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  • Letter
  • Open Access

Robust exceptional point chains and chirality switch in a vast optical parameter space

Chang-Hwan Yi and Jung-Wan Ryu

Tom Simon Rodemund and Martina Hentschel*

  • *Contact author: martina.hentschel@physik.tu-chemnitz.de
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Phys. Rev. A 112, L031501 – Published 22 September, 2025

DOI: https://doi.org/10.1103/6dgz-hzlm

Abstract

While the special properties of exceptional points (EPs) may improve application relevant features such as hypersensing, often their realization requires a precise fine-tuning of parameters. Here we report the robust formation of EP chains in coupled optical microcavities over intercavity distances D on the order of the cavity size. We find that coupling, or more generally, the availability of an outer (coupling) channel, is sufficient to induce EPs in the parameter space spanned by the refractive index n along with D. This occurs even at D of several wavelengths, yielding a network of EPs in parameter space with a periodicity of the order of the wavelength in the D direction. Upon the increase of n, we observe a sharp transition in the sign of the chirality measured in one of the cavities that further structures the system properties. While the details of the Riemannian surfaces associated with the formation of exceptional points are mode dependent and allow for a variety of single-cavity chiralities, we find the underlying mechanism to be universal, robust, applicable to other and more general coupled systems, and promising for potential applications such as optical measurements of pressure, voltages, or distances.

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References (54)

  1. K. J. Vahala, Optical microcavities, Nature (London) 424, 839 (2003).
  2. H. Cao and J. Wiersig, Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics, Rev. Mod. Phys. 87, 61 (2015).
  3. 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).
  4. M.-A. Miri and A. Alu, Exceptional points in optics and photonics, Science 363, eaar7709 (2019).
  5. N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University, Cambridge, England, 2011).
  6. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  7. T. Kato, Perturbation Theory for Linear Operators, Classics in Mathematics Vol. 132 (Springer, Berlin, 1976).
  8. W. D. Heiss and A. L. Sannino, Avoided level crossing and exceptional points, J. Phys. A: Math. Gen. 23, 1167 (1990).
  9. W. D. Heiss, Repulsion of resonance states and exceptional points, Phys. Rev. E 61, 929 (2000).
  10. J. Wiersig, Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities, Phys. Rev. Lett. 97, 253901 (2006).
  11. I. Rotter, A non-Hermitian Hamilton operator and the physics of open quantum systems, J. Phys. A: Math. Theor. 42, 153001 (2009).
  12. H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Parity-time–symmetric microring lasers, Science 346, 975 (2014).
  13. L. Feng, Zi Jing Wong, R.-M. Ma, Y. Wang, and X. Zhang, Single-mode laser by parity-time symmetry breaking, Science 346, 972 (2014).
  14. P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, Orbital angular momentum microlaser, Science 353, 464 (2016).
  15. B. Peng, Ş. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, Chiral modes and directional lasing at exceptional points, Proc. Natl. Acad. Sci. USA 113, 6845 (2016).
  16. S. Longhi, Non-Hermitian gauged topological laser arrays, Ann. Phys. 530, 1800023 (2018).
  17. B. Zhu, Q. Wang, D. Leykam, H. Xue, Q. J. Wang, and Y. D. Chong, Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect, Phys. Rev. Lett. 129, 013903 (2022).
  18. J. Wiersig, Sensors operating at exceptional points: General theory, Phys. Rev. A 93, 033809 (2016).
  19. W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature (London) 548, 192 (2017).
  20. H. Hodaei, 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 (London) 548, 187 (2017).
  21. J. Wiersig, Review of exceptional point-based sensors, Photonics Res. 8, 1457 (2020).
  22. R. Kononchuk, J. Cai, F. Ellis, R. Thevamaran, and T. Kottos, Exceptional-point-based accelerometers with enhanced signal-to-noise ratio, Nature (London) 607, 697 (2022).
  23. W. Mao, Z. Fu, Y. Li, F. Li, and L. Yang, Exceptional–point–enhanced phase sensing, Sci. Adv. 10, eadl5037 (2024).
  24. M. Parto, C. Leefmans, J. Williams, R. M. Gray, and A. Marandi, Enhanced sensitivity via non-Hermitian topology, Light: Sci. Appl. 14, 6 (2025).
  25. M. Yang, Z. Ye, H. Pan, M. Farhat, A. E. Cetin, and P.-Y. Chen, Electromagnetically unclonable functions generated by non-Hermitian absorber-emitter, Sci. Adv. 9, eadg7481 (2023).
  26. H. Zhao, X. Qiao, T. Wu, B. Midya, S. Longhi, and L. Feng, Non-Hermitian topological light steering, Science 365, 1163 (2019).
  27. 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).
  28. 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).
  29. S. Xia, D. Kaltsas, D. Song, I. Komis, J. Xu, A. Szameit, H. Buljan, K. G. Makris, and Z. Chen, Nonlinear tuning of PT symmetry and non-Hermitian topological states, Science 372, 72 (2021).
  30. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  31. S. Sunada and T. Harayama, Design of resonant microcavities: Application to optical gyroscopes, Opt. Express 15, 16245 (2007).
  32. W. Liang, V. S. Ilchenko, A. A. Savchenkov, E. Dale, D. Eliyahu, A. B. Matsko, and L. Maleki, Resonant microphotonic gyroscope, Optica 4, 114 (2017).
  33. C. Shi, M. Dubois, Y. Chen, L. Cheng, H. Ramezani, Y. Wang, and X. Zhang, Accessing the exceptional points of parity-time symmetric acoustics, Nat. Commun. 7, 11110 (2016).
  34. Z. Gu, H. Gao, H. Xue, J. Li, Z. Su, and J. Zhu, Transient non-Hermitian skin effect, Nat. Commun. 13, 7668 (2022).
  35. H. Xu, D. Mason, L. Jiang, and J. G. E. Harris, Topological energy transfer in an optomechanical system with exceptional points, Nature (London) 537, 80 (2016).
  36. H. Yang, C. Wang, T. Yu, Y. Cao, and P. Yan, Antiferromagnetism emerging in a ferromagnet with gain, Phys. Rev. Lett. 121, 197201 (2018).
  37. Y. Xu, L. Li, H. Jeong, S. Kim, I. Kim, J. Rho, and Y. Liu, Subwavelength control of light transport at the exceptional point by non-Hermitian metagratings, Sci. Adv. 9, eadf3510 (2023).
  38. W. Deng, W. Zhu, T. Chen, H. Sun, and X. Zhang, Ultrasensitive integrated circuit sensors based on high-order non-Hermitian topological physics, Sci. Adv. 10, eadp6905 (2024).
  39. J. Wiersig, Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles, Phys. Rev. A 84, 063828 (2011).
  40. J. Wiersig and M. Hentschel, Combining directional light output and ultralow loss in deformed microdisks, Phys. Rev. Lett. 100, 033901 (2008).
  41. S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Ray-wave correspondence in limaçon-shaped semiconductor microcavities, Phys. Rev. A 80, 031801(R) (2009).
  42. R. Ketzmerick, F. Lorenz, and J. R. Schmidt, Semiclassical limit of resonance states in chaotic scattering, Phys. Rev. Lett. 134, 020404 (2025).
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6dgz-hzlm for details of the spectral properties of EPs and the analytic modeling.
  44. J. Wiersig, Boundary element method for resonances in dielectric microcavities, J. Opt. A: Pure Appl. Opt. 5, 53 (2003).
  45. S.-Y. Lee, Geometrical phase imprinted on eigenfunctions near an exceptional point, Phys. Rev. A 82, 064101 (2010).
  46. S.-Y. Lee, J.-W. Ryu, S. W. Kim, and Y. Chung, Geometric phase around multiple exceptional points, Phys. Rev. A 85, 064103 (2012).
  47. H. Eleuch and I. Rotter, Clustering of exceptional points and dynamical phase transitions, Phys. Rev. A 93, 042116 (2016).
  48. J. Wiersig, Petermann factors and phase rigidities near exceptional points, Phys. Rev. Res. 5, 033042 (2023).
  49. J.-W. Ryu, J.-H. Han, and C.-H. Yi, Realization of geometric-phase topology induced by multiple exceptional points, Phys. Rev. A 110, 052221 (2024).
  50. F.-J. Shu, C.-L. Zou, W.-C. Chen, and F.-W. Sun, Ultralong distance coupling between deformed circular microcavities, J. Opt. Soc. Am. B 31, 478 (2014).
  51. H.-H. Yu, S. Gwak, H. Kim, J.-W. Ryu, C.-M. Kim, and C.-H. Yi, Salient role of the non-Hermitian coupling for optimizing conditions in multiple maximizations of inter-cavity light transfer, Opt. Express 29, 19998 (2021).
  52. G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories (Springer, Berlin, 2011).
  53. D. Gagnon and L. J. Dubé, Lorenz–Mie theory for 2D scattering and resonance calculations, J. Opt. 17, 103501 (2015).
  54. T. S. Rodemund, S. N. Chormaic, and M. Hentschel, Coupled deformed microdisk cavities featuring non-Hermitian properties, Appl. Phys. Lett. 124, 051107 (2024).

Outline

Information

Phys. Rev. A 112, L031501– Published 22 September, 2025
  • Received 28 March 2025
  • Accepted 25 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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