Transformation acoustics correlates complex material properties in physical space with distorted wave manipulations in virtual space, such that wave propagation patterns can be determined by mathematical coordinate transformations. These transformations allow for accurate modeling of acoustic propagation in complex materials. Such models are relevant for both biomedical ultrasound therapies and integrated on-chip systems, where muscle fibers and piezoelectric substrates act as effective anisotropic media, respectively. Without considering the anisotropic density of these sophisticated media, attempts to beamform acoustic patterns by phase engineering result in a heavily distorted signal. This distortion is detrimental to the performance of high intensity focused ultrasound acoustic tweezers for noninvasive surgeries, cell trapping, and cell sorting. Here, we demonstrate that the distortion effects can be corrected by transformation acoustics in which the phased array profile is adjusted to account for the corresponding anisotropy. We perform experiments to verify this transformation acoustic correction for arbitrary focused and self-bending beams with two-dimensional anisotropic spoof surface acoustic waves. The benefit of transformation acoustics in suppressing undesired anisotropic effects on beamformed waves improves the precision and efficacy of medical treatments that facilitate noninvasive ultrasound therapies and integrated on-chip applications.

1.
R. V.
Craster
and
S.
Guenneau
,
Acoustic Metamaterials: Negative Refraction, Imaging, Lensing, and Cloaking
(
Springer
,
Dordrecht
,
2013
), Chap. 8.
2.
H.
Chen
and
C. T.
Chan
, “
Acoustic cloaking and transformational acoustics
,”
J. Phys. D
43
,
113001
(
2010
).
3.
F.
Zhong
,
J.
Li
,
H.
Liu
, and
S.
Zhu
, “
Controlling surface plasmons through covariant transformation of the spin-dependent geometric phase between curved metamaterials
,”
Phys. Rev. Lett.
120
,
243901
(
2018
).
4.
J.
Li
and
J. B.
Pendry
, “
Hiding under the carpet: A new strategy for cloaking
,”
Phys. Rev. Lett.
101
,
203901
(
2008
).
5.
B.
Popa
,
L.
Zigoneanu
, and
S. A.
Cummer
, “
Experimental acoustics ground cloak in air
,”
Phys. Rev. Lett.
106
,
253901
(
2011
).
6.
L. Y.
Zheng
,
Y.
Wu
,
X.
Ni
,
Z. G.
Chen
,
M. H.
Lu
, and
Y. F.
Chen
, “
Acoustic cloaking by a near-zero-index phononic crystal
,”
Appl. Phys. Lett.
104
,
161904
(
2014
).
7.
M.
Dubois
,
C.
Shi
,
Y.
Wang
, and
X.
Zhang
, “
A thin and conformal metasurface for illusion acoustics of rapidly changing profiles
,”
Appl. Phys. Lett.
110
,
151902
(
2017
).
8.
J. B.
Pendry
,
D.
Schurig
, and
D. R.
Smith
, “
Controlling electromagnetic fields
,”
Science
312
,
1780
(
2006
).
9.
U.
Leonhardt
, “
Optical conformal mapping
,”
Science
312
,
1777
(
2006
).
10.
D.
Schurig
,
J. B.
Pendry
, and
D. R.
Smith
, “
Calculation of material properties and ray tracing in transformational media
,”
Opt. Express
14
,
9794
(
2006
).
11.
S. A.
Cummer
and
D.
Schurig
, “
One path to acoustic cloaking
,”
New J. Phys.
9
,
45
(
2007
).
12.
H.
Chen
and
C. T.
Chan
, “
Acoustic cloaking in three dimensions using acoustic metamaterials
,”
Appl. Phys. Lett.
91
,
183518
(
2007
).
13.
A.
Climente
,
D.
Torrent
, and
J.
Sanchez-Dehesa
, “
Sound focusing by gradient index sonic lenses
,”
Appl. Phys. Lett.
97
,
104103
(
2010
).
14.
B.
Popa
and
S. A.
Cummer
, “
Design and characteristics of broadband acoustic composite metamaterials
,”
Phys. Rev. B
80
,
174303
(
2009
).
15.
L.
Zigoneanu
,
B.
Popa
, and
S. A.
Cummer
, “
Design and measurements of a broadband two-dimensional acoustic lens
,”
Phys. Rev. B
84
,
024305
(
2011
).
16.
J. E.
Kennedy
,
F.
Wu
,
G. R.
Ter Haar
,
F. V.
Gleeson
,
R. R.
Phillips
,
M. R.
Middleton
, and
D.
Cranston
, “
High-intensity focused ultrasound for the treatment of liver tumours
,”
Ultrasonics
42
,
931
935
(
2004
).
17.
F.
Wu
,
Z. B.
Wang
,
W. Z.
Chen
,
J. Z.
Zou
,
J.
Bai
,
H.
Zhu
,
K. Q.
Li
,
F. L.
Xie
,
C. B.
Jin
,
H. B.
Su
 et al., “
Extracorporeal focused ultrasound surgery for treatment of human solid carcinomas: Early Chinese clinical experience
,”
Ultrasound Med. Biol.
30
,
245
260
(
2004
).
18.
F.
Wu
,
Z. B.
Wang
,
W. Z.
Chen
,
J.
Bai
,
H.
Zhu
, and
T. Y.
Qiao
, “
Preliminary experience using high intensity focused ultrasound for the treatment of patients with advanced stage renal malignancy
,”
J. Urol.
170
,
2237
2240
(
2003
).
19.
J.
Ninet
,
X.
Roques
,
R.
Seitelberger
,
C.
Deville
,
J. L.
Pomar
,
J.
Robin
,
O.
Jegaden
,
F.
Wellens
,
E.
Wolner
,
C.
Vedrinne
 et al., “
Surgical ablation of atrial fibrillation with off-pump, epicardial, high-intensity focused ultrasound: Results of a multicenter trial
,”
J. Thorac. Cardiovasc. Surg.
130
,
803-e1
(
2005
).
20.
J. E.
Kennedy
, “
High-intensity focused ultrasound in the treatment of solid tumours
,”
Nat. Rev. Cancer
5
,
321
(
2005
).
21.
J. E.
Kennedy
,
G. R.
Ter Haar
, and
D.
Cranston
, “
High intensity focused ultrasound: Surgery of the future?
,”
Br. J. Radiol.
76
,
590
599
(
2003
).
22.
O. A.
Sapozhnikov
,
A. D.
Maxwell
,
B.
MacConaghy
, and
M. R.
Bailey
, “
A mechanistic analysis of stone fracture in lithotripsy
,”
J. Acoust. Soc. Am.
121
,
1190
1202
(
2007
).
23.
Y.
Takakuwa
,
M.
Sarai
,
H.
Kawai
,
A.
Yamada
,
K.
Shiino
,
K.
Takada
,
Y.
Nagahara
,
M.
Miyagi
,
S.
Motoyama
,
H.
Toyama
 et al., “
Extracorporeal shock wave therapy for coronary artery disease: Relationship of symptom amelioration and ischemia improvement
,”
Asia Ocean. J. Nucl. Med. Biol.
6
,
1
(
2018
).
24.
T.
Nishida
,
H.
Shimokawa
,
K.
Oi
,
H.
Tatewaki
,
T.
Uwatoku
,
K.
Abe
,
Y.
Matsumoto
,
N.
Kajihara
,
M.
Eto
,
T.
Matsuda
 et al., “
Extracorporeal cardiac shock wave therapy markedly ameliorates ischemia-induced myocardial dysfunction in pigs in vivo
,”
Circulation
110
,
3055
3061
(
2004
).
25.
B. C.
Tran
,
J.
Seo
,
T. L.
Hall
,
J. B.
Fowlkes
, and
C. A.
Cain
, “
Microbubble-enhanced cavitation for noninvasive ultrasound surgery
,”
IEEE. Trans. Ultrason. Ferroelectr., Freq. Control
50
,
10
(
2003
).
26.
K.
Hynynen
,
W. R.
Freund
,
H. E.
Cline
,
A. H.
Chung
,
R. D.
Watkins
,
J. P.
Vetro
, and
F. A.
Jolesz
, “
A clinical, noninvasive, MR imaging-monitored ultrasound surgery method
,”
RadioGraphics
16
(
1
),
185
(
1996
).
27.
S.
Wang
,
J.
Lin
,
T.
Wang
,
X.
Chen
, and
P.
Huang
, “
Recent advances in photoacoustic imaging for deep-tissue biomedical applications
,”
Theranostics
6
,
2394
(
2016
).
28.
C.
Errico
,
J.
Pierre
,
S.
Pezet
,
Y.
Desailly
,
Z.
Lenkei
,
O.
Couture
, and
M.
Tanter
, “
Ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging
,”
Nat. Lett.
527
,
499
(
2015
).
29.
M.
Tanter
and
M.
Fink
, “
Ultrafast imaging in biomedical ultrasound
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
61
,
1
(
2014
).
30.
S.
Jiménez-Gambín
,
N.
Jiménez
,
J. M.
Benlloch
, and
F.
Camarena
, “
Holograms to focus arbitrary ultrasonic fields through the skull
,”
Phys. Rev. Appl.
12
,
014016
(
2019
).
31.
D. J.
Collins
,
A.
Neild
, and
Y.
Ai
, “
Highly focused high-frequency travelling surface acoustic waves (SAW) for rapid single-particle sorting
,”
Lab Chip
16
,
471
479
(
2016
).
32.
A.
Riaud
,
J. L.
Thomas
,
M.
Baudoin
, and
O. B.
Matar
, “
Taming the degeneration of Bessel beams at an anisotropic-isotropic interface: Toward three-dimensional control of confined vortical waves
,”
Phys. Rev. E
92
,
063201
(
2015
).
33.
T.
Liu
,
F.
Chen
,
S.
Liang
,
H.
Gao
, and
J.
Zhu
, “
Subwavelength sound focusing and imaging via gradient metasurface-enabled spoof surface acoustic wave modulation
,”
Phys. Rev. Appl.
11
,
034061
(
2019
).
34.
H.
Jia
,
M.
Lu
,
X.
Ni
,
M.
Bao
, and
X.
Li
, “
Spatial separation of spoof surface acoustic waves on the graded groove grating
,”
J. Appl. Phys.
116
,
124504
(
2014
).
35.
J.
Zhu
,
Y.
Chen
,
X.
Zhu
,
F. J.
Garcia-Vidal
,
X.
Yin
,
W.
Zhang
, and
X.
Zhang
, “
Acoustic rainbow trapping
,”
Sci. Rep.
3
,
1728
(
2013
).
36.
E.
Greenfield
,
M.
Segev
,
W.
Walasik
, and
O.
Raz
, “
Accelerating light beams along arbitrary convex trajectories
,”
Phys. Rev. Lett.
106
,
213902
(
2011
).
37.
D. C.
Chen
,
X. F.
Zhu
,
Q.
Wei
,
D. J.
Wu
, and
X. J.
Liu
, “
Dynamic generation and modulation of acoustic bottle-beams by metasurfaces
,”
Sci. Rep.
8
,
12682
(
2018
).
38.
S.
Zhao
,
Y.
Hu
,
J.
Lu
,
X.
Qiu
,
J.
Cheng
, and
I.
Burnett
, “
Delivering sound energy along an arbitrary convex trajectory
,”
Sci. Rep.
4
,
6628
(
2015
).
39.
J.
Lan
,
X.
Zhang
,
X.
Liu
, and
Y.
Li
, “
Wavefront manipulation based on transmissive acoustic metasurface with membrane-type hybrid structure
,”
Sci. Rep.
8
,
14171
(
2018
).
40.
Y.
Li
,
X.
Jiang
,
R. Q.
Li
,
B.
Liang
,
X. Y.
Zou
,
L. L.
Yin
, and
J. C.
Cheng
, “
Experimental realization of full control of reflected waves with subwavelength acoustic metasurfaces
,”
Phys. Rev. Appl.
2
,
064002
(
2014
).

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