W. Kim, D. K. Han, and H. Ko, ?DEEP NEURAL NETWORK 
BASED LEARNING AND TRANSFERRING MID-LEVEL AUDIO 
FEATURES FOR ACOUSTIC SCENE CLASSIFICATION,? IEEE Int. Conf. 
Acoust. Speech, Signal Process. 2017, pp. 796?800, 2017. 
 
[102] K. A. McGowan and L. N. Kloepper, ?Different as night and day: wild bats 
modify echolocation in complex environments when visual cues are present,? 
Anim. Behav., vol. 168, pp. 1?6, 2020. 
 
[103] I. T. Jollife and J. Cadima, ?Principal component analysis: A review and recent 
developments,? Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 374, no. 
2065, 2016. 
 
125