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Chin. Phys. B, 2022, Vol. 31(12): 124301    DOI: 10.1088/1674-1056/ac90b3

One-dimensional $\mathcal{PT}$-symmetric acoustic heterostructure

Hai-Xiao Zhang(张海啸)1,2, Wei Xiong(熊威)1, Ying Cheng(程营)1,3,†, and Xiao-Jun Liu(刘晓峻)1,3,‡
1 Department of Physics, MOE Key Laboratory of Modern Acoustics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China;
2 School of Electrical and Information Engineering, Changzhou Institute of Technology, Changzhou 213032, China;
3 State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
Abstract  The explorations of parity-time ($\mathcal{PT}$)-symmetric acoustics have resided at the frontier in physics, and the pre-existing accessing of exceptional points typically depends on Fabry-Perot resonances of the coupling interlayer sandwiched between balanced gain and loss components. Nevertheless, the concise $\mathcal{PT}$-symmetric acoustic heterostructure, eliminating extra interactions caused by the interlayer, has not been researched in depth. Here we derive the generalized unitary relation for one-dimensional (1D) $\mathcal{PT}$-symmetric heterostructure of arbitrary complexity, and demonstrate four disparate patterns of anisotropic transmission resonances (ATRs) accompanied by corresponding spontaneous phase transitions. As a special case of ATR, the occasional bidirectional transmission resonance reconsolidates the ATR frequencies that split when waves incident from opposite directions, whose spatial profiles distinguish from a unitary structure. The derived theoretical relation can serve as a predominant signature for the presence of $\mathcal{PT}$ symmetry and $\mathcal{PT}$-symmetry-breaking transition, which may provide substantial support for the development of prototype devices with asymmetric acoustic responses.
Keywords:  acoustic $\mathcal{PT}$-symmetric heterostructure      anisotropic transmission resonance      occasional bidirectional transmission resonance  
Received:  05 August 2022      Revised:  08 September 2022      Accepted manuscript online:  09 September 2022
PACS:  43.20.+g (General linear acoustics)  
  43.35.+d (Ultrasonics, quantum acoustics, and physical effects of sound)  
  43.20.El (Reflection, refraction, diffraction of acoustic waves)  
  43.20.Fn (Scattering of acoustic waves)  
Fund: Project supported by the National Basic Research Program of China (Grant No. 2017YFA0303702) and the National Natural Science Foundation of China (Grant Nos. 12225408, 12074183, 11922407, 11904035, 11834008, and 11874215).
Corresponding Authors:  Ying Cheng, Xiao-Jun Liu     E-mail:;

Cite this article: 

Hai-Xiao Zhang(张海啸), Wei Xiong(熊威), Ying Cheng(程营), and Xiao-Jun Liu(刘晓峻) One-dimensional $\mathcal{PT}$-symmetric acoustic heterostructure 2022 Chin. Phys. B 31 124301

[1] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[2] Bender C M, Boettcher S and Meisinger P N 1999 J. Math. Phys. 40 2201
[3] Bender C M, Brody D C and Jones H F 2002 Phys. Rev. Lett. 89 270401
[4] Mostafazadeh A 2009 Phys. Rev. Lett. 102 220402
[5] Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192
[6] Longhi S 2010 Phys. Rev. A 82 031801
[7] Chong Y, Ge L and Stone A D 2011 Phys. Rev. Lett. 106 093902
[8] Lin Z, Ramezani H, Eichelkraut T, Kottos T, Cao H and Christodoulides D N 2011 Phys. Rev. Lett. 106 213901
[9] Ge L, Chong Y and Stone A D 2012 Phys. Rev. A 85 023802
[10] Feng L, Xu Y, Fegadolli W S, Lu M, Oliveira J E, Almeida Y R, Chen Y and Scherer A 2013 Nat. Mater. 12 108
[11] Fleury R, Sounas D L and Alú A 2014 Phys. Rev. Lett. 113 023903
[12] Wong Z J, Xu Y, Kim J, O'Brien K, Wang Y, Feng L and Zhang X 2016 Nat. Photon. 10 796
[13] Zhu X, Ramezani H, Shi C, Zhu J and Zhang X 2014 Phys. Rev. X 4 031042
[14] Fleury R, Sounas D L and Alú A 2015 Nat. Commun. 6 5905
[15] Fleury R, Sounas D L and Alú A 2016 IEEE J. Sel. Top. Quant. 22 121
[16] Shi C, Dubois M, Chen Y, Cheng L, Ramezani H, Wang Y and Zhang X 2016 Nat. Commun. 7 11110
[17] Aurégan Y and Pagneux V 2017 Phys. Rev. Lett. 118 174301
[18] Achilleos V, Aurégan Y and Pagneux V 2017 Phys. Rev. Lett. 119 243904
[19] Hou Z and Assouar B 2018 J. Appl. Phys. 123 085101
[20] Christensen J, Willatzen M, Velasco V and Lu M 2016 Phys. Rev. Lett. 116 207601
[21] Ji W, Wei Q, Zhu X, Wu D and Liu X 2019 Europhys. Lett. 125 58002
[22] Zhang H, Liu X, Bao Y, Zhang Y and Zhao J 2022 Symmetry 14 965
[23] Zhang H, Zhang Y, Liu X, Bao Y and Zhao J 2022 AIP Adv. 12 065217
[24] Schindler J, Li A, Zheng M C, Ellis F M and Kottos T 2011 Phys. Rev. A 84 040101
[25] Zhou J, Zhang B, Xiao W, Qiu D and Chen Y 2018 IEEE T. Ind. Electron. 66 4097
[26] Xiao Z, Rádi Y, Tretyakov S and Alú A 2019 Research 2019 7108494
[27] Li Y, Peng Y, Han L, Miri M A, Li W, Xiao M, Zhu X, Zhao J, Alú A, Fan S and Qiu C 2019 Science 364 170
[28] El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S and Christodoulides D N 2018 Nat. Phys. 14 11
[29] Özdemir Ş K, Rotter S, Nori F and Yang L 2019 Nat. Mater. 18 783
[30] Klauck F, Teuber L, Ornigotti M, Heinrich M, Scheel S and Szameit A 2019 Nat. Photon. 13 883
[31] Miri M A and Alú A 2019 Science 363 eaar7709
[32] Shen C, Li J, Peng X and Cummer S A 2018 Phys. Rev. Mater. 2 125203
[33] Liu T, Zhu X, Chen F, Liang S and Zhu J 2018 Phys. Rev. Lett. 120 124502
[34] Xiao L, Chen Z, Feng C, Liu L, Bai Z, Wang Y, Qian L, Zhang Y, Li Q, Jiang K and Fan S 2008 Nano Lett. 8 4539
[35] Suzuki K, Sakakibara S, Okada M, Neo Y, Mimura H, Inoue Y and Murata T 2011 Jpn. J. Appl. Phys. 50 01BJ10
[36] Suk J W, Kirk K, Hao Y, Hall N A and Ruoff R S 2012 Adv. Mater. 24 6342
[37] BarnardA R, Jenkins D M, Brungart T A, McDevitt T M and Kline B L 2013 J. Acoust. Soc. Am. 134 EL276
[38] Hu B, Zhang Z, Zhang H, Zheng L, Xiong W, Yue Z, Wang X, Xu J, Cheng Y, Liu X and Christensen J 2021 Nature 597 655
[39] Tian Y, Tian H, Wu Y, Zhu L, Tao L, Zhang W, Shu Y, Xie D, Yang Y, Wei Z, Lu X, Ren T, Shih C and Zhao J 2015 Sci. Rep. 5 10582
[40] Giorgianni F, Vicario C, Shalaby M, Tenuzzo L D, Marcelli A, Zhang T, Zhao K, Chen Y, Hauri C and Lupi S 2018 Adv. Funct. Mater. 28 1702652
[41] Pozar D M 2011 Microwave engineering, 4th edn. (John Wiley & sons) p. 190
[42] Jin L 2018 Phys. Rev. A 98 022117
[43] Longhi S 2011 J. Phys. A: Math. Theor. 44 485302
[44] Wu H, Yang X, Deng D and Liu H 2019 Phys. Rev. A 100 033832
[45] Hou Z, Ni H and Assouar B 2018 Phys. Rev. Appl. 10 044071
[46] Wu Q, Chen Y and Huang G 2019 J. Acoust. Soc. Am. 146 850
[47] Farhat M, Chen P, Guenneau S and Wu Y 2021 Phys. Rev. B 103 134101
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