Exceptional points and non-Hermitian photonics at the nanoscale
Source abstract
Abstract
Exceptional points (EPs) arising in non-Hermitian systems have led to a variety of intriguing wave phenomena, and have been attracting increased interest in various physical platforms. In this Review, we highlight the latest fundamental advances in the context of EPs in various nanoscale systems, and overview the theoretical progress related to EPs, including higher-order EPs, bulk Fermi arcs and Weyl exceptional rings. We peek into EP-associated emerging technologies, in particular focusing on the influence of noise for sensing near EPs, improving the efficiency in asymmetric transmission based on EPs, optical isolators in nonlinear EP systems and novel concepts to implement EPs in topological photonics. We also discuss the constraints and limitations of the applications relying on EPs, and offer parting thoughts about promising ways to tackle them for advanced nanophotonic applications.
Source: europepmc · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Quantum Mechanics and Non-Hermitian Physics · Advanced Fiber Laser Technologies · Mechanical and Optical Resonators
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).10.1103/PhysRevLett.80.5243 ↗
2. Mostafazadeh, A. Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. J. Math. Phys. 43, 205–214 (2002).10.1063/1.1418246 ↗
3. Mostafazadeh, A. Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum. J. Math. Phys. 43, 2814–2816 (2002).10.1063/1.1461427 ↗
4. Bender, C. M., Boettcher, S. & Meisinger, P. N. PT-symmetric quantum mechanics. J. Math. Phys. 40, 2201–2229 (1999).10.1063/1.532860 ↗
5. Kato, T. Perturbation Teory of Linear Operators (Springer, 1966).10.1007/978-3-662-12678-3 ↗
6. Berry, M. V. & Wilkinson, M. Diabolical points in the spectra of triangles. Proc. R. Soc. Lond. A 392, 15–43 (1984).10.1098/rspa.1984.0022 ↗
7. Keck, F., Korsch, H. J. & Mossmann, S. Unfolding a diabolic point: a generalized crossing scenario. J. Phys. A 36, 2125–2137 (2003).10.1088/0305-4470/36/8/310 ↗
8. Yang, J. et al. Diabolical points in coupled active cavities with quantum emitters. Light. Sci. Appl. 9, 6 (2020).10.1038/s41377-020-0244-9 ↗
9. Heiss, W. D. Repulsion of resonance states and exceptional points. Phys. Rev. E 61, 929–932 (2000).10.1103/PhysRevE.61.929 ↗
10. El-Ganainy, R., Makris, K. G., Christodoulides, D. N. & Musslimani, Z. H. Theory of coupled optical PT-symmetric structures. Opt. Lett. 32, 2632–2634 (2007).10.1364/OL.32.002632 ↗
11. Guo, A. et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009).10.1103/PhysRevLett.103.093902 ↗
12. Rüter, C. E. et al. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010).10.1038/nphys1515 ↗
13. Kottos, T. Broken symmetry makes light work. Nat. Phys. 6, 166–167 (2010).10.1038/nphys1612 ↗
14. Miri, M.-A. & Alù, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).10.1126/science.aar7709 ↗
15. Özdemir, Ş. K., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry and exceptional points in photonics. Nat. Mater. 18, 783–798 (2019).10.1038/s41563-019-0304-9 ↗
16. Hokmabadi, M. P., Schumer, A., Christodoulides, D. N. & Khajavikhan, M. Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity. Nature 576, 70–74 (2019).10.1038/s41586-019-1780-4 ↗
17. Song, W. et al. Breakup and recovery of topological zero modes in finite non-Hermitian optical lattices. Phys. Rev. Lett. 123, 165701 (2019).10.1103/PhysRevLett.123.165701 ↗
18. Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics based on parity–time symmetry. Nat. Photon. 11, 752–762 (2017).10.1038/s41566-017-0031-1 ↗
19. El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).10.1038/nphys4323 ↗
20. Wang, C. et al. Electromagnetically induced transparency at a chiral exceptional point. Nat. Phys. 16, 334–340 (2020).10.1038/s41567-019-0746-7 ↗
21. Zhang, F., Feng, Y., Chen, X., Ge, L. & Wan, W. Synthetic snti-PT symmetry in a single microcavity. Phys. Rev. Lett. 124, 053901 (2020).10.1103/PhysRevLett.124.053901 ↗
22. Zhang, H. et al. Breaking anti-PT symmetry by spinning a resonator. Nano Lett. 20, 7594–7599 (2020).10.1021/acs.nanolett.0c03119 ↗
23. Maayani, S. et al. Flying couplers above spinning resonators generate irreversible refraction. Nature 558, 569–572 (2018).10.1038/s41586-018-0245-5 ↗
24. 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 Photon. 8, 3241–3248 (2021).10.1021/acsphotonics.1c01083 ↗
25. Bergman, A. et al. Observation of anti-parity–time-symmetry, phase transitions and exceptional points in an optical fibre. Nat. Commun. 12, 486 (2021).10.1038/s41467-020-20797-7 ↗
26. Öztürk, F. E. et al. Observation of a non-Hermitian phase transition in an optical quantum gas. Science 372, 88–91 (2021).10.1126/science.abe9869 ↗
27. Hlushchenko, A. V., Novitsky, D. V., Shcherbinin, V. I. & Tuz, V. R. Multimode PT-symmetry thresholds and third-order exceptional points in coupled dielectric waveguides with loss and gain. J. Opt. 23, 125002 (2021).10.1088/2040-8986/ac31d4 ↗
28. Xia, S. et al. Higher-order exceptional point and Landau–Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices. APL Photon. 6, 126106 (2021).10.1063/5.0069633 ↗
29. Laha, A., Beniwal, D., Dey, S., Biswas, A. & Ghosh, S. Third-order exceptional point and successive switching among three states in an optical microcavity. Phys. Rev. A 101, 063829 (2020).10.1103/PhysRevA.101.063829 ↗
30. Habler, N. & Scheuer, J. Higher-order exceptional points: a route for flat-top optical filters. Phys. Rev. A 101, 043828 (2020).10.1103/PhysRevA.101.043828 ↗
31. Zhou, H. et al. Observation of bulk Fermi arc and polarization half charge from paired exceptional points. Science 359, 1009–1012 (2018).10.1126/science.aap9859 ↗
32. Xiao, Z. & Alù, A. Tailoring exceptional points in a hybrid PT-symmetric and anti-PT-symmetric scattering system. Nanophotonics 10, 3723–3733 (2021).10.1515/nanoph-2021-0245 ↗
33. 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).10.1073/pnas.2019578118 ↗
34. Bauer, T. et al. Observation of optical polarization Möbius strips. Science 347, 964–966 (2015).10.1126/science.1260635 ↗
35. Miyai, E. et al. Lasers producing tailored beams. Nature 441, 946–946 (2006).10.1038/441946a ↗
36. Ding, K., Ma, G., Zhang, Z. Q. & Chan, C. T. Experimental demonstration of an anisotropic exceptional point. Phys. Rev. Lett. 121, 085702 (2018).10.1103/PhysRevLett.121.085702 ↗
37. Liao, Q. et al. Experimental measurement of the divergent quantum metric of an exceptional point. Phys. Rev. Lett. 127, 107402 (2021).10.1103/PhysRevLett.127.107402 ↗
38. Zhang, S. M., Zhang, X. Z., Jin, L. & Song, Z. High-order exceptional points in supersymmetric arrays. Phys. Rev. A 101, 033820 (2020).10.1103/PhysRevA.101.033820 ↗
39. Jin, L., Wu, H. C., Wei, B.-B. & Song, Z. Hybrid exceptional point created from type-III Dirac point. Phys. Rev. B 101, 045130 (2020).10.1103/PhysRevB.101.045130 ↗
40. Liu, T., He, J. J., Yang, Z. & Nori, F. Higher-order Weyl-exceptional-ring semimetals. Phys. Rev. Lett. 127, 196801 (2021).10.1103/PhysRevLett.127.196801 ↗
41. Ma, Y., Dong, B. & Lee, C. Progress of infrared guided-wave nanophotonic sensors and devices. Nano Converg. 7, 12 (2020).10.1186/s40580-020-00222-x ↗
42. Shakoor, A., Grant, J., Grande, M. & Cumming, D. R. S. Towards portable nanophotonic sensors. Sensors 19, 1715 (2019).10.3390/s19071715 ↗
43. Karabchevsky, A., Katiyi, A., Ang, A. S. & Hazan, A. On-chip nanophotonics and future challenges. Nanophotonics 9, 3733–3753 (2020).10.1515/nanoph-2020-0204 ↗
44. Sreekanth, K. V. et al. Extreme sensitivity biosensing platform based on hyperbolic metamaterials. Nat. Mater. 15, 621–627 (2016).10.1038/nmat4609 ↗
45. Meng, Y. et al. Optical meta-waveguides for integrated photonics and beyond. Light. Sci. Appl. 10, 235 (2021).10.1038/s41377-021-00655-x ↗
46. Oh, S.-H. et al. Nanophotonic biosensors harnessing van der Waals materials. Nat. Commun. 12, 3824 (2021).
47. Warning, L. A. et al. Nanophotonic approaches for chirality sensing. ACS Nano 15, 15538–15566 (2021).10.1021/acsnano.1c04992 ↗
48. Soler, M., Estevez, M. C., Cardenosa-Rubio, M., Astua, A. & Lechuga, L. M. How nanophotonic label-free biosensors can contribute to rapid and massive diagnostics of respiratory virus infections: COVID-19 case. ACS Sens. 5, 2663–2678 (2020).10.1021/acssensors.0c01180 ↗
49. Fedyanin, D. Y. & Stebunov, Y. V. All-nanophotonic NEMS biosensor on a chip. Sci. Rep. 5, 10968 (2015).10.1038/srep10968 ↗
50. Kaushik, V. et al. On-chip nanophotonic broadband wavelength detector with 2D-electron gas: nanophotonic platform for wavelength detection in visible spectral region. Nanophotonics 11, 289–296 (2022).10.1515/nanoph-2021-0365 ↗
51. Yu, X.-C. et al. Optically sizing single atmospheric particulates with a 10-nm resolution using a strong evanescent field. Light. Sci. Appl. 7, 18003–18003 (2018).10.1038/lsa.2018.3 ↗
52. Yan, Y.-Z. et al. Packaged silica microsphere-taper coupling system for robust thermal sensing application. Opt. Express 19, 5753–5759 (2011).10.1364/OE.19.005753 ↗
53. Yao, B. et al. Graphene-enhanced brillouin optomechanical microresonator for ultrasensitive gas detection. Nano Lett. 17, 4996–5002 (2017).10.1021/acs.nanolett.7b02176 ↗
54. Katō, T. Perturbation Theory for Linear Operators (Springer, 1995).10.1007/978-3-642-66282-9 ↗
55. Berry, M. V. Physics of nonhermitian degeneracies. Czech. J. Phys. 54, 1039–1047 (2004).10.1023/B:CJOP.0000044002.05657.04 ↗
56. Zhu, J. et al. On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator. Nat. Photon. 4, 46–49 (2010).10.1038/nphoton.2009.237 ↗
57. Wiersig, J. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection. Phys. Rev. Lett. 112, 203901 (2014).10.1103/PhysRevLett.112.203901 ↗
58. Wiersig, J. Sensors operating at exceptional points: general theory. Phys. Rev. A 93, 033809 (2016).10.1103/PhysRevA.93.033809 ↗
59. Wiersig, J. Review of exceptional point-based sensors. Photon. Res. 8, 1457–1467 (2020).10.1364/PRJ.396115 ↗
60. Chen, W., Kaya Ozdemir, S., Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017).10.1038/nature23281 ↗
61. Carlo, M. D., Leonardis, F. D., Soref, R. A. & Passaro, V. M. N. Design of a trap-assisted exceptional-surface-enhanced silicon-on-insulator particle sensor. J. Lightwave Technol. 40, 6021–6029 (2022).10.1109/JLT.2022.3185829 ↗
62. Li, J. et al. Exceptional point of nanocylinder-loaded silicon microring for single nanoparticle detection. Proc. SPIE 11979, 1197903 (2022).10.1117/12.2613637 ↗
63. Jiang, S. et al. Enhanced nanoparticle sensing by mode intensity in a non-reciprocally coupled microcavity. J. Appl. Phys. 131, 103106 (2022).10.1063/5.0082364 ↗
64. Zhong, Q. et al. Sensing with exceptional surfaces in order to combine sensitivity with robustness. Phys. Rev. Lett. 122, 153902 (2019).10.1103/PhysRevLett.122.153902 ↗
65. Hodaei, H. et al. Enhanced sensitivity at higher-order exceptional points. Nature 548, 187–191 (2017).10.1038/nature23280 ↗
66. Farhat, M., Yang, M., Ye, Z. & Chen, P.-Y. PT-symmetric absorber-laser enables electromagnetic sensors with unprecedented sensitivity. ACS Photon.7, 2080–2088 (2020).10.1021/acsphotonics.0c00514 ↗
67. Park, J.-H. et al. Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing. Nat. Phys. 16, 462–468 (2020).10.1038/s41567-020-0796-x ↗
68. Jiang, H. et al. Exceptional points and enhanced nanoscale sensing with a plasmon–exciton hybrid system. Photon. Res. 10, 557–563 (2022).10.1364/PRJ.445855 ↗
69. Feng, Z. & Sun, X. Giant enhancement of rotation sensing with PT-symmetric circular bragg lasers. Phys. Rev. Appl. 13, 054078 (2020).10.1103/PhysRevApplied.13.054078 ↗
70. Li, W. et al. Exceptional-surface-enhanced rotation sensing with robustness in a whispering-gallery-mode microresonator. Phys. Rev. A 104, 033505 (2021).10.1103/PhysRevA.104.033505 ↗
71. Lai, Y.-H., Lu, Y.-K., Suh, M.-G., Yuan, Z. & Vahala, K. Observation of the exceptional-point-enhanced Sagnac effect. Nature 576, 65–69 (2019).10.1038/s41586-019-1777-z ↗
72. Zhang, H., Peng, M., Xu, X.-W. & Jing, H. Anti-PT-symmetric Kerr gyroscope. Chin. Phys. B 31, 14215–014215 (2022).10.1088/1674-1056/ac3988 ↗
73. Wu, Y., Zhou, P., Li, T., Wan, W. & Zou, Y. High-order exceptional point based optical sensor. Opt. Express 29, 6080–6091 (2021).10.1364/OE.418644 ↗
74. Soper, A., Leefmans, C., Parto, M., Williams, J. & Marandi, A. Experimental realization of a 64th order exceptional point on a time-multiplexed photonic resonator network. Proc. SPIE https://doi.org/10.1117/12.2613404 (2022).10.1117/12.2613404 ↗
75. Khanbekyan, M. & Scheel, S. Enantiomer-discriminating sensing using optical cavities at exceptional points. Phys. Rev. A 105, 053711 (2022).10.1103/PhysRevA.105.053711 ↗
76. Chen, L. Measuring Newtonian constant of gravitation at an exceptional point in an optomechanical system. Opt. Commun. 520, 128534 (2022).10.1016/j.optcom.2022.128534 ↗
77. Mortensen, N. A. et al. Fluctuations and noise-limited sensing near the exceptional point of parity–time-symmetric resonator systems. Optica 5, 1342–1346 (2018).10.1364/OPTICA.5.001342 ↗
78. Xiao, Z., Li, H., Kottos, T. & Alù, A. Enhanced sensing and nondegraded thermal noise performance based on PT-symmetric electronic circuits with a sixth-order exceptional point. Phys. Rev. Lett. 123, 213901 (2019).10.1103/PhysRevLett.123.213901 ↗
79. Wang, H., Lai, Y.-H., Yuan, Z., Suh, M.-G. & Vahala, K. Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope. Nat. Commun. 11, 1610 (2020).
80. Wiersig, J. Prospects and fundamental limits in exceptional point-based sensing. Nat. Commun. 11, 2454 (2020).10.1038/s41467-020-16373-8 ↗
81. Kononchuk, R., Feinberg, J., Knee, J. & Kottos, T. Enhanced avionic sensing based on Wigners cusp anomalies. Sci. Adv. 7, eabg8118 (2021).10.1126/sciadv.abg8118 ↗
82. Wiersig, J. Robustness of exceptional-point-based sensors against parametric noise: the role of Hamiltonian and Liouvillian degeneracies. Phys. Rev. A 101, 053846 (2020).10.1103/PhysRevA.101.053846 ↗
83. Duggan, R., A. Mann, S. & Alù, A. Limitations of sensing at an exceptional point. ACS Photon. 9, 1554–1566 (2022).10.1021/acsphotonics.1c01535 ↗
84. Wolff, C., Tserkezis, C. & Mortensen, N. A. On the time evolution at a fluctuating exceptional point. Nanophotonics 8, 1319–1326 (2019).10.1515/nanoph-2019-0036 ↗
85. Langbein, W. No exceptional precision of exceptional-point sensors. Phys. Rev. A 98, 023805 (2018).10.1103/PhysRevA.98.023805 ↗
86. Grant, M. J. & Digonnet, M. J. F. Rotation sensitivity and shot-noise-limited detection in an exceptional-point coupled-ring gyroscope. Opt. Lett. 46, 2936–2939 (2021).10.1364/OL.423700 ↗
87. Kim, J. et al. Practical lineshape of a laser operating near an exceptional point. Sci. Rep. 11, 6164 (2021).
88. Lau, H.-K. & Clerk, A. A. Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun. 9, 4320 (2018).
89. Chen, C., Jin, L. & Liu, R.-B. Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system. New J. Phys. 21, 083002 (2019).10.1088/1367-2630/ab32ab ↗
90. Peters, K. J. H. & Rodriguez, S. R. K. Exceptional precision of a nonlinear optical sensor at a square-root singularity. Phys. Rev. Lett. 129, 013901 (2022).10.1103/PhysRevLett.129.013901 ↗
91. Smith, D. D., Chang, H., Mikhailov, E. E. & Shahriar, S. M. Beyond the Petermann limit: prospect of increasing sensor precision near exceptional points. Phys. Rev. A 106, 013520 (2022).10.1103/PhysRevA.106.013520 ↗
92. Dembowski, C. et al. Encircling an exceptional point. Phys. Rev. E 69, 056216 (2004).10.1103/PhysRevE.69.056216 ↗
93. Gao, T. et al. Observation of non-Hermitian degeneracies in a chaotic exciton–polariton billiard. Nature 526, 554–558 (2015).10.1038/nature15522 ↗
94. Milburn, T. J. et al. General description of quasiadiabatic dynamical phenomena near exceptional points. Phys. Rev. A 92, 052124 (2015).10.1103/PhysRevA.92.052124 ↗
95. Doppler, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).10.1038/nature18605 ↗
96. Zhang, X.-L., Jiang, T. & Chan, C. T. Dynamically encircling an exceptional point in anti-parity–time symmetric systems: asymmetric mode switching for symmetry-broken modes. Light. Sci. Appl. 8, 88 (2019).10.1038/s41377-019-0200-8 ↗
97. Yoon, J. W. et al. Time-asymmetric loop around an exceptional point over the full optical communications band. Nature 562, 86–90 (2018).10.1038/s41586-018-0523-2 ↗
98. Liu, Q. et al. Efficient mode transfer on a compact silicon chip by encircling moving exceptional points. Phys. Rev. Lett. 124, 153903 (2020).10.1103/PhysRevLett.124.153903 ↗
99. Li, A. et al. Hamiltonian hopping for efficient chiral mode switching in encircling exceptional points. Phys. Rev. Lett. 125, 187403 (2020).10.1103/PhysRevLett.125.187403 ↗
100. Shu, X. et al. Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters. Nat. Commun. 13, 2123 (2022).