Non-Hermitian scattering systems respecting parity-time symmetry exhibit unidirectional invisibility or reflectionlessness at an exceptional point of the scattering matrix. In this study, we investigate the scattering properties of a one-dimensional acoustic parity-time-symmetric multilayered medium. Parity-time symmetry is defined by a spatial small-amplitude square-wave modulation of the medium parameters in the complex plane. Such a multilayered medium has been demonstrated to reach an exceptional point and support unidirectional invisibility for balanced real and imaginary part modulations of the refractive index. Through the analysis of interference within the medium, we show that the complex modulation of acoustic impedance instead of the refractive index governs the exceptional point of the scattering matrix and determines the occurrence of the unidirectional invisibility. This unidirectional invisibility is further investigated for more general cases of complex parameter distribution including unequal modulation amplitudes and rectangular wave modulation. Our study provides an intuitive physical picture of the occurrence of unidirectional invisibility induced by an exceptional point in acoustic wave systems. Moreover, this study could facilitate the design and practical realization of acoustic parity-time-symmetric structures.

1.
C. M.
Bender
and
S.
Boettcher
,
Phys. Rev. Lett.
80
(
24
),
5243
5246
(
1998
).
2.
S. K.
Ozdemir
,
S.
Rotter
,
F.
Nori
, and
L.
Yang
,
Nat. Mater.
18
(
8
),
783
798
(
2019
).
3.
M.-A.
Miri
and
A.
Alù
,
Science
363
(
6422
),
eaar7709
(
2019
).
4.
L.
Feng
,
R.
El-Ganainy
, and
L.
Ge
,
Nat. Photonics
11
(
12
),
752
762
(
2017
).
5.
S. K.
Gupta
,
Y.
Zou
,
X. Y.
Zhu
,
M. H.
Lu
,
L. J.
Zhang
,
X. P.
Liu
, and
Y. F.
Chen
,
Adv. Mater.
32
(
27
),
e1903639
(
2020
).
6.
R.
El-Ganainy
,
K. G.
Makris
,
M.
Khajavikhan
,
Z. H.
Musslimani
,
S.
Rotter
, and
D. N.
Christodoulides
,
Nat. Phys.
14
(
1
),
11
19
(
2018
).
7.
H.
Zhao
and
L.
Feng
,
Natl. Sci. Rev.
5
(
2
),
183
199
(
2018
).
8.
S.
Longhi
,
J. Phys. A: Math. Theor.
44
(
48
),
485302
(
2011
).
9.
Z.
Lin
,
H.
Ramezani
,
T.
Eichelkraut
,
T.
Kottos
,
H.
Cao
, and
D. N.
Christodoulides
,
Phys. Rev. Lett.
106
(
21
),
213901
(
2011
).
10.
L.
Feng
,
Y. L.
Xu
,
W. S.
Fegadolli
,
M. H.
Lu
,
J. E.
Oliveira
,
V. R.
Almeida
,
Y. F.
Chen
, and
A.
Scherer
,
Nat. Mater.
12
(
2
),
108
113
(
2013
).
11.
X.
Zhu
,
H.
Ramezani
,
C.
Shi
,
J.
Zhu
, and
X.
Zhang
,
Phys. Rev. X
4
(
3
),
031042
(
2014
).
12.
L.
Ge
,
Y. D.
Chong
, and
A. D.
Stone
,
Phys. Rev. A
85
(
2
),
023802
(
2012
).
13.
R.
Fleury
,
D.
Sounas
, and
A.
Alù
,
Nat. Commun.
6
(
1
),
5905
(
2015
).
14.
E.
Rivet
,
A.
Brandstötter
,
K. G.
Makris
,
H.
Lissek
,
S.
Rotter
, and
R.
Fleury
,
Nat. Phys.
14
(
9
),
942
947
(
2018
).
15.
Y.
Auregan
and
V.
Pagneux
,
Phys. Rev. Lett.
118
(
17
),
174301
(
2017
).
16.
W.
Zhu
,
X.
Fang
,
D.
Li
,
Y.
Sun
,
Y.
Li
,
Y.
Jing
, and
H.
Chen
,
Phys. Rev. Lett.
121
(
12
),
124501
(
2018
).
17.
A.
Merkel
,
V.
Romero-García
,
J.-P.
Groby
,
J.
Li
, and
J.
Christensen
,
Phys. Rev. B
98
(
20
),
201102
(
2018
).
18.
C.
Shen
,
J.
Li
,
X.
Peng
, and
S. A.
Cummer
,
Phys. Rev. Mater.
2
(
12
),
125203
(
2018
).
19.
V.
Domínguez-Rocha
,
R.
Thevamaran
,
F. M.
Ellis
, and
T.
Kottos
,
Phys. Rev. Appl.
13
(
1
),
014060
(
2020
).
20.
T.
Liu
,
X.
Zhu
,
F.
Chen
,
S.
Liang
, and
J.
Zhu
,
Phys. Rev. Lett.
120
(
12
),
124502
(
2018
).
21.
Y.
Yang
,
H.
Jia
,
Y.
Bi
,
H.
Zhao
, and
J.
Yang
,
Phys. Rev. Appl.
12
(
3
),
034040
(
2019
).
22.
H.-Z.
Chen
,
T.
Liu
,
H.-Y.
Luan
,
R.-J.
Liu
,
X.-Y.
Wang
,
X.-F.
Zhu
,
Y.-B.
Li
,
Z.-M.
Gu
,
S.-J.
Liang
,
H.
Gao
,
L.
Lu
,
L.
Ge
,
S.
Zhang
,
J.
Zhu
, and
R.-M.
Ma
,
Nat. Phys.
16
(
5
),
571
578
(
2020
).
23.
Y.
Yang
,
H.
Jia
,
S.
Wang
,
P.
Zhang
, and
J.
Yang
,
Appl. Phys. Lett.
116
(
21
),
213501
(
2020
).
24.
Y.
Yang
,
H.
Jia
, and
J.
Yang
,
J. Acoust. Soc. Am.
148
(
1
),
33
43
(
2020
).
25.
T.
Liu
,
G.
Ma
,
S.
Liang
,
H.
Gao
,
Z.
Gu
,
S.
An
, and
J.
Zhu
,
Phys. Rev. B
102
(
1
),
014306
(
2020
).
26.
C.
Shi
,
M.
Dubois
,
Y.
Chen
,
L.
Cheng
,
H.
Ramezani
,
Y.
Wang
, and
X.
Zhang
,
Nat. Commun.
7
(
1
),
11110
(
2016
).
27.
J.
Lan
,
L.
Wang
,
X.
Zhang
,
M.
Lu
, and
X.
Liu
,
Phys. Rev. Appl.
13
(
3
),
034047
(
2020
).
28.
B. J.
Tester
,
J. Sound Vib.
27
(
4
),
477
513
(
1973
).
29.
A. H.
Nayfeh
,
J. E.
Kaiser
, and
D. P.
Telionis
,
AIAA J.
13
(
2
),
130
153
(
1975
).
30.
C.
Cho
,
X.
Wen
,
N.
Park
, and
J.
Li
,
Nat. Commun.
11
(
1
),
251
(
2020
).
31.
B. H.
Song
and
J. S.
Bolton
,
J. Acoust. Soc. Am.
107
(
3
),
1131
1152
(
2000
).
You do not currently have access to this content.