- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Chiral-mode control around a Hermitian diabolic point in discrete non-Hermitian coupled resonators

Kota Yagi1,2, Takahiro Uemura1,2, Yuto Moritake1,3, Adam Mock4, and Masaya Notomi1,2,5,*

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

Phys. Rev. Research 8, 043022 – Published 7 October, 2026

DOI: https://doi.org/10.1103/mmg9-5hg2

Abstract

Motivated by the prospect of chiral-mode control in compact photonic systems, we analyze discrete coupled single-mode resonators. Using the minimal three-resonator model, we show that an infinitesimal complex on-site perturbation near a Hermitian diabolic point (DP) induces chiral-mode selection, governed by what we term an asymptotic exceptional point (AEP). Here, an AEP denotes a Hermitian DP equipped with a non-Hermitian perturbation that induces an asymptotically defective effective Hamiltonian. The eigenvectors coalesce in the asymptotic limit toward the DP, although the Hamiltonian at the point itself remains diagonalizable. Operationally, this AEP response realizes chirality switching from an achiral state to a chiral state. The associated eigenvalue response exhibits the anomalous fractional-power scaling Δλ∝ɛ3/2, distinct from the square-root response of an ordinary exceptional point (EP). We further show that, in a broader two-parameter perturbation space, ordinary EPs lie on exceptional-line branches that meet at the AEP. A finite-bias control sweep crosses these branches at an EP pair, enabling chirality reversal between opposite chiral states. The central message is therefore that the AEP organizes two related routes for chirality switching: direct switching from an achiral state to a chiral state via the AEP and switching between opposite chiral states via an EP2 pair in the vicinity of the AEP. Within a finite-resolution averaging model, these two operating points exhibit different practical performance characteristics, and under sufficiently high control resolution, the AEP operating point can become more favorable than the EP-pair operating point, suggesting a route toward compact and low-energy chiral photonic devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. X. Zhu, H. Ramezani, C. Shi, J. Zhu, and X. Zhang, PT-symmetric acoustics, Phys. Rev. X 4, 031042 (2014).
  2. 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).
  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. 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).
  5. M.-A. Miri and A. Alù, Exceptional points in optics and photonics, Science 363, eaar7709 (2019).
  6. W. D. Heiss, The physics of exceptional points, J. Phys. A: Math. Theor. 45, 444016 (2012).
  7. M. Berry, Physics of nonhermitian degeneracies, Czech. J. Phys. 54, 1039 (2004).
  8. J. Doppler, 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 (London) 537, 76 (2016).
  9. W. Heiss and H. Harney, The chirality of exceptional points, Eur. Phys. J. D 17, 149 (2001).
  10. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A 45, 8185 (1992).
  11. A. M. Yao and M. J. Padgett, Orbital angular momentum: Origins, behavior and applications, Adv. Opt. Photonics 3, 161 (2011).
  12. K. J. Vahala, Optical microcavities, Nature (London) 424, 839 (2003).
  13. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Terabit free-space data transmission employing orbital angular momentum multiplexing, Nat. Photonics 6, 488 (2012).
  14. A. E. Willner, K. Pang, H. Song, K. Zou, and H. Zhou, Orbital angular momentum of light for communications, Appl. Phys. Rev. 8, 041312 (2021).
  15. Z. Zhang, X. Qiao, B. Midya, K. Liu, J. Sun, T. Wu, W. Liu, R. Agarwal, J. M. Jornet, S. Longhi, N. M. Litchinitser, and L. Feng, Tunable topological charge vortex microlaser, Science 368, 760 (2020).
  16. W. E. Hayenga, M. Parto, J. Ren, F. O. Wu, M. P. Hokmabadi, C. Wolff, R. El-Ganainy, N. Asger Mortensen, D. N. Christodoulides, and M. Khajavikhan, Direct generation of tunable orbital angular momentum beams in microring lasers with broadband exceptional points, ACS Photonics 6, 1895 (2019).
  17. Z. Zhang, H. Zhao, D. G. Pires, X. Qiao, Z. Gao, J. M. Jornet, S. Longhi, N. M. Litchinitser, and L. Feng, Ultrafast control of fractional orbital angular momentum of microlaser emissions, Light: Sci. Appl. 9, 179 (2020).
  18. P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, Chiral quantum optics, Nature (London) 541, 473 (2017).
  19. 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).
  20. T. Kato, Perturbation Theory for Linear Operators, Classics in Mathematics (Springer, Berlin, 1995), reprint of the 1980 ed.
  21. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Unidirectional invisibility induced by PT-symmetric periodic structures, Phys. Rev. Lett. 106, 213901 (2011).
  22. X. Yin and X. Zhang, Unidirectional light propagation at exceptional points, Nat. Mater. 12, 175 (2013).
  23. P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, Orbital angular momentum microlaser, Science 353, 464 (2016).
  24. J. Wiersig, Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles, Phys. Rev. A 84, 063828 (2011).
  25. B. Peng, Ş. Kaya 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).
  26. A. Ø. Svela, J. M. Silver, L. Del Bino, S. Zhang, M. T. M. Woodley, M. R. Vanner, and P. Del’Haye, Coherent suppression of backscattering in optical microresonators, Light Sci. Appl. 9, 204 (2020).
  27. H. Lee, A. Kecebas, F. Wang, L. Chang, S. K. Özdemir, and T. Gu, Chiral exceptional point and coherent suppression of backscattering in silicon microring with low loss Mie scatterer, eLight 3, 20 (2023).
  28. A. Mock, D. Sounas, and A. Alù, Magnet-free circulator based on spatiotemporal modulation of photonic crystal defect cavities, ACS Photonics 6, 2056 (2019).
  29. C. F. Fong, Y. Ota, Y. Arakawa, S. Iwamoto, and Y. K. Kato, Chiral modes near exceptional points in symmetry broken H1 photonic crystal cavities, Phys. Rev. Res. 3, 043096 (2021).
  30. M. Takiguchi, R. Kuruma, Y. Moritake, P. Heidt, M. Ono, E. Kuramochi, H. Sumikura, and M. Notomi, Generation of OAM light using metal-loaded Si waveguides with a non-Hermitian perturbation, in CLEO 2026 (Optica Publishing Group, Washington, DC, 2026), STH2D.7.
  31. W. R. Sweeney, C. W. Hsu, S. Rotter, and A. D. Stone, Perfectly absorbing exceptional points and chiral absorbers, Phys. Rev. Lett. 122, 093901 (2019).
  32. 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).
  33. J. Zhu, C. Wang, C. Tao, Z. Fu, H. Liu, F. Bo, L. Yang, G. Zhang, and J. Xu, Local chirality at exceptional points in optical whispering-gallery microcavities, Phys. Rev. A 108, L041501 (2023).
  34. H.A. Haus and W. Huang, Coupled-mode theory, Proc. IEEE 79, 1505 (1991).
  35. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Coupled-resonator optical waveguide: A proposal and analysis, Opt. Lett. 24, 711 (1999).
  36. M. V. Berry, Mode degeneracies and the Petermann excess-noise factor for unstable lasers, J. Mod. Opt. 50, 63 (2003).
  37. E. N. Bulgakov, I. Rotter, and A. F. Sadreev, Phase rigidity and avoided level crossings in the complex energy plane, Phys. Rev. E 74, 056204 (2006).
