Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Photonic exceptional points in engineered materials and their emerging applications

Abstract

Enabled by the coalescence of eigenvalues and eigenstates, exceptional points (EPs) in non-Hermitian photonic systems have revolutionized the control of light–matter interactions and sparked growing interest across diverse material and structural platforms. This Review synthesizes advances in engineered materials that harness EPs across three key domains: band EPs in dielectric photonic crystals, wherein radiation-induced loss transforms Hermitian degeneracies into exceptional rings and bulk Fermi arcs; scattering EPs in hybrid dielectric or lossy metasurfaces, enabling unidirectional reflectionless propagation; and Jones EPs in plasmonic and anisotropic materials, which exploit chiral degeneracies for asymmetric scattering and holographic multiplexing. We highlight emerging phenomena in dynamic EP control using tunable materials such as graphene, phase-change media and micro-electromechanical systems, which enable real-time modulation, topological phase transitions and the direct observation of non-Hermitian braiding. The topological properties of EPs, manifested in phase accumulation and half-integer polarization charges, support key applications in wavefront shaping and singular optics. New frontiers involve the integration of EPs with other concepts, including bound states in the continuum, Dirac points, nonreciprocity and magnetic tunability. Bridging non-Hermitian physics with material-engineered platforms paves the way for adaptive photonic devices, topological meta-architectures and machine learning-driven designs, charting a path towards next-generation nanophotonics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Photonic EPs in engineered materials and their emerging applications.
Fig. 2: Band EPs.
Fig. 3: Scattering EPs.
Fig. 4: Jones EPs.
Fig. 5: Dynamic control and braiding of EP.
Fig. 6: Topological properties and wavefront engineering of EPs.
Fig. 7: Special EPs and new frontiers.

Similar content being viewed by others

References

  1. Li, Z. et al. Non-Hermitian electromagnetic metasurfaces at exceptional points. Prog. Electromagn. Res. 171, 1–20 (2021).

    Article  CAS  Google Scholar 

  2. Li, A. et al. Exceptional points and non-Hermitian photonics at the nanoscale. Nat. Nanotechnol. 18, 706–720 (2023).

    Article  CAS  PubMed  Google Scholar 

  3. Özdemir, ŞK., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry and exceptional points in photonics. Nat. Mater. 18, 783–798 (2019).

    Article  PubMed  Google Scholar 

  4. Miri, M.-A. & Alù, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).

    Article  CAS  PubMed  Google Scholar 

  5. El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

    Article  CAS  Google Scholar 

  6. El-Ganainy, R., Khajavikhan, M., Christodoulides, D. N. & Ozdemir, S. K. The dawn of non-Hermitian optics. Commun. Phys. 2, 37 (2019).

    Article  Google Scholar 

  7. Ashida, Y., Gong, Z. & Ueda, M. Non-Hermitian physics. Adv. Phys. 69, 249–435 (2020).

    Article  Google Scholar 

  8. Ding, K., Fang, C. & Ma, G. Non-Hermitian topology and exceptional-point geometries. Nat. Rev. Phys. 4, 745–760 (2022).

    Article  Google Scholar 

  9. Doppler, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).

    Article  CAS  PubMed  Google Scholar 

  10. Wiersig, J. Review of exceptional point-based sensors. Photonics Res. 8, 1457–1467 (2020).

    Article  Google Scholar 

  11. Xu, J. et al. Single-cavity loss-enabled nanometrology. Nat. Nanotechnol. 19, 1472–1477 (2024).

    Article  CAS  PubMed  Google Scholar 

  12. Mao, W., Fu, Z., Li, Y., Li, F. & Yang, L. Exceptional-point-enhanced phase sensing. Sci. Adv. 10, eadl5037 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  13. Chen, W., Kaya Özdemir, Ş, Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017).

    Article  CAS  PubMed  Google Scholar 

  14. Li, Z., Prasad, C. S., Wang, X., Zhang, D. & Naik, G. V. Sensing beyond the exceptional point for high detectivity. ACS Photonics 11, 2954–2960 (2024).

    Article  CAS  Google Scholar 

  15. Huang, Y., Shen, Y., Min, C., Fan, S. & Veronis, G. Unidirectional reflectionless light propagation at exceptional points. Nanophotonics 6, 977–996 (2017).

    Article  Google Scholar 

  16. Peng, B. et al. Chiral modes and directional lasing at exceptional points. Proc. Natl Acad. Sci. USA 113, 6845–6850 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Song, Q., Odeh, M., Zúñiga-Pérez, J., Kanté, B. & Genevet, P. Plasmonic topological metasurface by encircling an exceptional point. Science 373, 1133–1137 (2021).

    Article  CAS  PubMed  Google Scholar 

  18. Sun, J. & Zhou, J. Metamaterials: the art in materials science. Engineering 44, 145–161 (2024).

    Article  Google Scholar 

  19. Qiu, C.-W., Zhang, T., Hu, G. & Kivshar, Y. Quo vadis, metasurfaces? Nano Lett. 21, 5461–5474 (2021).

    Article  CAS  PubMed  Google Scholar 

  20. Liu, Y. & Zhang, X. Metamaterials: a new frontier of science and technology. Chem. Soc. Rev. 40, 2494–2507 (2011).

    Article  CAS  PubMed  Google Scholar 

  21. Schulz, S. A. et al. Roadmap on photonic metasurfaces. Appl. Phys. Lett. 124, 260701 (2024).

    Article  CAS  Google Scholar 

  22. Bentata, F. et al. Spatially-controlled planar guided crystallization of low-loss phase change materials for programmable photonics. Adv. Mater. 38, e06609 (2026).

    Article  CAS  PubMed  Google Scholar 

  23. Cui, T., Bai, B. & Sun, H.-B. Tunable metasurfaces based on active materials. Adv. Funct. Mater. 29, 1806692 (2019).

    Article  Google Scholar 

  24. Jung, C., Lee, E. & Rho, J. The rise of electrically tunable metasurfaces. Sci. Adv. 10, eado8964 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Gu, T., Kim, H. J., Rivero-Baleine, C. & Hu, J. Reconfigurable metasurfaces towards commercial success. Nat. Photonics 17, 48–58 (2023).

    Article  CAS  Google Scholar 

  26. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics 11, 816–865 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Lawrence, M. et al. Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces. Phys. Rev. Lett. 113, 093901 (2014).

    Article  CAS  PubMed  Google Scholar 

  28. Baek, S. et al. Non-Hermitian chiral degeneracy of gated graphene metasurfaces. Light Sci. Appl. 12, 87 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Jin, B. et al. High-performance terahertz sensing at exceptional points in a bilayer structure. Adv. Theory Simul. 1, 1800070 (2018).

    Article  Google Scholar 

  30. Park, J.-H. et al. Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing. Nat. Phys. 16, 462–468 (2020).

    Article  CAS  Google Scholar 

  31. Nag Chowdhury, B., Lahiri, P., Johnson, N. P., De La Rue, R. M. & Lahiri, B. Exceptional-point-enhanced superior sensing using asymmetric coupled-lossy-resonator based optical metasurface. Laser Photonics Rev. 19, 2401661 (2024).

    Article  Google Scholar 

  32. Wang, L. et al. Resonant exceptional points sensing in terahertz metasurfaces. Appl. Phys. Lett. 124, 131701 (2024).

    Article  CAS  Google Scholar 

  33. Li, T. et al. Chip-scale metaphotonic singularities: topological, dynamical, and practical aspects. Chip 3, 100109 (2024).

    Article  Google Scholar 

  34. Chen, J. et al. Continuous lines of topological singularities in metasurface scattering matrices: from nodal to exceptional. ACS Photonics 12, 3208–3216 (2025).

    Article  CAS  Google Scholar 

  35. Su, V.-C., Chu, C. H., Sun, G. & Tsai, D. P. Advances in optical metasurfaces: fabrication and applications [Invited]. Opt. Express 26, 13148 (2018).

    Article  CAS  PubMed  Google Scholar 

  36. Chen, Z. & Segev, M. Highlighting photonics: looking into the next decade. eLight 1, 2 (2021).

    Article  CAS  Google Scholar 

  37. Özdemir, ŞK. Fermi arcs connect topological degeneracies. Science 359, 995–996 (2018).

    Article  PubMed  Google Scholar 

  38. Huang, X., Lai, Y., Hang, Z. H., Zheng, H. & Chan, C. T. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater. 10, 582–586 (2011).

    Article  CAS  PubMed  Google Scholar 

  39. Lu, L. et al. Experimental observation of Weyl points. Science 349, 622–624 (2015).

    Article  CAS  PubMed  Google Scholar 

  40. Zhen, B. et al. Spawning rings of exceptional points out of Dirac cones. Nature 525, 354–358 (2015).

    Article  CAS  PubMed  Google Scholar 

  41. Sakoda, K. Proof of the universality of mode symmetries in creating photonic Dirac cones. Opt. Express 20, 25181–25194 (2012).

    Article  PubMed  Google Scholar 

  42. Zhou, H. et al. Observation of bulk Fermi arc and polarization half charge from paired exceptional points. Science 359, 1009–1012 (2018).

