Bender, C. M. & Boettcher, S. Actual spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).
Mostafazadeh, A. Pseudo-Hermiticity versus PT symmetry: the required situation for the fact of the spectrum of a non-Hermitian Hamiltonian. J. Math. Phys. 43, 205–214 (2002).
Mostafazadeh, A. Pseudo-Hermiticity versus PT-symmetry. II. An entire characterization of non-Hermitian Hamiltonians with an actual spectrum. J. Math. Phys. 43, 2814–2816 (2002).
Bender, C. M., Boettcher, S. & Meisinger, P. N. PT-symmetric quantum mechanics. J. Math. Phys. 40, 2201–2229 (1999).
Kato, T. Perturbation Teory of Linear Operators (Springer, 1966).
Berry, M. V. & Wilkinson, M. Diabolical factors within the spectra of triangles. Proc. R. Soc. Lond. A 392, 15–43 (1984).
Keck, F., Korsch, H. J. & Mossmann, S. Unfolding a diabolic level: a generalized crossing state of affairs. J. Phys. A 36, 2125–2137 (2003).
Yang, J. et al. Diabolical factors in coupled energetic cavities with quantum emitters. Mild. Sci. Appl. 9, 6 (2020).
Heiss, W. D. Repulsion of resonance states and distinctive factors. Phys. Rev. E 61, 929–932 (2000).
El-Ganainy, R., Makris, Okay. G., Christodoulides, D. N. & Musslimani, Z. H. Idea of coupled optical PT-symmetric constructions. Decide. Lett. 32, 2632–2634 (2007).
Guo, A. et al. Remark of PT-symmetry breaking in advanced optical potentials. Phys. Rev. Lett. 103, 093902 (2009).
Rüter, C. E. et al. Remark of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010).
Kottos, T. Damaged symmetry makes mild work. Nat. Phys. 6, 166–167 (2010).
Miri, M.-A. & Alù, A. Distinctive factors in optics and photonics. Science 363, eaar7709 (2019).
Özdemir, Ş. Okay., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry and distinctive factors in photonics. Nat. Mater. 18, 783–798 (2019).
Hokmabadi, M. P., Schumer, A., Christodoulides, D. N. & Khajavikhan, M. Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity. Nature 576, 70–74 (2019).
Track, W. et al. Breakup and restoration of topological zero modes in finite non-Hermitian optical lattices. Phys. Rev. Lett. 123, 165701 (2019).
Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics primarily based on parity–time symmetry. Nat. Photon. 11, 752–762 (2017).
El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).
Wang, C. et al. Electromagnetically induced transparency at a chiral distinctive level. Nat. Phys. 16, 334–340 (2020).
Zhang, F., Feng, Y., Chen, X., Ge, L. & Wan, W. Artificial snti-PT symmetry in a single microcavity. Phys. Rev. Lett. 124, 053901 (2020).
Zhang, H. et al. Breaking anti-PT symmetry by spinning a resonator. Nano Lett. 20, 7594–7599 (2020).
Maayani, S. et al. Flying couplers above spinning resonators generate irreversible refraction. Nature 558, 569–572 (2018).
Park, S. H., Xia, S., Oh, S.-H., Avouris, P. & Low, T. Accessing the distinctive factors in a graphene plasmon–vibrational mode coupled system. ACS Photon. 8, 3241–3248 (2021).
Bergman, A. et al. Remark of anti-parity–time-symmetry, section transitions and distinctive factors in an optical fibre. Nat. Commun. 12, 486 (2021).
Öztürk, F. E. et al. Remark of a non-Hermitian section transition in an optical quantum fuel. Science 372, 88–91 (2021).
Hlushchenko, A. V., Novitsky, D. V., Shcherbinin, V. I. & Tuz, V. R. Multimode PT-symmetry thresholds and third-order distinctive factors in coupled dielectric waveguides with loss and achieve. J. Decide. 23, 125002 (2021).
Xia, S. et al. Larger-order distinctive level and Landau–Zener Bloch oscillations in pushed non-Hermitian photonic Lieb lattices. APL Photon. 6, 126106 (2021).
Laha, A., Beniwal, D., Dey, S., Biswas, A. & Ghosh, S. Third-order distinctive level and successive switching amongst three states in an optical microcavity. Phys. Rev. A 101, 063829 (2020).
Habler, N. & Scheuer, J. Larger-order distinctive factors: a route for flat-top optical filters. Phys. Rev. A 101, 043828 (2020).
Zhou, H. et al. Remark of bulk Fermi arc and polarization half cost from paired distinctive factors. Science 359, 1009–1012 (2018).
Xiao, Z. & Alù, A. Tailoring distinctive factors in a hybrid PT-symmetric and anti-PT-symmetric scattering system. Nanophotonics 10, 3723–3733 (2021).
Chen, W., Yang, Q., Chen, Y. & Liu, W. Evolution and world cost conservation for polarization singularities rising from non-Hermitian degeneracies. Proc. Natl Acad. Sci. USA 118, e2019578118 (2021).
Bauer, T. et al. Remark of optical polarization Möbius strips. Science 347, 964–966 (2015).
Miyai, E. et al. Lasers producing tailor-made beams. Nature 441, 946–946 (2006).
Ding, Okay., Ma, G., Zhang, Z. Q. & Chan, C. T. Experimental demonstration of an anisotropic distinctive level. Phys. Rev. Lett. 121, 085702 (2018).
Liao, Q. et al. Experimental measurement of the divergent quantum metric of an distinctive level. Phys. Rev. Lett. 127, 107402 (2021).
Zhang, S. M., Zhang, X. Z., Jin, L. & Track, Z. Excessive-order distinctive factors in supersymmetric arrays. Phys. Rev. A 101, 033820 (2020).
Jin, L., Wu, H. C., Wei, B.-B. & Track, Z. Hybrid distinctive level created from type-III Dirac level. Phys. Rev. B 101, 045130 (2020).
Liu, T., He, J. J., Yang, Z. & Nori, F. Larger-order Weyl-exceptional-ring semimetals. Phys. Rev. Lett. 127, 196801 (2021).
Ma, Y., Dong, B. & Lee, C. Progress of infrared guided-wave nanophotonic sensors and units. Nano Converg. 7, 12 (2020).
Shakoor, A., Grant, J., Grande, M. & Cumming, D. R. S. In direction of transportable nanophotonic sensors. Sensors 19, 1715 (2019).
Karabchevsky, A., Katiyi, A., Ang, A. S. & Hazan, A. On-chip nanophotonics and future challenges. Nanophotonics 9, 3733–3753 (2020).
Sreekanth, Okay. V. et al. Excessive sensitivity biosensing platform primarily based on hyperbolic metamaterials. Nat. Mater. 15, 621–627 (2016).
Meng, Y. et al. Optical meta-waveguides for built-in photonics and past. Mild. Sci. Appl. 10, 235 (2021).
Oh, S.-H. et al. Nanophotonic biosensors harnessing van der Waals supplies. Nat. Commun. 12, 3824 (2021).
Warning, L. A. et al. Nanophotonic approaches for chirality sensing. ACS Nano 15, 15538–15566 (2021).
Soler, M., Estevez, M. C., Cardenosa-Rubio, M., Astua, A. & Lechuga, L. M. How nanophotonic label-free biosensors can contribute to fast and large diagnostics of respiratory virus infections: COVID-19 case. ACS Sens. 5, 2663–2678 (2020).
Fedyanin, D. Y. & Stebunov, Y. V. All-nanophotonic NEMS biosensor on a chip. Sci. Rep. 5, 10968 (2015).
Kaushik, V. et al. On-chip nanophotonic broadband wavelength detector with 2D-electron fuel: nanophotonic platform for wavelength detection in seen spectral area. Nanophotonics 11, 289–296 (2022).
Yu, X.-C. et al. Optically sizing single atmospheric particulates with a 10-nm decision utilizing a powerful evanescent area. Mild. Sci. Appl. 7, 18003–18003 (2018).
Yan, Y.-Z. et al. Packaged silica microsphere-taper coupling system for sturdy thermal sensing utility. Decide. Specific 19, 5753–5759 (2011).
