In this work, we propose a simple scheme to realize an acoustic coherent perfect absorber (CPA) and laser modes by embedding a non-Hermitian dopant in a zero index metamaterial. When the dopant is filled with a loss medium at a specific level, the sample can absorb the incident waves completely. On the other hand, when the dopant is filled with a gain medium, the sample can act as a laser oscillator to boost the incident waves. The theoretical derivation based on the scattering matrix and the numerical simulation based on the finite element method are performed and both show good agreement with each other. We also discover that the CPA and laser modes are very sensitive and can be controlled by adjusting the structure parameters or the relative phase of the incident waves. Moreover, the case that asymmetric incidences have different beam widths is considered. We envision that our work may have potential applications in designing acoustic devices, such as absorbers, transducers, and receivers.
REFERENCES
1.
Y.
Li
, S.
Kita
, P.
Muñoz
, O.
Reshef
, D. I.
Vulis
, M.
Yin
, M.
Lončar
, and E.
Mazur
, “On-chip zero-index metamaterials
,” Nat. Photonics
9
, 738
–742
(2015
). 2.
P.
Moitra
, Y.
Yang
, Z.
Anderson
, I. I.
Kravchenko
, D. P.
Briggs
, and J.
Valentine
, “Realization of an all-dielectric zero-index optical metamaterial
,” Nat. Photonics
7
, 791
–795
(2013
). 3.
X.
Huang
, Y.
Lai
, Z. H.
Hang
, H.
Zheng
, and C. T.
Chan
, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials
,” Nat. Mater.
10
, 582
–586
(2011
). 4.
Y.
Li
, B.
Liang
, Z.-M.
Gu
, X.-Y.
Zou
, and J.-C.
Cheng
, “Unidirectional acoustic transmission through a prism with near-zero refractive index
,” Appl. Phys. Lett.
103
, 053505
(2013
). 5.
Z.-M.
Gu
, B.
Liang
, X.-Y.
Zou
, J.
Yang
, Y.
Li
, J.
Yang
, and J.-C.
Cheng
, “One-way acoustic mirror based on anisotropic zero-index media
,” Appl. Phys. Lett.
107
, 213503
(2015
). 6.
Y.
Gu
, Y.
Cheng
, J.
Wang
, and X.
Liu
, “Controlling sound transmission with density-near-zero acoustic membrane network
,” J. Appl. Phys.
118
, 024505
(2015
). 7.
C.
Xu
, G.
Ma
, Z. G.
Chen
, J.
Luo
, J.
Shi
, Y.
Lai
, and Y.
Wu
, “Three-dimensional acoustic double-zero-index medium with a fourfold degenerate Dirac-like point
,” Phys. Rev. Lett.
124
, 074501
(2020
). 8.
F.
Liu
and Z.
Liu
, “Elastic waves scattering without conversion in metamaterials with simultaneous zero indices for longitudinal and transverse waves
,” Phys. Rev. Lett.
115
, 175502
(2015
). 9.
Z.
Wang
, W.
Wei
, N.
Hu
, R.
Min
, L.
Pei
, Y.
Chen
, F.
Liu
, and Z.
Liu
, “Manipulation of elastic waves by zero index metamaterials
,” J. Appl. Phys.
116
, 204501
(2014
). 10.
R.
Fleury
and A.
Alù
, “Extraordinary sound transmission through density-near-zero ultranarrow channels
,” Phys. Rev. Lett.
111
, 055501
(2013
). 11.
Y.
Fu
, L.
Xu
, Z.
Hong Hang
, and H.
Chen
, “Unidirectional transmission using array of zero-refractive-index metamaterials
,” Appl. Phys. Lett.
104
, 193509
(2014
). 12.
C.
Shen
, Y.
Xie
, J.
Li
, S. A.
Cummer
, and Y.
Jing
, “Asymmetric acoustic transmission through near-zero-index and gradient-index metasurfaces
,” Appl. Phys. Lett.
108
, 223502
(2016
). 13.
X.-F.
Zhu
, “Effective zero index in locally resonant acoustic material
,” Phys. Lett. A
377
, 1784
–1787
(2013
). 14.
I.
Liberal
, A. M.
Mahmoud
, Y.
Li
, B.
Edwards
, and N.
Engheta
, “Photonic doping of epsilon-near-zero media
,” Science
355
, 1058
–1062
(2017
). 15.
I.
Liberal
, Y.
Li
, and N.
Engheta
, “Reconfigurable epsilon-near-zero metasurfaces via photonic doping
,” Nanophotonics
7
, 1117
–1127
(2018
). 16.
M.
Coppolaro
, M.
Moccia
, G.
Castaldi
, N.
Engheta
, and V.
Galdi
, “Non-Hermitian doping of epsilon-near-zero media
,” Proc. Natl. Acad. Sci. U.S.A.
117
(25
), 13921
–13928
(2020
). 17.
W.
Wan
, Y.
Chong
, L.
Ge
, H.
Noh
, A. D.
Stone
, and H.
Cao
, “Time-reversed lasing and interferometric control of absorption
,” Science
331
, 889
–892
(2011
). 18.
C.
Meng
, X.
Zhang
, S. T.
Tang
, M.
Yang
, and Z.
Yang
, “Acoustic coherent perfect absorbers as sensitive null detectors
,” Sci. Rep.
7
, 43574
(2017
). 19.
Y.
Sun
, W.
Tan
, H. Q.
Li
, J.
Li
, and H.
Chen
, “Experimental demonstration of a coherent perfect absorber with PT phase transition
,” Phys. Rev. Lett.
112
, 143903
(2014
). 20.
Y. D.
Chong
, L.
Ge
, and A. D.
Stone
, “PT-symmetry breaking and laser-absorber modes in optical scattering systems
,” Phys. Rev. Lett.
106
, 093902
(2011
). 21.
Y. D.
Chong
, L.
Ge
, H.
Cao
, and A. D.
Stone
, “Coherent perfect absorbers: Time-reversed lasers
,” Phys. Rev. Lett.
105
, 053901
(2010
). 22.
D. G.
Baranov
, A.
Krasnok
, T.
Shegai
, A.
Alù
, and Y.
Chong
, “Coherent perfect absorbers: Linear control of light with light
,” Nat. Rev. Mater.
2
, 17064
(2017
). 23.
P.
Wei
, C.
Croënne
, S.
Tak Chu
, and J.
Li
, “Symmetrical and anti-symmetrical coherent perfect absorption for acoustic waves
,” Appl. Phys. Lett.
104
, 121902
(2014
). 24.
J. Z.
Song
, P.
Bai
, Z. H.
Hang
, and Y.
Lai
, “Acoustic coherent perfect absorbers
,” New J. Phys.
16
, 033026
(2014
). 25.
B.
Baum
, H.
Alaeian
, and J.
Dionne
, “A parity-time symmetric coherent plasmonic absorber-amplifier
,” J. Appl. Phys.
117
, 063106
(2015
). 26.
J.
Luo
, B.
Liu
, Z. H.
Hang
, and Y.
Lai
, “Coherent perfect absorption via photonic doping of zero-index media
,” Laser Photonics Rev.
12
(8
), 1800001
(2018
). 27.
P.
Bai
, K.
Ding
, G.
Wang
, J.
Luo
, Z.-Q.
Zhang
, C. T.
Chan
, Y.
Wu
, and Y.
Lai
, “Simultaneous realization of a coherent perfect absorber and laser by zero-index media with both gain and loss
,” Phys. Rev. A
94
, 063841
(2016
). 28.
M.
Dubois
, C.
Shi
, X.
Zhu
, Y.
Wang
, and X.
Zhang
, “Observation of acoustic Dirac-like cone and double zero refractive index
,” Nat. Commun.
8
, 14871
(2017
). 29.
Z.
Gu
, H.
Gao
, T.
Liu
, Y.
Li
, and J.
Zhu
, “Dopant-modulated sound transmission with zero index acoustic metamaterials
,” J. Acoust. Soc. Am.
148
, 1636
(2020
). 30.
M.
Malléjac
, A.
Merkel
, V.
Tournat
, J. P.
Groby
, and V.
Romero-García
, “Doping of a plate-type acoustic metamaterial
,” Phys. Rev. B
102
, 060302(R)
, (2020
). 31.
H.
Gao
, H.
Xue
, Q.
Wang
, Z.
Gu
, T.
Liu
, J.
Zhu
, and B.
Zhang
, “Observation of topological edge states induced solely by non-hermiticity in an acoustic crystal
,” Phys. Rev. B
101
, 180303(R)
, (2020
). 32.
T.
Liu
, G.
Ma
, S.
Liang
, H.
Gao
, Z.
Gu
, S.
An
, and J.
Zhu
, “Single-sided acoustic beam splitting based on parity-time symmetry
,” Phys. Rev. B
102
, 014306
(2020
). 33.
C.
Cho
, X.
Wen
, N.
Park
, and J.
Li
, “Digitally virtualized atoms for acoustic metamaterials
,” Nat. Commun.
11
, 251
(2020
). 34.
M.
Willatzen
, P.
Gao
, J.
Christensen
, and Z. L.
Wang
, “Acoustic gain in solids due to piezoelectricity, flexoelectricity, and electrostriction
,” Adv. Funct. Mater.
30
, 2003503
(2020
). 35.
V. C.
Nguyen
, L.
Chen
, and K.
Halterman
, “Total transmission and total reflection by zero index metamaterials with defects
,” Phys. Rev. Lett.
105
, 233908
(2010
). © 2021 Author(s). Published under an exclusive license by AIP Publishing.
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