  38. J. Wiersig, Petermann factors and phase rigidities near exceptional points, Phys. Rev. Res. 5, 033042 (2023).
  39. H. Schomerus, Eigenvalue sensitivity from eigenstate geometry near and beyond arbitrary-order exceptional points, Phys. Rev. Res. 6, 013044 (2024).
  40. H. Feshbach, The optical model and its justification, Annu. Rev. Nucl. Sci. 8, 49 (1958).
  41. J. Moro, J. V. Burke, and M. L. Overton, On the Lidskii–Vishik–Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure, SIAM J. Matrix Anal. Appl. 18, 793 (1997).
  42. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, Photonic crystal nanocavity laser with a single quantum dot gain, Opt. Express 17, 15975 (2009).
  43. B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vučković, Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser, Nat. Photonics 5, 297 (2011).
  44. K. Takata and M. Notomi, PT-symmetric coupled-resonator waveguide based on buried heterostructure nanocavities, Phys. Rev. Appl. 7, 054023 (2017).
  45. M. Brunstein, R. Braive, R. Hostein, A. Beveratos, I. Rober-Philip, I. Sagnes, T. J. Karle, A. M. Yacomotti, J. A. Levenson, V. Moreau, G. Tessier, and Y. De Wilde, Thermo-optical dynamics in an optically pumped photonic crystal nano-cavity, Opt. Express 17, 17118 (2009).
  46. M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, and H. Taniyama, On-chip all-optical switching and memory by silicon photonic crystal nanocavities, Adv. Opt. Technol. 2008, 568936 (2008).
  47. T. Tanabe, K. Nishiguchi, E. Kuramochi, and M. Notomi, Low power and fast electro-optic silicon modulator with lateral p−i−n embedded photonic crystal nanocavity, Opt. Express 17, 22505 (2009).
  48. S. Iadanza, M. Clementi, C. Hu, S. A. Schulz, D. Gerace, M. Galli, and L. O’Faolain, Model of thermo-optic nonlinear dynamics of photonic crystal cavities, Phys. Rev. B 102, 245404 (2020).
  49. C. J. Chen, J. Zheng, T. Gu, J. F. McMillan, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, Selective tuning of high-Q silicon photonic crystal nanocavities via laser-assisted local oxidation, Opt. Express 19, 12480 (2011).
  50. F. Intonti, N. Caselli, S. Vignolini, F. Riboli, S. Kumar, A. Rastelli, O. G. Schmidt, M. Francardi, A. Gerardino, L. Balet, L. H. Li, A. Fiore, and M. Gurioli, Mode tuning of photonic crystal nanocavities by photoinduced non-thermal oxidation, Appl. Phys. Lett. 100, 033116 (2012).
  51. T. Uemura, Y. Moritake, T. Yoda, H. Chiba, Y. Tanaka, M. Ono, E. Kuramochi, and M. Notomi, Photonic topological phase transition induced by material phase transition, Sci. Adv. 10, eadp7779 (2024).
  52. Y. Chu, Y. Liu, H. Liu, and J. Cai, Quantum sensing with a single-qubit pseudo-Hermitian system, Phys. Rev. Lett. 124, 020501 (2020).
  53. Q.-C. Wu, Y.-H. Zhou, B.-L. Ye, T. Liu, Y.-H. Kang, Q.-P. Su, and C.-P. Yang, Parameter trajectory engineering for state transfer and quantum sensing in non-Hermitian two-level systems, Phys. Rev. A 114, 022610 (2026).
  54. N. B. Tomazio, L. O. Trinchão, E. S. Gonçalves, L. F. dos Santos, F. G. S. Santos, P. F. Jarschel, T. P. M. Alegre, and G. S. Wiederhecker, Tunable degenerate optical parametric oscillation with coupled microresonators, ACS Photonics 12, 227 (2025).
  55. K. Takata, K. Nozaki, E. Kuramochi, S. Matsuo, K. Takeda, T. Fujii, S. Kita, A. Shinya, and M. Notomi, Observing exceptional point degeneracy of radiation with electrically pumped photonic crystal coupled-nanocavity lasers, Optica 8, 184 (2021).

Outline

Information

Phys. Rev. Research 8, 043022– Published 7 October, 2026
  • Received 10 June 2026
  • Accepted 19 September 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation