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2022-10-29
Exceptional Ring by Non-Hermitian Sonic Crystals
By
Progress In Electromagnetics Research, Vol. 176, 1-10, 2023
Abstract
Exceptional point (EP) and exceptional ring (ER) are unique features for non-Hermitian systems, which have recently attracted great attentions in acoustics due to their rich physical significances and various potential applications. Despite the rapid development about the study of the EP and ER in one-dimensional acoustic systems, the realization of them in two-dimensional (2D) non-Hermitian structures is still facing a great challenge. To overcome this, we numerically and theoretically realize an ER in 2D reciprocal space based on a square-lattice non-Hermitian sonic crystal (SC). By introducing radiation loss caused by circular holes of each resonator in a Hermitian SC, we realize the conversion between a Dirac cone and the ER. Based on the theoretical analysis with the effective Hamiltonian, we obtain that the formation of the ER is closely related to different radiation losses of dipole and quadrupole modes in the resonators. Additionally, in the non-Hermitian SC, two eigenfunctions can be merged into a single self-orthogonal one on the ER, which does not exist in the Hermitian SC. Finally, by verifying the existence of the EP in every direction of 2D reciprocal space, we further demonstrate the ER in the proposed non-Hermitian SC. Our work may provide theoretical schemes and concrete methods for designing various types of non-Hermitian acoustic devices.
Citation
Bing-Bing Wang Yong Ge Shou-Qi Yuan Ding Jia Hong-Xiang Sun , "Exceptional Ring by Non-Hermitian Sonic Crystals," Progress In Electromagnetics Research, Vol. 176, 1-10, 2023.
doi:10.2528/PIER22090301
http://www.jpier.org/PIER/pier.php?paper=22090301
References

1. Bender, C. M. and S. Boettcher, "Real spectra in non-Hermitian Hamiltonians having PT symmetry," Phys. Rev. Lett., Vol. 80, No. 24, 5243, 1998.
doi:10.1103/PhysRevLett.80.5243

2. El-Ganainy, C. M., K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, "Non-Hermitian physics and PT symmetry," Nat. Phys., Vol. 14, No. 1, 11-19, 2018.
doi:10.1038/nphys4323

3. Gong, Z. P., Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, "Topological phases of non-Hermitian systems," Phys. Rev. X, Vol. 8, No. 3, 031079, 2018.

4. Bergholtz, E. J., J. C. Budich, and F. K. Kunst, "Exceptional topology of non-Hermitian systems," Rev. Mod. Phys., Vol. 91, No. 1, 015005, 2021.
doi:10.1103/RevModPhys.93.015005

5. Ramezani, H., T. Kottos, R. El-Ganainy, and D. N. Christodoulides, "Unidirectional nonlinear PT-symmetric optical structures," Phys. Rev. A, Vol. 82, No. 4, 043803, 2010.
doi:10.1103/PhysRevA.82.043803

6. Lin, Z., H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, "Unidirectional invisibility induced by PT-symmetric periodic structures," Phys. Rev. Lett., Vol. 106, No. 21, 213901, 2011.
doi:10.1103/PhysRevLett.106.213901

7. Regensburger, A., C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, "Parity-time synthetic photonic lattices," Nature, Vol. 488, No. 8, 167-171, 2012.
doi:10.1038/nature11298

8. Liu, Z. P., J. Zhang, Ş. K. Ozdemir, B. Peng, H. Jing, X.-Y. Lu, C.-W. Li, L. Yang, F. Nori, and Y. Liu, "Metrology with PT-symmetric cavities: Enhanced sensitivity near the PT-phase transition," Phys. Rev. Lett., Vol. 117, No. 11, 110802, 2016.
doi:10.1103/PhysRevLett.117.110802

9. Chen, W., Ş. K. Ozdemir, G. Zhao, J. Wiersig, and L. Yang, "Exceptional points enhance sensing in an optical microcavity," Nature, Vol. 548, No. 8, 192-196, 2017.
doi:10.1038/nature23281

10. Hodaei, H., A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, "Enhanced sensitivity at higher-order exceptional points," Nature, Vol. 548, No. 8, 187-191, 2017.
doi:10.1038/nature23280

11. Chen, P.-Y., M. Sakhdari, M. Hajizadegan, Q. Cui, M. M.-C. Cheng, R. El-Ganainy, and A. Alù, "Generalized parity-time symmetry condition for enhanced sensor telemetry," Nat. Electron., Vol. 1, No. 5, 297-304, 2018.
doi:10.1038/s41928-018-0072-6

12. Chong, Y. D., L. Ge, and A. D. Stone, "PT-symmetry breaking and laser-absorber modes in optical scattering systems," Phys. Rev. Lett., Vol. 106, No. 9, 093902, 2011.
doi:10.1103/PhysRevLett.106.093902

13. Liertzer, M., L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, "Pump-induced exceptional points in lasers," Phys. Rev. Lett., Vol. 108, No. 17, 173901, 2012.
doi:10.1103/PhysRevLett.108.173901

14. Feng, L., Z. J. Wong, R.-M. Ma, Y. Wang, and X. Zhang, "Single-mode laser by parity-time symmetry breaking," Science, Vol. 346, No. 6212, 972-975, 2014.
doi:10.1126/science.1258479

15. Hodaei, H., M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, "Parity-time-symmetric microring lasers," Science, Vol. 346, No. 6212, 975-978, 2014.
doi:10.1126/science.1258480

16. Doppler, J., A. A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, and S. Rotter, "Dynamically encircling an exceptional point for asymmetric mode switching," Nature, Vol. 537, No. 9, 76-79, 2016.
doi:10.1038/nature18605

17. Xu, H., D. Mason, L. Jiang, and J. G. E. Harris, "Topological energy transfer in an optomechanical system with exceptional points," Nature, Vol. 537, No. 9, 80-83, 2016.
doi:10.1038/nature18604

18. Li, Z. P., G. T. Cao, C. H. Li, S. H. Dong, Y. Deng, X. K. Liu, J. S. Ho, and C. W. Qiu, "Non-Hermitian electromagnetic metasurfaces at exceptional points," Prog. Electromagn. Res., Vol. 171, 1-20, 2021.
doi:10.2528/PIER21051703

19. Yan, Q. H., H. S. Chen, and Y. H. Yang, "Non-Hermitian skin effect and delocalized edge states in photonic crystals with anomalous parity-time symmetry," Prog. Electromagn. Res., Vol. 172, 33-40, 2021.
doi:10.2528/PIER21111602

20. Christensen, J., M. Willatzen, V. R. Velasco, and M.-H. Lu, "Parity-time synthetic phononic media," Phys. Rev. Lett., Vol. 116, No. 20, 207601, 2016.
doi:10.1103/PhysRevLett.116.207601

21. Hou, Z. and B. Assouar, "Tunable elastic parity-time symmetric structure based on the shunted piezoelectric materials," J. Appl. Phys., Vol. 123, No. 8, 085101, 2018.
doi:10.1063/1.5009129

22. Wu, Q., Y. Chen, and G. Huang, "Asymmetric scattering of flexural waves in a parity-time symmetric metamaterial beam," J. Acoust. Soc. Am., Vol. 146, No. 1, 850, 2019.
doi:10.1121/1.5116561

23. Domínguez-Rocha, V., R. Thevamaran, F. M. Ellis, and T. Kottos, "Environmentally induced exceptional points in elastodynamics," Phys. Rev. Applied, Vol. 13, No. 1, 014060, 2020.
doi:10.1103/PhysRevApplied.13.014060

24. Shmuel, G. and N. Moiseyev, "Linking scalar elastodynamics and non-Hermitian quantum mechanics," Phys. Rev. Applied, Vol. 13, No. 2, 024074, 2020.
doi:10.1103/PhysRevApplied.13.024074

25. Kononchuk, R. and T. Kottos, "Orientation-sensed optomechanical accelerometers based on exceptional points," Phys. Rev. Research, Vol. 2, No. 2, 023252, 2020.
doi:10.1103/PhysRevResearch.2.023252

26. Rosa, M. I. N., M. Mazzotti, and M. Ruzzene, "Exceptional points and enhanced sensitivity in PT-symmetric continuous elastic media," J. Mech. Phys. Solids, Vol. 149, 104325, 2021.
doi:10.1016/j.jmps.2021.104325

27. Achilleos, V., G. Theocharis, O. Richoux, and V. Pagneux, "Non-Hermitian acoustic metamaterials: Role of exceptional points in sound absorption," Phys. Rev. B, Vol. 95, No. 14, 144303, 2017.
doi:10.1103/PhysRevB.95.144303

28. Yang, H., X. Zhang, Y. Liu, Y. Yao, F. Wu, and D. Zhao, "Novel acoustic flat focusing based on the asymmetric response in parity-time-symmetric phononic crystals," Sci. Rep., Vol. 9, 10048, 2019.
doi:10.1038/s41598-019-46467-3

29. Zhu, X. F., H. Ramezani, C. Z. Shi, J. Zhu, and X. Zhang, "PT-symmetric acoustics," Phys. Rev. X, Vol. 4, No. 3, 031042, 2014.

30. Fleury, R., D. Sounas, and A. Alù, "An invisible acoustic sensor based on parity-time symmetry," Nat. Commun., Vol. 6, 5905, 2015.
doi:10.1038/ncomms6905

31. Shi, C. Z., M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, "Accessing the exceptional points of parity-time symmetric acoustics," Nat. Commun., Vol. 7, 11110, 2016.
doi:10.1038/ncomms11110

32. Liu, T., X. Zhu, F. Chen, S. Liang, and J. Zhu, "Unidirectional wave vector manipulation in two-dimensional space with an all passive acoustic parity-time-symmetric metamaterials crystal," Phys. Rev. Lett., Vol. 120, No. 12, 124502, 2018.
doi:10.1103/PhysRevLett.120.124502

33. Ding, K., G. Ma, M. Xiao, Z. Q. Zhang, and C. T. Chan, "Emergence, coalescence, and topological properties of multiple exceptional points and their experimental realization," Phys. Rev. X, Vol. 6, No. 2, 021007, 2016.

34. Ding, K., G. Ma, Z. Q. Zhang, and C. T. Chan, "Experimental demonstration of an anisotropic exceptional point," Phys. Rev. Lett., Vol. 121, No. 8, 085702, 2018.
doi:10.1103/PhysRevLett.121.085702

35. Zhu, W., X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, "Simultaneous observation of a topological edge state and exceptional points in an open and non-Hermitian acoustic system," Phys. Rev. Lett., Vol. 121, No. 121, 124501, 2018.
doi:10.1103/PhysRevLett.121.124501

36. Shen, C., J. F. Li, X. Y. Peng, and S. A. Cummer, "Synthetic exceptional points and unidirectional zero reflection in non-Hermitian acoustic systems," Phys. Rev. Materials, Vol. 2, No. 12, 125203, 2018.
doi:10.1103/PhysRevMaterials.2.125203

37. Gu, Z., H. Gao, T. Liu, S. Liang, S. An, Y. Li, and J. Zhu, "Topologically protected exceptional point with local non-Hermitian modulation in an acoustic crystal," Phys. Rev. Applied, Vol. 15, No. 1, 014025, 2021.
doi:10.1103/PhysRevApplied.15.014025

38. Wang, X., X. S. Fang, D. X. Mao, Y. Jing, and Y. Li, "Extremely asymmetrical acoustic metasurface mirror at the exceptional point," Phys. Rev. Lett., Vol. 123, No. 21, 214302, 2019.
doi:10.1103/PhysRevLett.123.214302

39. Jia, D., Y. Wang, Y. Ge, S. Q. Yuan, and H. X. Sun, "Tunable topological refractions in valley sonic crystals with triple valley hall phase transitions," Prog. Electromagn. Res., Vol. 172, 13-22, 2021.
doi:10.2528/PIER21102002

40. Zhen, B., C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S.-L. Chua, J. D. Joannopoulos, and M. Soljačić, "Spawning rings of exceptional points out of Dirac cones," Nature, Vol. 525, No. 9, 354-358, 2015.
doi:10.1038/nature14889

41. Wang, H. F., B. Y. Xie, S. K. Gupta, X. Y. Zhu, L. Liu, X. P. Liu, M. H. Lu, and Y. F. Chen, "Exceptional concentric rings in a non-Hermitian bilayer photonic system," Phys. Rev. B, Vol. 100, No. 16, 165134, 2019.
doi:10.1103/PhysRevB.100.165134

42. Kolkowski, R., S. Kovaios, and A. F. Koenderink, "Pseudochirality at exceptional rings of optical metasurfaces," Phys. Rev. Research, Vol. 3, No. 2, 023185, 2021.
doi:10.1103/PhysRevResearch.3.023185

43. Cerjan, A., S. Huang, M. Wang, K. P. Chen, Y. D. Chong, and M. C. Rechtsman, "Experimental realization of a Weyl exceptional ring," Nat. Photon., Vol. 13, No. 9, 623-628, 2019.
doi:10.1038/s41566-019-0453-z

44. Xu, Y., S. T. Wang, and L. M. Duan, "Weyl exceptional rings in a three-dimensional dissipative cold atomic gas," Phys. Rev. Lett., Vol. 118, No. 4, 045701, 2017.
doi:10.1103/PhysRevLett.118.045701

45. Liu, J. J., Z. W. Li, Z. G. Chen, W. Y. Tang, A. Chen, B. Liang, G. C. Ma, and J. C. Cheng, "Experimental realization ofWeyl exceptional rings in a synthetic three-dimensional non-Hermitian phononic crystal," Phys. Rev. Lett., Vol. 129, No. 8, 084301, 2022.
doi:10.1103/PhysRevLett.129.084301