    Article  CAS  PubMed  Google Scholar 

  43. Cerjan, A. et al. Experimental realization of a Weyl exceptional ring. Nat. Photonics 13, 623–628 (2019).

    Article  CAS  Google Scholar 

  44. Chen, W., Yang, Q., Chen, Y. & Liu, W. Evolution and global charge conservation for polarization singularities emerging from non-Hermitian degeneracies. Proc. Natl Acad. Sci. USA 118, e2019578118 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Deng, Z.-L., Li, F.-J., Li, H., Li, X. & Alù, A. Extreme diffraction control in metagratings leveraging bound states in the continuum and exceptional points. Laser Photonics Rev. 16, 2100617 (2022).

    Article  Google Scholar 

  46. Lin, Z., Pick, A., Lončar, M. & Rodriguez, A. W. Enhanced spontaneous emission at third-order Dirac exceptional points in inverse-designed photonic crystals. Phys. Rev. Lett. 117, 107402 (2016).

    Article  PubMed  Google Scholar 

  47. Yang, Y. et al. Photonic flatband resonances for free-electron radiation. Nature 613, 42–47 (2023).

    Article  CAS  PubMed  Google Scholar 

  48. Vicencio Poblete, R. A. Photonic flat band dynamics. Adv. Phys. X 6, 1878057 (2021).

    Google Scholar 

  49. Mao, X.-R., Shao, Z.-K., Luan, H.-Y., Wang, S.-L. & Ma, R.-M. Magic-angle lasers in nanostructured Moiré superlattice. Nat. Nanotechnol. 16, 1099–1105 (2021).

    Article  CAS  PubMed  Google Scholar 

  50. Kolkowski, R., Kovaios, S. & Koenderink, A. F. Pseudochirality at exceptional rings of optical metasurfaces. Phys. Rev. Res. 3, 023185 (2021).

    Article  CAS  Google Scholar 

  51. Masharin, M. A. et al. Room-temperature exceptional-point-driven polariton lasing from perovskite metasurface. Adv. Funct. Mater. 33, 2215007 (2023).

    Article  CAS  Google Scholar 

  52. Masharin, M. A. et al. Giant ultrafast all-optical modulation based on exceptional points in exciton–polariton perovskite metasurfaces. ACS Nano 18, 3447–3455 (2024).

    Article  CAS  PubMed  Google Scholar 

  53. Wang, J. et al. Optical bound states in the continuum in periodic structures: mechanisms, effects, and applications. Photonics Insights 3, R01 (2024).

    Article  Google Scholar 

  54. Zhang, Y. et al. Observation of polarization vortices in momentum space. Phys. Rev. Lett. 120, 186103 (2018).

    Article  CAS  PubMed  Google Scholar 

  55. Zhang, Y. et al. Momentum-space imaging spectroscopy for the study of nanophotonic materials. Sci. Bull. 66, 824–838 (2021).

    Article  CAS  Google Scholar 

  56. Cerjan, A., Raman, A. & Fan, S. Exceptional contours and band structure design in parity-time symmetric photonic crystals. Phys. Rev. Lett. 116, 203902 (2016).

    Article  PubMed  Google Scholar 

  57. Wang, H. et al. Exceptional concentric rings in a non-Hermitian bilayer photonic system. Phys. Rev. B 100, 165134 (2019).

    Article  CAS  Google Scholar 

  58. Zhou, H., Lee, J. Y., Liu, S. & Zhen, B. Exceptional surfaces in PT-symmetric non-Hermitian photonic systems. Optica 6, 190 (2019).

    Article  CAS  Google Scholar 

  59. Isobe, T., Yoshida, T. & Hatsugai, Y. Topological band theory of a generalized eigenvalue problem with Hermitian matrices: symmetry-protected exceptional rings with emergent symmetry. Phys. Rev. B 104, L121105 (2021).

    Article  CAS  Google Scholar 

  60. Isobe, T., Yoshida, T. & Hatsugai, Y. A symmetry-protected exceptional ring in a photonic crystal with negative index media. Nanophotonics 12, 2335–2346 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  61. Kang, M., Zhang, T., Zhao, B., Sun, L. & Chen, J. Chirality of exceptional points in bianisotropic metasurfaces. Opt. Express 29, 11582–11590 (2021).

    Article  PubMed  Google Scholar 

  62. Wang, C., Sweeney, W. R., Stone, A. D. & Yang, L. Coherent perfect absorption at an exceptional point. Science 373, 1261–1265 (2021).

    Article  CAS  PubMed  Google Scholar 

  63. Zhou, H.-T. et al. Underwater scattering exceptional point by metasurface with fluid-solid interaction. Adv. Funct. Mater. 34, 2404282 (2024).

    Article  CAS  Google Scholar 

  64. Zhou, Z., Jia, B., Wang, N., Wang, X. & Li, Y. Observation of perfectly-chiral exceptional point via bound state in the continuum. Phys. Rev. Lett. 130, 116101 (2023).

    Article  CAS  PubMed  Google Scholar 

  65. Colom, R. et al. Crossing of the branch cut: the topological origin of a universal 2π-phase retardation in non-Hermitian metasurfaces. Laser Photonics Rev. 17, 2200976 (2023).

    Article  Google Scholar 

  66. Mikheeva, E. et al. Asymmetric phase modulation of light with parity-symmetry broken metasurfaces. Optica 10, 1287 (2023).

    Article  CAS  Google Scholar 

  67. Ge, L., Chong, Y. D. & Stone, A. D. Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures. Phys. Rev. A 85, 023802 (2012).

    Article  Google Scholar 

  68. Feng, L. et al. Demonstration of a large-scale optical exceptional point structure. Opt. Express 22, 1760–1767 (2014).

    Article  CAS  PubMed  Google Scholar 

  69. Gu, X. et al. Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling. Opt. Express 25, 11778 (2017).

    Article  CAS  PubMed  Google Scholar 

  70. Dong, S. et al. Loss-assisted metasurface at an exceptional point. ACS Photonics 7, 3321–3327 (2020).

    Article  CAS  Google Scholar 

  71. He, T. et al. Scattering exceptional point in the visible. Light Sci. Appl. 12, 229 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Liu, Q. et al. Exceptional points in Fano-resonant graphene metamaterials. Opt. Express 25, 7203–7212 (2017).

    Article  CAS  PubMed  Google Scholar 

  73. Gao, F., Zhou, J., Liu, H., Deng, J. & Yan, B. Topological metasurface of tunable, chiral VO2-based system with exceptional points in the dual band. J. Appl. Phys. 135, 063104 (2024).

    Article  CAS  Google Scholar 

  74. Feng, X. et al. Non-Hermitian hybrid silicon photonic switching. Nat. Photonics 19, 264–270 (2025).

    Article  CAS  Google Scholar 

  75. Collett, E. Field Guide to Polarization (SPIE, 2005).

  76. Balthasar Mueller, J. P., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017).

    Article  CAS  PubMed  Google Scholar 

  77. Kang, M., Chen, J. & Chong, Y. D. Chiral exceptional points in metasurfaces. Phys. Rev. A 94, 033834 (2016).

    Article  Google Scholar 

  78. Park, S. H. et al. Observation of an exceptional point in a non-Hermitian metasurface. Nanophotonics 9, 1031–1039 (2020).

    Article  Google Scholar 

  79. Yang, Z. et al. Creating pairs of exceptional points for arbitrary polarization control: asymmetric vectorial wavefront modulation. Nat. Commun. 15, 232 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Yang, Z. et al. Asymmetric full-color vectorial meta-holograms empowered by pairs of exceptional points. Nano Lett. 24, 844–851 (2024).

    Article  CAS  PubMed  Google Scholar 

  81. Wu, X., Zhao, X., Lin, Y., Lin, F. & Fang, Z. Twins of exceptional points with opposite chirality for non-Hermitian metasurfaces. ACS Photonics 11, 2054–2060 (2024).

    Article  CAS  Google Scholar 

  82. Fu, P. et al. Deep learning enabled topological design of exceptional points for multi-optical-parameter control. Commun. Phys. 6, 254 (2023).

    Article  Google Scholar 

  83. Gao, F. et al. High-performance full-Stokes polarization detection at exceptional point in a non-Hermitian metasurface. Appl. Phys. Lett. 123, 011705 (2023).

    Article  CAS  Google Scholar 

  84. Gao, F., Liu, H., Zhou, J., Deng, J. & Yan, B. The exceptional point of PT-symmetry metasurface: topological phase studies and highly sensitive refractive index sensing applications. J. Appl. Phys. 134, 093104 (2023).

    Article  CAS  Google Scholar 

  85. Hu, S., Wang, C., Du, S., Han, Z. & Gu, C. Dynamic and polarization-independent wavefront control based on hybrid topological metasurfaces. Nano Lett. 24, 2041–2047 (2024).

    Article  CAS  PubMed  Google Scholar 

  86. Indu Krishna, K. N. & Roy Chowdhury, D. Thin film sensing near exceptional point utilizing terahertz plasmonic metasurfaces. N. J. Phys. 26, 053033 (2024).

    Article  Google Scholar 

  87. Leung, H. M. et al. Exceptional point-based plasmonic metasurfaces for vortex beam generation. Opt. Express 28, 503–510 (2020).

    Article  CAS  PubMed  Google Scholar 

  88. Li, J., Fu, J., Liao, Q. & Ke, S. Exceptional points in chiral metasurface based on graphene strip arrays. J. Opt. Soc. Am. B 36, 2492–2498 (2019).

    Article  CAS  Google Scholar 

  89. Li, Y. et al. Bifunctional sensing based on an exceptional point with bilayer metasurfaces. Opt. Express 31, 492–501 (2023).

    Article  CAS  PubMed  Google Scholar 

  90. Li, Z. et al. Parity-time symmetry transition and exceptional points in terahertz metal–graphene hybrid metasurface with switchable transmission and reflection characteristics. Phys. Chem. Chem. Phys. 25, 6510–6518 (2023).

    Article  CAS  PubMed  Google Scholar 

  91. Li, Y. et al. Independent control of circularly polarized light with exceptional topological phase coding metasurfaces. Photonics Res. 12, 534–542 (2024).

    Article  CAS  Google Scholar 

  92. Li, H. et al. Nonlocal metasurface with chiral exceptional points in the telecom-band. Nano Lett. 24, 2087–2093 (2024).

    Article  CAS  PubMed  Google Scholar 

  93. Zhao, X. et al. Mode-interference-induced chiral exceptional points in momentum space. Laser Photonics Rev. 18, 2301257 (2024).

    Article  Google Scholar 

  94. Xie, X. et al. Generalized Pancharatnam-Berry phase in rotationally symmetric meta-atoms. Phys. Rev. Lett. 126, 183902 (2021).

    Article  CAS  PubMed  Google Scholar 

  95. Menzel, C., Rockstuhl, C. & Lederer, F. Advanced Jones calculus for the classification of periodic metamaterials. Phys. Rev. A 82, 053811 (2010).

    Article  Google Scholar 

  96. Qin, H. et al. Sphere of arbitrarily polarized exceptional points with a single planar metasurface. Nat. Commun. 16, 2656 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Ergoktas, M. S. et al. Topological engineering of terahertz light using electrically tunable exceptional point singularities. Science 376, 184–188 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  98. Ding, F., Deng, Y., Meng, C., Thrane, P. C. V. & Bozhevolnyi, S. I. Electrically tunable topological phase transition in non-Hermitian optical MEMS metasurfaces. Sci. Adv. 10, eadl4661 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  99. Yu, Z. et al. Creating anti-chiral exceptional points in non-Hermitian metasurfaces for efficient terahertz switching. Adv. Sci. 11, 2402615 (2024).

    Article  CAS  Google Scholar 

  100. He, W. et al. Loss-enabled chirality inversion in terahertz metasurfaces. Phys. Rev. Lett. 134, 106901 (2025).

    Article  CAS  PubMed  Google Scholar 

  101. Wang, L. et al. Photoswitchable exceptional points derived from bound states in the continuum. Light Sci. Appl. 14, 377 (2025).

    Article  PubMed  PubMed Central  Google Scholar 

  102. Zhao, H. et al. Non-Hermitian topological light steering. Science 365, 1163–1166 (2019).

    Article  CAS  PubMed  Google Scholar 

  103. Dai, T. et al. Non-Hermitian topological phase transitions controlled by nonlinearity. Nat. Phys. 20, 101–108 (2024).

    Article  CAS  Google Scholar 

  104. Ha, S. T. et al. Optoelectronic metadevices. Science 386, eadm7442 (2024).

    Article  CAS  PubMed  Google Scholar 

  105. Lee, H. et al. Chiral exceptional point enhanced active tuning and nonreciprocity in micro-resonators. Light Sci. Appl. 14, 45 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  106. Chen, P.-Y. & Jung, J. PT symmetry and singularity-enhanced sensing based on photoexcited graphene metasurfaces. Phys. Rev. Appl. 5, 064018 (2016).

    Article  Google Scholar 

  107. Farhat, M., Yang, M., Ye, Z. & Chen, P.-Y. PT-symmetric absorber-laser enables electromagnetic sensors with unprecedented sensitivity. ACS Photonics 7, 2080–2088 (2020).

    Article  CAS  Google Scholar 

  108. Park, S. H., Xia, S., Oh, S.-H., Avouris, P. & Low, T. Accessing the exceptional points in a graphene plasmon–vibrational mode coupled system. ACS Photonics 8, 3241–3248 (2021).

    Article  CAS  Google Scholar 

  109. Hu, Y. et al. Ultrafast control of braiding topology in non-Hermitian metasurfaces. Preprint at https://doi.org/10.48550/arXiv.2410.16756 (2024).

  110. Zheludev, N. I. & Kivshar, Y. S. From metamaterials to metadevices. Nat. Mater. 11, 917–924 (2012).

    Article  CAS  PubMed  Google Scholar 

  111. Wang, K., Dutt, A., Wojcik, C. C. & Fan, S. Topological complex-energy braiding of non-Hermitian bands. Nature 598, 59–64 (2021).

    Article  CAS  PubMed  Google Scholar 

  112. Tong, S. et al. Observation of Floquet-Bloch braids in non-Hermitian spatiotemporal lattices. Phys. Rev. Lett. 134, 126603 (2025).

    Article  CAS  PubMed  Google Scholar 

  113. Yang, Y. et al. Non-Abelian physics in light and sound. Science 383, eadf9621 (2024).

    Article  CAS  PubMed  Google Scholar 

  114. Guo, C.-X., Chen, S., Ding, K. & Hu, H. Exceptional non-Abelian topology in multiband non-Hermitian systems. Phys. Rev. Lett. 130, 157201 (2023).

    Article  CAS  PubMed  Google Scholar 

  115. Long, Y., Xue, H. & Zhang, B. Unsupervised learning of topological non-Abelian braiding in non-Hermitian bands. Nat. Mach. Intell. 6, 904–910 (2024).

    Article  Google Scholar 

  116. Zhang, Q. et al. Experimental characterization of three-band braid relations in non-Hermitian acoustic lattices. Phys. Rev. Res. 5, L022050 (2023).

    Article  CAS  Google Scholar 

  117. Patil, Y. S. S. et al. Measuring the knot of non-Hermitian degeneracies and non-commuting braids. Nature 607, 271–275 (2022).

    Article  CAS  PubMed  Google Scholar 

  118. Guria, C. et al. Resolving the topology of encircling multiple exceptional points. Nat. Commun. 15, 1369 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  119. Wojcik, C. C., Wang, K., Dutt, A., Zhong, J. & Fan, S. Eigenvalue topology of non-Hermitian band structures in two and three dimensions. Phys. Rev. B 106, L161401 (2022).

    Article  CAS  Google Scholar 

  120. Zhang, X.-L. et al. Non-Abelian braiding on photonic chips. Nat. Photonics 16, 390–395 (2022).

    Article  CAS  Google Scholar 

  121. Bonesteel, N. E., Hormozi, L., Zikos, G. & Simon, S. H. Braid topologies for quantum computation. Phys. Rev. Lett. 95, 140503 (2005).

    Article  CAS  PubMed  Google Scholar 

  122. Parto, M., Liu, Y. G. N., Bahari, B., Khajavikhan, M. & Christodoulides, D. N. Non-Hermitian and topological photonics: optics at an exceptional point. Nanophotonics 10, 403–423 (2021).

    Article  Google Scholar 

  123. Wang, H. et al. Topological physics of non-Hermitian optics and photonics: a review. J. Opt. 23, 123001 (2021).

    Article  CAS  Google Scholar 

  124. Nasari, H., Pyrialakos, G. G., Christodoulides, D. N. & Khajavikhan, M. Non-Hermitian topological photonics. Opt. Mater. Express 13, 870–885 (2023).

    Article  CAS  Google Scholar 

  125. Song, Q., Liu, X., Qiu, C.-W. & Genevet, P. Vectorial metasurface holography. Appl. Phys. Rev. 9, 011311 (2022).

    Article  CAS  Google Scholar 

  126. Shi, Y. et al. Optical manipulation with metamaterial structures. Appl. Phys. Rev. 9, 031303 (2022).

    Article  CAS  Google Scholar 

  127. Deng, Z.-L. & Li, G. Metasurface optical holography. Mater. Today Phys. 3, 16–32 (2017).

    Article  Google Scholar 

  128. Li, J. et al. Exploiting hidden singularity on the surface of the Poincaré sphere. Nat. Commun. 16, 5953 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  129. Azzam, S. I. & Kildishev, A. V. Photonic bound states in the continuum: from basics to applications. Adv. Opt. Mater. 9, 2001469 (2021).

    Article  CAS  Google Scholar 

  130. Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D. & Soljačić, M. Bound states in the continuum. Nat. Rev. Mater. 1, 16048 (2016).

    Article  CAS  Google Scholar 

  131. Qin, H. et al. Disorder-assisted real–momentum topological photonic crystal. Nature 639, 602–608 (2025).

    Article  CAS  PubMed  Google Scholar 

  132. Qin, H. et al. Arbitrarily polarized bound states in the continuum with twisted photonic crystal slabs. Light Sci. Appl. 12, 66 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  133. Canós Valero, A., Sztranyovszky, Z., Muljarov, E. A., Bogdanov, A. & Weiss, T. Exceptional bound states in the continuum. Phys. Rev. Lett. 134, 103802 (2025).

    Article  PubMed  Google Scholar 

  134. Qin, H. et al. Metasurface-embedded topological photonic crystal. Laser Photonics Rev. https://doi.org/10.1002/lpor.202501032 (2025).

  135. Rivero, J. H. D., Feng, L. & Ge, L. Imaginary gauge transformation in momentum space and Dirac exceptional point. Phys. Rev. Lett. 129, 243901 (2022).

    Article  CAS  PubMed  Google Scholar 

  136. Wu, Y., Zhu, D., Wang, Y., Rong, X. & Du, J. Experimental observation of Dirac exceptional points. Phys. Rev. Lett. 134, 153601 (2025).

    Article  CAS  PubMed  Google Scholar 

  137. Wang, J., Liu, J., Hu, P., Jiang, Q. & Han, D. Topological polarization singularities induced by non-Hermitian Dirac points. Phys. Rev. B 111, 035430 (2025).

    Article  CAS  Google Scholar 

  138. Li, H. et al. Manifestation of super chiral exceptional points in a plasmonic metasurface. Photonics Res. 12, 2863–2872 (2024).

    Article  Google Scholar 

  139. Oh, D. et al. Complete asymmetric polarization conversion at zero-eigenvalue exceptional points of non-Hermitian metasurfaces. Nanophotonics 13, 4409–4416 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  140. Baranov, D. G., Krasnok, A., Shegai, T., Alù, A. & Chong, Y. Coherent perfect absorbers: linear control of light with light. Nat. Rev. Mater. 2, 17064 (2017).

    Article  CAS  Google Scholar 

  141. Qin, H., Zhang, Z., Wang, J. & Fleury, R. Topological hysteretic winding for temporal anti-lasing. Nat. Commun. 16, 6189 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  142. Ramezani, H., Wang, Y., Yablonovitch, E. & Zhang, X. Unidirectional perfect absorber. IEEE J. Sel. Top. Quantum Electron. 22, 115–120 (2016).

    Article  Google Scholar 

  143. Jin, L. & Song, Z. Incident direction independent wave propagation and unidirectional lasing. Phys. Rev. Lett. 121, 073901 (2018).

    Article  CAS  PubMed  Google Scholar 

  144. Chen, J. et al. Observation of hybrid degenerate point in projected non-Hermitian metasurfaces. Phys. Rev. Lett. 135, 116601 (2025).

    Article  CAS  PubMed  Google Scholar 

  145. Caloz, C. et al. Electromagnetic nonreciprocity. Phys. Rev. Appl. 10, 047001 (2018).

    Article  CAS  Google Scholar 

  146. Mahmoud, A. M., Davoyan, A. R. & Engheta, N. All-passive nonreciprocal metastructure. Nat. Commun. 6, 8359 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  147. Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017).

    Article  CAS  PubMed  Google Scholar 

  148. You, J. W. et al. Topological metasurface: from passive toward active and beyond. Photonics Res. 11, B65–B102 (2023).

    Article  Google Scholar 

  149. Qian, C., Kaminer, I. & Chen, H. A guidance to intelligent metamaterials and metamaterials intelligence. Nat. Commun. 16, 1154 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  150. Ruan, Y.-P. et al. Observation of loss-enhanced magneto-optical effect. Nat. Photonics 9, 109–115 (2024).

    Google Scholar 

  151. Rao, Z. et al. Braiding reflectionless states in non-Hermitian magnonics. Nat. Phys. 20, 1904–1911 (2024).

    Article  CAS  Google Scholar 

  152. Ji, K. et al. Tracking exceptional points above the lasing threshold. Nat. Commun. 14, 8304 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  153. Xue, Z. et al. Fully forward mode training for optical neural networks. Nature 632, 280–286 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  154. Fu, P. et al. Achieving higher-order exceptional points in a terahertz metasurface. Nano Lett. 25, 3773–3780 (2025).

    Article  CAS  PubMed  Google Scholar 

  155. Gao, X., He, H., Sobolewski, S., Cerjan, A. & Hsu, C. W. Dynamic gain and frequency comb formation in exceptional-point lasers. Nat. Commun. 15, 8618 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  156. Wang, C. et al. Enhancement of magnonic frequency combs by exceptional points. Nat. Phys. 20, 1139–1144 (2024).

    Article  CAS  Google Scholar 

  157. Zhu, Y. et al. Storing light near an exceptional point. Nat. Commun. 15, 8101 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  158. Guo, T. et al. Durable and programmable ultrafast nanophotonic matrix of spectral pixels. Nat. Nanotechnol. 19, 1635–1643 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  159. Tripathi, A. et al. Tunable Mie-resonant dielectric metasurfaces based on VO2 phase-transition materials. ACS Photonics 8, 1206–1213 (2021).

    Article  CAS  Google Scholar 

  160. Chu, C. H. et al. Active dielectric metasurface based on phase-change medium. Laser Photonics Rev. 10, 986–994 (2016).

    Article  CAS  Google Scholar 

  161. Sha, X. et al. Chirality tuning and reversing with resonant phase-change metasurfaces. Sci. Adv. 10, eadn9017 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  162. Tian, J. et al. Phase-change perovskite microlaser with tunable polarization vortex. Adv. Mater. 35, 2207430 (2023).

    Article  CAS  Google Scholar 

  163. Lv, W. et al. Robust generation of intrinsic C points with magneto-optical bound states in the continuum. Sci. Adv. 10, eads0157 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  164. Kim, D., Baucour, A., Choi, Y.-S., Shin, J. & Seo, M.-K. Spontaneous generation and active manipulation of real-space optical vortices. Nature 611, 48–54 (2022).

    Article  CAS  PubMed  Google Scholar 

  165. Kim, D. et al. Dynamic realization of emergent high-dimensional optical vortices. Nat. Commun. 16, 9788 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  166. Engheta, N. Four-dimensional optics using time-varying metamaterials. Science 379, 1190–1191 (2023).

    Article  CAS  PubMed  Google Scholar 

  167. Galiffi, E. et al. Photonics of time-varying media. Adv. Photonics 4, 014002 (2022).

    Article  CAS  Google Scholar 

  168. Yin, S., Galiffi, E. & Alù, A. Floquet metamaterials. eLight 2, 8 (2022).

    Article  Google Scholar 

  169. Tang, W. et al. Exceptional nexus with a hybrid topological invariant. Science 370, 1077–1080 (2020).

    Article  CAS  PubMed  Google Scholar 

  170. Zenbaa, N. et al. A universal inverse-design magnonic device. Nat. Electron. 8, 106–115 (2025).

    Google Scholar 

  171. Zheng, H. et al. Multichannel meta-imagers for accelerating machine vision. Nat. Nanotechnol. 19, 471–478 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  172. Nadell, C. C., Huang, B., Malof, J. M. & Padilla, W. J. Deep learning for accelerated all-dielectric metasurface design. Opt. Express 27, 27523–27535 (2019).

    Article  CAS  PubMed  Google Scholar 

  173. Wu, N. et al. Intelligent nanophotonics: when machine learning sheds light. eLight 5, 5 (2025).

    Article  Google Scholar 

  174. Fadelli, I. The first experimental observation of Dirac exceptional points. Phys.org https://phys.org/news/2025-04-experimental-dirac-exceptional.html (2025).

  175. Horn, R. A. & Johnson, C. R. Matrix Analysis (Cambridge Univ. Press, 2012).

  176. Haus, H. A. & Huang, W. Coupled-mode theory. Proc. IEEE 79, 1505–1518 (1991).

    Article  Google Scholar 

  177. Chong, Y. D., Ge, L. & Stone, A. D. PT-symmetry breaking and laser-absorber modes in optical scattering systems. Phys. Rev. Lett. 106, 093902 (2011).

    Article  CAS  PubMed  Google Scholar 

  178. Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).

    Article  Google Scholar 

  179. Heiss, W. D. The physics of exceptional points. J. Phys. A Math. Theor. 45, 444016 (2012).

    Article  Google Scholar 

  180. Schucan, T. H. & Weidenmüller, H. A. The effective interaction in nuclei and its perturbation expansion: an algebraic approach. Ann. Phys. 73, 108–135 (1972).

    Article  CAS  Google Scholar 

  181. Bender, C. M. & Hook, D. W. PT -symmetric quantum mechanics. Rev. Mod. Phys. 96, 045002 (2024).

    Article  CAS  Google Scholar 

  182. Wiersig, J. Petermann factors and phase rigidities near exceptional points. Phys. Rev. Res. 5, 033042 (2023).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

H.Q. and Z.Z. thank J. Wang and Q. Chen for the helpful discussions. C.-W.Q. acknowledges the financial support of the Ministry of Education, Republic of Singapore (grant numbers A-8002152-00-00, A-8002458-00-00 and A-8003643-00-00), and the Competitive Research Program Award (NRF-CRP26-2021-0004 and NRF-CRP30-2023-0003) from the National Research Foundation, Prime Minister’s Office, Singapore. Q.S. acknowledges funding support from the National Natural Science Foundation of China (no. 12474388) and the Guangdong Basic and Applied Basic Research Foundation (no. 2025A1515011483).

Author information

Authors and Affiliations

Authors

Contributions

C.-W.Q., P.G., R.F., H.Q., Q.S., B.L. and J.Z. discussed the content of the Review. H.Q., W.L., Z.Z., M.L., Z.Y., J.L. and Q.S. wrote the first draft. All authors reviewed and edited the final manuscript.

Corresponding authors

Correspondence to Romain Fleury, Patrice Genevet, Qinghua Song or Cheng-Wei Qiu.

Ethics declarations

Competing interests

The authors declare no conflict of interest.

Peer review

Peer review information

Nature Reviews Materials thanks Liang Feng for his contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, H., Lv, W., Zhang, Z. et al. Photonic exceptional points in engineered materials and their emerging applications. Nat Rev Mater (2026). https://doi.org/10.1038/s41578-026-00896-5

Download citation

  • Accepted:

  • Published:

  • Version of record:

  • DOI: https://doi.org/10.1038/s41578-026-00896-5

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing