Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Optical non-Hermitian skin effect in uniform media

Taiki Yoda1, Yuto Moritake1, Kenta Takata2,3, Kazuki Yokomizo4, Shuichi Murakami1, and Masaya Notomi1,2,3,*

  • *Contact author: notomi@phys.sci.isct.ac.jp

Phys. Rev. Research 7, 033214 – Published 3 September, 2025

DOI: https://doi.org/10.1103/3tlp-16mc

Abstract

Non-Hermitian skin effect (NHSE), which is a localization phenomenon in non-Hermitian systems, has recently been of great interest. Most previous works in various systems studied periodic systems. However, electromagnetic waves do not feel the periodicity of a system if the wavelength is sufficiently long, and it has not been clear that electromagnetic waves exhibit the localization caused by the non-Hermiticity itself even in uniform systems without the periodicity. Here, we establish the theory of the optical NHSE in non-Hermitian uniform media and show that the optical NHSE occurs even in uniform media. We apply our theory to subwavelength metamaterials and demonstrate the existence of a non-Hermitian skin mode in a multilayer metamaterial. Finally, we propose a concept of a stationarily excited skin mode to describe a lossy system under stationary excitation with real excitation frequency.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (70)

  1. L. Feng, R. El-Ganainy, and L. Ge, Non-Hermitian photonics based on parity–time symmetry, Nat. Photon. 11, 752 (2017).
  2. R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys. 14, 11 (2018).
  3. Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, Parity–time symmetry and exceptional points in photonics, Nat. Mater. 18, 783 (2019).
  4. Y. Ota, K. Takata, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, and S. Iwamoto, Active topological photonics, Nanophotonics 9, 547 (2020).
  5. S. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
  6. S. Yao, F. Song, and Z. Wang, Non-Hermitian Chern bands, Phys. Rev. Lett. 121, 136802 (2018).
  7. K. Yokomizo and S. Murakami, Non-Bloch band theory of non-Hermitian systems, Phys. Rev. Lett. 123, 066404 (2019).
  8. D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Non-Hermitian boundary modes and topology, Phys. Rev. Lett. 124, 056802 (2020).
  9. N. Okuma, K. Kawabata, K. Shiozaki, and M. Sato, Topological origin of non-Hermitian skin effects, Phys. Rev. Lett. 124, 086801 (2020).
  10. K. Kawabata, N. Okuma, and M. Sato, Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class, Phys. Rev. B 101, 195147 (2020).
  11. J. Zhong, K. Wang, Y. Park, V. Asadchy, C. C. Wojcik, A. Dutt, and S. Fan, Nontrivial point-gap topology and non-Hermitian skin effect in photonic crystals, Phys. Rev. B 104, 125416 (2021).
  12. Q. Yan, H. Chen, and Y. Yang, Non-Hermitian skin effect and delocalized edge states in photonic crystals with anomalous parity-time symmetry, Prog. Electromagn. Res. 172, 33 (2021).
  13. K. Yokomizo, T. Yoda, and S. Murakami, Non-Hermitian waves in a continuous periodic model and application to photonic crystals, Phys. Rev. Res. 4, 023089 (2022).
  14. Z. Fang, M. Hu, L. Zhou, and K. Ding, Geometry-dependent skin effects in reciprocal photonic crystals, Nanophotonics 11, 3447 (2022).
  15. T. Ochiai, Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals, Phys. Rev. B 106, 195412 (2022).
  16. W. Zhu and J. Gong, Photonic corner skin modes in non-Hermitian photonic crystals, Phys. Rev. B 108, 035406 (2023).
  17. A. Poddubny, J. Zhong, and S. Fan, Mesoscopic non-Hermitian skin effect, Phys. Rev. A 109, L061501 (2024).
  18. M. Brandenbourger, X. Locsin, E. Lerner, and C. Coulais, Non-reciprocal robotic metamaterials, Nat. Commun. 10, 4608 (2019).
  19. A. Ghatak, M. Brandenbourger, J. Van Wezel, and C. Coulais, Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial, Proc. Natl. Acad. Sci. USA 117, 29561 (2020).
  20. Y. Chen, X. Li, C. Scheibner, V. Vitelli, and G. Huang, Realization of active metamaterials with odd micropolar elasticity, Nat. Commun. 12, 5935 (2021).
  21. T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. Molenkamp, C. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys. 16, 747 (2020).
  22. S. Liu, R. Shao, S. Ma, L. Zhang, O. You, H. Wu, Y. J. Xiang, T. J. Cui, and S. Zhang, Non-Hermitian skin effect in a non-Hermitian electrical circuit, Research 2021, 5608038 (2021).
  23. T. Hofmann, T. Helbig, F. Schindler, N. Salgo, M. Brzezińska, M. Greiter, T. Kiessling, D. Wolf, A. Vollhardt, A. Kabaši, C. H. Lee, A. Bilušić, R. Thomale, and T. Neupert, Reciprocal skin effect and its realization in a topolectrical circuit, Phys. Rev. Res. 2, 023265 (2020).
  24. D. Zou, T. Chen, W. He, J. Bao, C. H. Lee, H. Sun, and X. Zhang, Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits, Nat. Commun. 12, 7201 (2021).
  25. S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, and A. Szameit, Topological funneling of light, Science 368, 311 (2020).
  26. L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, and P. Xue, Non-Hermitian bulk–boundary correspondence in quantum dynamics, Nat. Phys. 16, 761 (2020).
  27. X. Zhang, Y. Tian, J.-H. Jiang, M.-H. Lu, and Y.-F. Chen, Observation of higher-order non-Hermitian skin effect, Nat. Commun. 12, 5377 (2021).
  28. L. Zhang, Y. Yang, Y. Ge, Y.-J. Guan, Q. Chen, Q. Yan, F. Chen, R. Xi, Y. Li, D. Jia, S.-Q. Yuan, H.-X. Sun, H. Chen, and B. Zhang, Acoustic non-Hermitian skin effect from twisted winding topology, Nat. Commun. 12, 6297 (2021).
  29. Z. Gu, H. Gao, H. Xue, J. Li, Z. Su, and J. Zhu, Transient non-Hermitian skin effect, Nat. Commun. 13, 7668 (2022).
  30. Q. Zhou, J. Wu, Z. Pu, J. Lu, X. Huang, W. Deng, M. Ke, and Z. Liu, Observation of geometry-dependent skin effect in non-Hermitian phononic crystals with exceptional points, Nat. Commun. 14, 4569 (2023).
  31. Y. G. Liu, Y. Wei, O. Hemmatyar, G. G. Pyrialakos, P. S. Jung, D. N. Christodoulides, and M. Khajavikhan, Complex skin modes in non-Hermitian coupled laser arrays, Light Sci. Appl. 11, 336 (2022).
  32. T. Liu, Y.-R. Zhang, Q. Ai, Z. Gong, K. Kawabata, M. Ueda, and F. Nori, Second-order topological phases in non-Hermitian systems, Phys. Rev. Lett. 122, 076801 (2019).
  33. K. Kawabata, M. Sato, and K. Shiozaki, Higher-order non-Hermitian skin effect, Phys. Rev. B 102, 205118 (2020).
  34. T. Yoshida, T. Mizoguchi, and Y. Hatsugai, Mirror skin effect and its electric circuit simulation, Phys. Rev. Res. 2, 022062(R) (2020).
  35. C. Scheibner, W. T. M. Irvine, and V. Vitelli, Non-Hermitian band topology and skin modes in active elastic media, Phys. Rev. Lett. 125, 118001 (2020).
  36. R. Okugawa, R. Takahashi, and K. Yokomizo, Second-order topological non-Hermitian skin effects, Phys. Rev. B 102, 241202(R) (2020).
  37. R. Okugawa, R. Takahashi, and K. Yokomizo, Non-Hermitian band topology with generalized inversion symmetry, Phys. Rev. B 103, 205205 (2021).
  38. K. Zhang, Z. Yang, and C. Fang, Universal non-Hermitian skin effect in two and higher dimensions, Nat. Commun. 13, 2496 (2022).
  39. K. Yokomizo and S. Murakami, Non-Bloch bands in two-dimensional non-Hermitian systems, Phys. Rev. B 107, 195112 (2023).
  40. L. D. Landau, J. Bell, M. Kearsley, L. Pitaevskii, E. Lifshitz, and J. Sykes, Electrodynamics of Continuous Media (Elsevier, Amsterdam, 2013), Vol. 8.
  41. F. Liu and J. Li, Gauge field optics with anisotropic media, Phys. Rev. Lett. 114, 103902 (2015).
  42. Y. Chen, R.-Y. Zhang, Z. Xiong, Z. H. Hang, J. Li, J. Q. Shen, and C. T. Chan, Non-Abelian gauge field optics, Nat. Commun. 10, 3125 (2019).
  43. N. Hatano and D. R. Nelson, Localization transitions in non-Hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996).
  44. S. M. Hashemi and I. S. Nefedov, Wideband perfect absorption in arrays of tilted carbon nanotubes, Phys. Rev. B 86, 195411 (2012).
  45. I. S. Nefedov, C. A. Valagiannopoulos, S. M. Hashemi, and E. I. Nefedov, Total absorption in asymmetric hyperbolic media, Sci. Rep. 3, 2662 (2013).
  46. I. S. Nefedov, C. A. Valagiannopoulos, and L. A. Melnikov, Perfect absorption in graphene multilayers, J. Opt. 15, 114003 (2013).
  47. S. Debnath, E. Khan, and E. E. Narimanov, Incoherent perfect absorption in lossy anisotropic materials, Opt. Express 27, 9561 (2019).
  48. S. Longhi, Non-Hermitian skin effect beyond the tight-binding models, Phys. Rev. B 104, 125109 (2021).
  49. M. G. Silveirinha, Chern invariants for continuous media, Phys. Rev. B 92, 125153 (2015).
  50. Z. Zhao, C. Guo, and S. Fan, Connection of temporal coupled-mode-theory formalisms for a resonant optical system and its time-reversal conjugate, Phys. Rev. A 99, 033839 (2019).
  51. S. Buddhiraju, A. Song, G. T. Papadakis, and S. Fan, Nonreciprocal metamaterial obeying time-reversal symmetry, Phys. Rev. Lett. 124, 257403 (2020).
  52. C. Guo, Z. Zhao, and S. Fan, Internal transformations and internal symmetries in linear photonic systems, Phys. Rev. A 105, 023509 (2022).
  53. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, Oxford, 2007).
  54. P. B. Johnson and R. W. Christy, Optical constants of the noble metals, Phys. Rev. B 6, 4370 (1972).
  55. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, Hyperbolic metamaterials, Nat. Photon. 7, 948 (2013).
  56. E. E. Narimanov and A. V. Kildishev, Naturally hyperbolic, Nat. Photon. 9, 214 (2015).
  57. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Hoboken, 1999).
  58. D. M. Pozar, Microwave Engineering (John Wiley & Sons, Hoboken, 2011).
  59. M. Davanço, Y. Urzhumov, and G. Shvets, The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction, Opt. Express 15, 9681 (2007).
  60. C. Fietz, Y. Urzhumov, and G. Shvets, Complex k band diagrams of 3D metamaterial/photonic crystals, Opt. Express 19, 19027 (2011).
  61. G. Parisi, P. Zilio, and F. Romanato, Complex Bloch-modes calculation of plasmonic crystal slabs by means of finite elements method, Opt. Express 20, 16690 (2012).
  62. X. Gao, B. Zhen, M. Soljačić, H. Chen, and C. W. Hsu, Bound states in the continuum in fiber Bragg gratings, ACS Photon. 6, 2996 (2019).
  63. H. Schomerus, Nonreciprocal response theory of non-Hermitian mechanical metamaterials: Response phase transition from the skin effect of zero modes, Phys. Rev. Res. 2, 013058 (2020).
  64. H. Schomerus, Fundamental constraints on the observability of non-Hermitian effects in passive systems, Phys. Rev. A 106, 063509 (2022).
  65. F. D. M. Haldane and S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett. 100, 013904 (2008).
  66. S. Raghu and F. D. M. Haldane, Analogs of quantum-Hall-effect edge states in photonic crystals, Phys. Rev. A 78, 033834 (2008).
  67. Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, Reflection-free one-way edge modes in a gyromagnetic photonic crystal, Phys. Rev. Lett. 100, 013905 (2008).
  68. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Observation of unidirectional backscattering-immune topological electromagnetic states, Nature (London) 461, 772 (2009).
  69. C. Scheibner, A. Souslov, D. Banerjee, P. Surówka, W. T. Irvine, and V. Vitelli, Odd elasticity, Nat. Phys. 16, 475 (2020).
  70. A. E. Siegman, Lasers (University Science Books, Melville, 1986).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation