Time reversal focusing above an array of resonators creates subwavelength–sized features when compared to wavelengths in free space. Previous work has shown the ability to focus acoustic waves near the resonators with and without time reversal with an array placed coplanar with acoustic sources, principally using direct sound emissions. In this work, a two-dimensional array of resonators is studied with a full three-dimensional aperture of waves in a reverberation chamber and including significant reverberation within the time reversed emissions. The full impulse response is recorded, and the spatial inverse filter is used to produce a focus among the resonators. Additionally, images of complex sources are produced by extending the spatial inverse filter to create focal images, such as dipoles and quadrupoles. Although waves at oblique angles would be expected to degrade the focal quality, it is shown that complex focal images can still be achieved with super resolution fidelity when compared to free space wavelengths.

1.
B.
Zimmermann
and
C.
Studer
, “
FPGA-based real-time acoustic camera prototype
,” in
Proceedings of 2010 IEEE International Symposium on Circuits and Systems
, Salt Lake City, UT (American Rock Mechanics Association, Alexandria, VA, 2010), pp. 1419–1422.
2.
A. A.
Maznev
and
O. B.
Wright
, “
Upholding the diffraction limit in the focusing of light and sound
,”
Wave Motion
68
,
182
189
(
2017
).
3.
A.
Parvulescu
and
C. S.
Clay
, “
Reproducibility of signal transmissions in the ocean
,”
Radio Electron. Eng. UK.
29
(
4
),
223
228
(
1965
).
4.
M.
Fink
, “
Time reversed acoustics
,”
Phys. Today
50
(
3
),
34
40
(
1997
).
5.
B. E.
Anderson
,
M.
Griffa
,
C.
Larmat
,
T. J.
Ulrich
, and
P. A.
Johnson
, “
Time reversal
,”
Acoust. Today
4
(
1
),
5
16
(
2008
).
6.
C. S.
Clay
and
B. E.
Anderson
, “
Matched signals: The beginnings of time reversal
,”
Proc. Mtgs. Acoust.
12
,
055001
(
2011
).
7.
J.-L.
Thomas
,
F.
Wu
, and
M.
Fink
, “
Time reversal focusing applied to lithotripsy
,”
Ultrason. Imaging
18
(
2
),
106
121
(
1996
).
8.
M.
Tanter
,
J.-L.
Thomas
, and
M.
Fink
, “
Focusing and steering through absorbing and aberating layers: Application to ultrasonic propagation through the skull
,”
J. Acoust. Soc. Am.
103
(
5
),
2403
2410
(
1998
).
9.
G.
Montaldo
,
P.
Roux
,
A.
Derode
,
C.
Negreira
, and
M.
Fink
, “
Ultrasound shock wave generator with one-bit time reversal in a dispersive medium, application to lithotripsy
,”
Appl. Phys. Lett.
80
(
5
),
897
899
(
2002
).
10.
M.
Fink
,
G.
Montaldo
, and
M.
Tanter
, “
Time-reversal acoustics in biomedical engineering
,”
Annu. Rev. Biomed. Eng.
5
,
465
497
(
2003
).
11.
S.
Dos Santos
and
Z.
Prevorovsky
, “
Imaging of human tooth using ultrasound-based chirp-coded nonlinear time reversal acoustics
,”
Ultrasonics
51
(
6
),
667
674
(
2011
).
12.
C.
Prada
and
M.
Fink
, “
Separation of interfering acoustic scattered signals using the invariant of the time-reversal operator. Application to Lamb waves characterization
,”
J. Acoust. Soc. Am.
104
,
801
807
(
1998
).
13.
E.
Kerbrat
,
R. K.
Ing
,
C.
Prada
,
D.
Cassereau
, and
M.
Fink
, “
The D.O.R.T. method applied to detection and imaging in plates using Lamb waves
,”
AIP Conf. Proc.
557
,
934
940
(
2001
).
14.
E.
Kerbrat
,
C.
Prada
,
D.
Cassereau
, and
M.
Fink
, “
Ultrasonic nondestructive testing of scattering media using the decomposition of the time reversal operator
,”
IEEE Trans. Ultrason, Ferroelect, Freq. Contr.
49
,
1103
1113
(
2002
).
15.
C.
Prada
,
E.
Kerbrat
,
D.
Cassereau
, and
M.
Fink
, “
Time reversal techniques in ultrasonic nondestructive testing of scattering media
,”
Inverse. Probl.
18
,
1761
1773
(
2002
).
16.
B. E.
Anderson
,
M.
Griffa
,
P.-Y. L.
Bas
,
T. J.
Ulrich
, and
P. A.
Johnson
, “
Experimental implementation of reverse time migration for nondestructive evaluation applications
,”
J. Acoust. Soc. Am
129
(
1
),
EL8
EL14
(
2011
).
17.
M. A.
Jaimes
and
R.
Snieder
, “
Spatio-temporal resolution improvement via weighted time-reversal
,”
Wave Motion
106
,
102803
(
2021
).
18.
T. J.
Ulrich
,
A. M.
Sutin
,
T.
Claytor
,
P.
Papin
,
P.-Y.
Le Bas
, and
J. A.
TenCate
, “
The time reversed elastic nonlinearity diagnostic applied to evaluation of diffusion bonds
,”
Appl. Phys. Lett.
93
(
15
),
151914
(
2008
).
19.
B. E.
Anderson
,
M.
Griffa
,
T. J.
Ulrich
,
P.-Y. L.
Bas
,
R. A.
Guyer
, and
P. A.
Johnson
, “
Crack localization and characterization in solid media using time reversal techniques
,” in
Proceedings of the 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium
, paper No. ARMA-10-154 (
2010
).
20.
P.-Y. L.
Bas
,
M. C.
Remillieux
,
L.
Pieczonka
,
J. A.
Ten Cate
,
B. E.
Anderson
, and
T. J.
Ulrich
, “
Damage imaging in a laminated composite plate using an air-coupled time reversal mirror
,”
Appl. Phys. Lett.
107
(
18
),
184102
(
2015
).
21.
B. E.
Anderson
,
L.
Pieczonka
,
M. C.
Remillieux
,
T. J.
Ulrich
, and
P.-Y.
Le Bas
, “
Stress corrosion crack depth investigation using the time reversed elastic nonlinearity diagnostic
,”
J. Acoust. Soc. Am.
141
(
1
),
EL76
EL81
(
2017
).
22.
B. E.
Anderson
,
M. C.
Remillieux
,
P.-Y. L.
Bas
, and
T. J.
Ulrich
, “
Time reversal techniques
,” in
Nonlinear Acoustic Techniques for Nondestructive Evaluation
,
1st ed.
, edited by
T.
Kundu
(
Springer and Acoustical Society of America
,
2018
), pp.
547
581
.
23.
S. M.
Young
,
B. E.
Anderson
,
S. M.
Hogg
,
P.-Y. L.
Bas
, and
M. C.
Remillieux
, “
Nonlinearity from stress corrosion cracking as a function of chloride exposure time using the time reversed elastic nonlinearity diagnostic
,”
J. Acoust. Soc. Am.
145
(
1
),
382
391
(
2019
).
24.
S. M.
Young
,
B. E.
Anderson
,
M. L.
Willardson
,
P. E.
Simpson
, and
P.-Y.
Le Bas
, “
A comparison of impulse response modification techniques for time reversal with application to crack detection
,”
J. Acoust. Soc. Am.
145
(
5
),
3195
3207
(
2019
).
25.
M. L.
Willardson
,
B. E.
Anderson
,
S. M.
Young
,
M. H.
Denison
, and
B. D.
Patchett
, “
Time reversal focusing of high amplitude sound in a reverberation chamber
,”
J. Acoust. Soc. Am.
143
(
2
),
696
705
(
2018
).
26.
C. B.
Wallace
and
B. E.
Anderson
, “
High-amplitude time reversal focusing of airborne ultrasound to generate a focused nonlinear difference frequency
,”
J. Acoust. Soc. Am.
150
(
2
),
1411
1423
(
2021
).
27.
B. D.
Patchett
and
B. E.
Anderson
, “
Nonlinear characteristics of high amplitude focusing using time reversal in a reverberation chamber
,”
J. Acoust. Soc. Am.
151
(
6
),
3603
3614
(
2022
).
28.
C.
Heaton
,
B. E.
Anderson
, and
S. M.
Young
, “
Time reversal focusing of elastic waves in plates for an educational demonstration
,”
J. Acoust. Soc. Am.
141
,
1084
1092
(
2017
).
29.
L. A.
Barnes
,
B. E.
Anderson
,
P.-Y.
Le Bas
,
A. D.
Kingsley
,
A. C.
Brown
, and
H. R.
Thomsen
, “
The physics of knocking over LEGO minifigures with time reversal focused vibrations
,”
J. Acoust. Soc. Am.
151
(
2
),
738
751
(
2022
).
30.
C.
Larmat
,
J.-P.
Montagner
,
M.
Fink
,
Y.
Capdeville
,
A.
Tourin
, and
E.
Clévédé
, “
Time-reversal imaging of seismic sources and application to the great Sumatra earthquake
,”
Geophys. Res. Lett.
33
,
L19312
, https://doi.org/10.1029/2006GL026336 (
2006
).
31.
C.
Larmat
,
J.
Tromp
,
Q.
Liu
, and
J.-P.
Montagner
, “
Time reversal location of glacial earthquakes
,”
J. Geophys. Res.
113
(
B9
),
B09314
, https://doi.org/10.1029/2008JB005607 (
2008
).
32.
C.
Larmat
,
R. A.
Guyer
, and
P. A.
Johnson
, “
Tremor source location using time-reversal: Selecting the appropriate imaging field
,”
Geophys. Res. Lett.
36
(
22
),
L22304
, https://doi.org/10.1029/2009GL040099 (
2009
).
33.
C. S.
Larmat
,
R. A.
Guyer
, and
P. A.
Johnson
, “
Time-reversal methods in geophysics
,”
Phys. Today
63
(
8
),
31
35
(
2010
).
34.
I.
Rakotoarisoa
,
J.
Fischer
,
V.
Valeau
,
D.
Marx
,
C.
Prax
, and
L.-E.
Brizzi
, “
Time-domain delay and sum beamforming for time-reversal detection of intermittent acoustic sources in flows
,”
J. Acoust. Soc. Am.
136
(
5
),
2675
2686
(
2014
).
35.
A.
Mimani
,
Z.
Prime
,
C. J.
Doolan
, and
P. R.
Medwell
, “
A sponge-layer damping technique for aeroacoustic time-reversal
,”
J. Sound Vib.
342
,
124
151
(
2015
).
36.
A.
Mimani
,
Z.
Prime
,
D. J.
Moreau
, and
C. J.
Doolan
, “
An experimental application of aeroacoustic time-reversal to the Aeolian tone
,”
J. Acoust. Soc. Am.
139
(
2
),
740
763
(
2016
).
37.
A.
Mimani
, “
A point-like enhanced resolution of experimental Aeolian tone using an iterative point-time-reversal-sponge-layer damping technique
,”
Mech. Syst. Signal. Process.
151
,
107411
(
2021
).
38.
B.
Van Damme
,
K.
Van Den Abeele
,
Y.
Li
, and
O.
Bou Matar
, “
Time reversed acoustics techniques for elastic imaging in reverberant and nonreverberant media: An experimental study of the chaotic cavity transducer concept
,”
J. Appl. Phys.
109
(
10
),
104910
(
2011
).
39.
B. E.
Anderson
,
M.
Clemens
, and
M. L.
Willardson
, “
The effect of transducer directionality on time reversal focusing
,”
J. Acoust. Soc. Am.
142
(
1
),
EL95
EL101
(
2017
).
40.
F.
Ma
,
Z.
Huang
,
C.
Liu
, and
J. H.
Wu
, “
Acoustic focusing and imaging via phononic crystal and acoustic metamaterials
,”
J. Appl. Phys.
131
,
011103
(
2022
).
41.
J.
de Rosny
and
M.
Fink
, “
Publisher's Note Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink [Phys. Rev. Lett. 89(12), 124301 (2002)]
,”
Phys. Rev. Lett.
89
(
12
),
219901
(
2002
).
42.
G.
Ma
,
X.
Fan
,
F.
Ma
,
J.
de Rosny
,
P.
Sheng
, and
M.
Fink
, “
Towards anti-casual Green's function for three-dimensional sub-diffraction focusing
,”
Nat. Phys.
14
(
6
),
608
612
(
2018
).
43.
F.
Ma
,
J.
Chen
,
J.
Wu
, and
H.
Jia
, “
Realizing broadband sub-wavelength focusing and a high intensity enhancement with a space-time synergetic modulated acoustic prison
,”
J. Mater. Chem. C
8
,
9511
9519
(
2020
).
44.
G.
Lerosey
,
J.
de Rosny
,
A.
Tourin
, and
M.
Fink
, “
Focusing beyond the diffraction limit with far-field time reversal
,”
Science
315
(
5815
),
1120
1122
(
2007
).
45.
S. G.
Conti
,
P.
Roux
, and
W. A.
Kuperman
, “
Near-field time-reversal amplification
,”
J. Acoust. Soc. Am.
121
(
6
),
3602
3606
(
2007
).
46.
F.
Lemoult
,
M.
Fink
, and
G.
Lerosey
, “
Acoustic resonators for far-field control of sound on a subwavelength scale
,”
Phys. Rev. Lett.
107
(
6
),
064301
(
2011
).
47.
A. D.
Kingsley
,
B. E.
Anderson
, and
T. J.
Ulrich
, “
Super-resolution within a one-dimensional phononic crystal of resonators using time reversal in an equivalent circuit model
,”
J. Acoust. Soc. Am.
152
(
3
),
1263
1271
(
2022
).
48.
A. D.
Kingsley
and
B. E.
Anderson
, “
Time reversal in a phononic crystal using finite-element modeling and an equivalent circuit model
,”
JASA Express Lett.
2
(
12
),
124002
(
2022
).
49.
E. D.
Golightly
,
B. E.
Anderson
,
A. D.
Kingsley
,
R.
Russell
, and
R.
Higgins
, “
Super resolution, time reversal focusing using path diverting properties of scatterers
,”
Appl. Acoust.
206
,
109308
(
2023
).
50.
M.
Tanter
,
J.
Thomas
, and
M.
Fink
, “
Time reversal and the inverse filter
,”
J. Acoust. Soc. Am.
108
(
1
),
223
234
(
2000
).
51.
K. F.
Warnick
, “
MIMO communications and inverse scattering
,” in
2009 IEEE Antennas and Propagation Society International Symposium
, North Charleston, SC (IEEE, Piscataway, NJ,
2009
), pp.
1
4
.
52.
C.
Prada
and
M.
Fink
, “
Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media
,”
Wave Motion
20
,
151
163
(
1994
).
53.
C.
Prada
and
J.-L.
Thomas
, “
Experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix
,”
J. Acoust. Soc. Am.
114
,
235
243
(
2003
).
54.
B.
Orazbayev
and
R.
Fleury
, “
Far-field subwavelength acoustic imaging by deep learning
,”
Phys. Rev. X
10
,
031029
(
2020
).
55.
A.
Maznev
,
G.
Gu
,
S-y
Sun
,
J.
Xu
,
Y.
Shen
,
N. X.
Fang
, and
S.-y.
Zhang
, “
Extraordinary focusing of sound above a soda can array without time reversal
,”
New J. Phys.
17
(
4
),
042001
(
2015
).
56.
B. D.
Patchett
,
B. E.
Anderson
, and
A. D.
Kingsley
, “
The impact of room location on time reversal focusing amplitudes
,”
J. Acoust. Soc. Am.
150
(
2
),
1424
1433
(
2021
).
57.
A. D.
Kingsley
,
J. M.
Clift
,
B. E.
Anderson
,
J. E.
Ellsworth
,
T. J.
Ulrich
, and
P.-Y. L.
Bas
, “
Development of software for performing acoustic time reversal with multiple inputs and outputs
,”
Proc. Mtgs. Acoust.
46
,
055003
(
2022
).
58.
C.
Prada
,
F.
Wu
, and
M.
Fink
, “
The iterative time reversal mirror: A solution to self-focusing in the pulse-echo mode
,”
J. Acoust. Soc. Am.
90
(
2
),
1119
1129
(
1991
).
59.
C.
Prada
,
J.-L.
Thomas
, and
M.
Fink
, “
The iterative time reversal process: Analysis of the convergence
,”
J. Acoust. Soc. Am.
97
(
1
),
62
71
(
1995
).
60.
G.
Montaldo
,
M.
Tanter
, and
M.
Fink
, “
Real time inverse filter focusing through iterative time reversal
,”
J. Acoust. Soc. Am.
115
(
2
),
768
775
(
2004
).
61.
I. E.
Psarobas
,
A.
Modinos
,
R.
Sainidou
, and
N.
Stefanou
, “
Acoustic properties of colloidal crystals
,”
Phys. Rev. B
65
,
064307
(
2002
).
62.
R. S.
Penciu
,
H.
Kriegs
,
G.
Petekidis
,
G.
Fytas
, and
E. N.
Economou
, “
Phonons in colloidal systems
,”
J. Chem. Phys.
118
(
11
),
5224
5240
(
2003
).
63.
V.
Leroy
,
A.
Strybulevych
,
M. G.
Scanlon
, and
J. H.
Page
, “
Transmission of ultrasound through a single layer of bubbles
,”
Eur. Phys. J. E
29
,
123
130
(
2009
).
64.
M. L.
Cowan
,
J. H.
Page
, and
P.
Sheng
, “
Ultrasonic wave transport in a system of disordered resonant scatterers: Propagating resonant modes and hybridization gaps
,”
Phys. Rev. B
84
,
094305
(
2011
).
65.
F.
Lemoult
,
N.
Kaina
,
M.
Fink
, and
G.
Lerosey
, “
Wave propagation control at the deep subwavelength scale in metamaterials
,”
Nat. Phys.
9
,
55
60
(
2013
).
66.
F.
Lemoult
,
N.
Kaina
,
M.
Fink
, and
G.
Lerosey
, “
Soda cans metamaterial: A subwavelength-scaled phononic crystal
,”
Crystals
6
(
7
),
82
(
2016
).
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