Yao, B. et al. Graphene-enhanced brillouin optomechanical microresonator for ultrasensitive fuel detection. Nano Lett. 17, 4996–5002 (2017).
Katō, T. Perturbation Idea for Linear Operators (Springer, 1995).
Berry, M. V. Physics of nonhermitian degeneracies. Czech. J. Phys. 54, 1039–1047 (2004).
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).
Wiersig, J. Enhancing the sensitivity of frequency and vitality splitting detection through the use of distinctive factors: utility to microcavity sensors for single-particle detection. Phys. Rev. Lett. 112, 203901 (2014).
Wiersig, J. Sensors working at distinctive factors: normal idea. Phys. Rev. A 93, 033809 (2016).
Wiersig, J. Assessment of outstanding point-based sensors. Photon. Res. 8, 1457–1467 (2020).
Chen, W., Kaya Ozdemir, S., Zhao, G., Wiersig, J. & Yang, L. Distinctive factors improve sensing in an optical microcavity. Nature 548, 192–196 (2017).
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).
Li, J. et al. Distinctive level of nanocylinder-loaded silicon microring for single nanoparticle detection. Proc. SPIE 11979, 1197903 (2022).
Jiang, S. et al. Enhanced nanoparticle sensing by mode depth in a non-reciprocally coupled microcavity. J. Appl. Phys. 131, 103106 (2022).
Zhong, Q. et al. Sensing with distinctive surfaces with a view to mix sensitivity with robustness. Phys. Rev. Lett. 122, 153902 (2019).
Hodaei, H. et al. Enhanced sensitivity at higher-order distinctive factors. Nature 548, 187–191 (2017).
Farhat, M., Yang, M., Ye, Z. & Chen, P.-Y. PT-symmetric absorber-laser allows electromagnetic sensors with unprecedented sensitivity. ACS Photon.7, 2080–2088 (2020).
Park, J.-H. et al. Symmetry-breaking-induced plasmonic distinctive factors and nanoscale sensing. Nat. Phys. 16, 462–468 (2020).
Jiang, H. et al. Distinctive factors and enhanced nanoscale sensing with a plasmon–exciton hybrid system. Photon. Res. 10, 557–563 (2022).
Feng, Z. & Solar, X. Large enhancement of rotation sensing with PT-symmetric round bragg lasers. Phys. Rev. Appl. 13, 054078 (2020).
Li, W. et al. Distinctive-surface-enhanced rotation sensing with robustness in a whispering-gallery-mode microresonator. Phys. Rev. A 104, 033505 (2021).
Lai, Y.-H., Lu, Y.-Okay., Suh, M.-G., Yuan, Z. & Vahala, Okay. Remark of the exceptional-point-enhanced Sagnac impact. Nature 576, 65–69 (2019).
Zhang, H., Peng, M., Xu, X.-W. & Jing, H. Anti-PT-symmetric Kerr gyroscope. Chin. Phys. B 31, 14215–014215 (2022).
Wu, Y., Zhou, P., Li, T., Wan, W. & Zou, Y. Excessive-order distinctive level primarily based optical sensor. Decide. Specific 29, 6080–6091 (2021).
Soper, A., Leefmans, C., Parto, M., Williams, J. & Marandi, A. Experimental realization of a sixty fourth order distinctive level on a time-multiplexed photonic resonator community. Proc. SPIE https://doi.org/10.1117/12.2613404 (2022).
Khanbekyan, M. & Scheel, S. Enantiomer-discriminating sensing utilizing optical cavities at distinctive factors. Phys. Rev. A 105, 053711 (2022).
Chen, L. Measuring Newtonian fixed of gravitation at an distinctive level in an optomechanical system. Decide. Commun. 520, 128534 (2022).
Mortensen, N. A. et al. Fluctuations and noise-limited sensing close to the distinctive level of parity–time-symmetric resonator techniques. Optica 5, 1342–1346 (2018).
Xiao, Z., Li, H., Kottos, T. & Alù, A. Enhanced sensing and nondegraded thermal noise efficiency primarily based on PT-symmetric digital circuits with a sixth-order distinctive level. Phys. Rev. Lett. 123, 213901 (2019).
Wang, H., Lai, Y.-H., Yuan, Z., Suh, M.-G. & Vahala, Okay. Petermann-factor sensitivity restrict close to an distinctive level in a Brillouin ring laser gyroscope. Nat. Commun. 11, 1610 (2020).
Wiersig, J. Prospects and basic limits in distinctive point-based sensing. Nat. Commun. 11, 2454 (2020).
Kononchuk, R., Feinberg, J., Knee, J. & Kottos, T. Enhanced avionic sensing primarily based on Wigners cusp anomalies. Sci. Adv. 7, eabg8118 (2021).
Wiersig, J. Robustness of exceptional-point-based sensors towards parametric noise: the function of Hamiltonian and Liouvillian degeneracies. Phys. Rev. A 101, 053846 (2020).
Duggan, R., A. Mann, S. & Alù, A. Limitations of sensing at an distinctive level. ACS Photon. 9, 1554–1566 (2022).
Wolff, C., Tserkezis, C. & Mortensen, N. A. On the time evolution at a fluctuating distinctive level. Nanophotonics 8, 1319–1326 (2019).
Langbein, W. No distinctive precision of exceptional-point sensors. Phys. Rev. A 98, 023805 (2018).
Grant, M. J. & Digonnet, M. J. F. Rotation sensitivity and shot-noise-limited detection in an exceptional-point coupled-ring gyroscope. Decide. Lett. 46, 2936–2939 (2021).
Kim, J. et al. Sensible lineshape of a laser working close to an distinctive level. Sci. Rep. 11, 6164 (2021).
Lau, H.-Okay. & Clerk, A. A. Elementary limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun. 9, 4320 (2018).
Chen, C., Jin, L. & Liu, R.-B. Sensitivity of parameter estimation close to the distinctive level of a non-Hermitian system. New J. Phys. 21, 083002 (2019).
Peters, Okay. J. H. & Rodriguez, S. R. Okay. Distinctive precision of a nonlinear optical sensor at a square-root singularity. Phys. Rev. Lett. 129, 013901 (2022).
Smith, D. D., Chang, H., Mikhailov, E. E. & Shahriar, S. M. Past the Petermann restrict: prospect of accelerating sensor precision close to distinctive factors. Phys. Rev. A 106, 013520 (2022).
Dembowski, C. et al. Encircling an distinctive level. Phys. Rev. E 69, 056216 (2004).
Gao, T. et al. Remark of non-Hermitian degeneracies in a chaotic exciton–polariton billiard. Nature 526, 554–558 (2015).
Milburn, T. J. et al. Basic description of quasiadiabatic dynamical phenomena close to distinctive factors. Phys. Rev. A 92, 052124 (2015).
Doppler, J. et al. Dynamically encircling an distinctive level for uneven mode switching. Nature 537, 76–79 (2016).
Zhang, X.-L., Jiang, T. & Chan, C. T. Dynamically encircling an distinctive level in anti-parity–time symmetric techniques: uneven mode switching for symmetry-broken modes. Mild. Sci. Appl. 8, 88 (2019).
Yoon, J. W. et al. Time-asymmetric loop round an distinctive level over the complete optical communications band. Nature 562, 86–90 (2018).
Liu, Q. et al. Environment friendly mode switch on a compact silicon chip by encircling shifting distinctive factors. Phys. Rev. Lett. 124, 153903 (2020).
Li, A. et al. Hamiltonian hopping for environment friendly chiral mode switching in encircling distinctive factors. Phys. Rev. Lett. 125, 187403 (2020).
Shu, X. et al. Quick encirclement of an distinctive level for extremely environment friendly and compact chiral mode converters. Nat. Commun. 13, 2123 (2022).
Wei, Y. et al. Anti-parity–time symmetry enabled on-chip chiral polarizer. Photon. Res. 10, 76–83 (2022).
Zhang, X.-L. & Chan, C. T. Dynamically encircling distinctive factors in a three-mode waveguide system. Commun. Phys. 2, 63 (2019).
Yu, F., Zhang, X.-L., Tian, Z.-N., Chen, Q.-D. & Solar, H.-B. Basic guidelines governing the dynamical encircling of an arbitrary variety of distinctive factors. Phys. Rev. Lett. 127, 253901 (2021).
Hassan, A. U. et al. Chiral state conversion with out encircling an distinctive level. Phys. Rev. A 96, 052129 (2017).
Liu, Q., Liu, J., Zhao, D. & Wang, B. On-chip experiment for chiral mode switch with out enclosing an distinctive level. Phys. Rev. A 103, 023531 (2021).
Nasari, H. et al. Remark of chiral state switch with out encircling an distinctive level. Nature 605, 256–261 (2022).
Khurgin, J. B. et al. Emulating exceptional-point encirclements utilizing imperfect (leaky) photonic parts: uneven mode-switching and omni-polarizer motion. Optica 8, 563–569 (2021).
Schumer, A. et al. Topological modes in a laser cavity by means of distinctive state switch. Science 375, 884–888 (2022).
Zhang, J.-Q. et al. Topological optomechanical amplifier in artificial PT-symmetry. Nanophotonics 11, 1149–1158 (2022).
Wang, H., Assawaworrarit, S. & Fan, S. Dynamics for encircling an distinctive level in a nonlinear non-Hermitian system. Decide. Lett. 44, 638–641 (2019).
Wang, Okay., Dutt, A., Wojcik, C. C. & Fan, S. Topological complex-energy braiding of non-Hermitian bands. Nature 598, 59–64 (2021).
Wojcik, C. C., Wang, Okay., Dutt, A., Zhong, J. & Fan, S. Eigenvalue topology of non-Hermitian band constructions in two and three dimensions. Phys. Rev. B 106, L161401 (2022).
Konotop, V. V., Yang, J. & Zezyulin, D. A. Nonlinear waves in PT-symmetric techniques. Rev. Mod. Phys. 88, 035002 (2016).
Liu, Z. et al. Excessive-Q quasibound states within the continuum for nonlinear metasurfaces. Phys. Rev. Lett. 123, 253901 (2019).
Hu, G. et al. Coherent steering of nonlinear chiral valley photons with an artificial Au–WS2 metasurface. Nat. Photon. 13, 467–472 (2019).
Choi, Y., Hahn, C., Yoon, J. W., Track, S. H. & Berini, P. Extraordinarily broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps close to distinctive factors. Nat. Commun. 8, 14154 (2017).
Ramezanpour, S. & Bogdanov, A. Tuning distinctive factors with Kerr nonlinearity. Phys. Rev. A 103, 043510 (2021).
Suwunnarat, S. et al. Non-linear coherent excellent absorption within the proximity of outstanding factors. Commun. Phys. 5, 5 (2022).
Assawaworrarit, S., Yu, X. & Fan, S. Strong wi-fi energy switch utilizing a nonlinear parity–time-symmetric circuit. Nature 546, 387–390 (2017).
Hassan, A. U., Hodaei, H., Miri, M.-A., Khajavikhan, M. & Christodoulides, D. N. Nonlinear reversal of the PT-symmetric section transition in a system of coupled semiconductor microring resonators. Phys. Rev. A 92, 063807 (2015).
Qin, L., Cling, C. & Huang, G. Controllable PT section transition and uneven soliton scattering in atomic gases with linear and nonlinear potentials. Phys. Rev. A 99, 043832 (2019).
Laha, A., Dey, S., Gandhi, H. Okay., Biswas, A. & Ghosh, S. Distinctive level and towards mode-selective optical isolation. ACS Photon. 7, 967–974 (2020).
Li, T., Gao, Z. & Xia, Okay. Nonlinear-dissipation-induced nonreciprocal distinctive factors. Decide. Specific 29, 17613–17627 (2021).
McIsaac, P. R. Mode orthogonality in reciprocal and nonreciprocal waveguides. IEEE Trans. Microw. Idea Tech. 39, 1808–1816 (1991).
Lahini, Y. et al. Impact of nonlinearity on adiabatic evolution of sunshine. Phys. Rev. Lett. 101, 193901 (2008).
Suwunnarat, S. et al. Enhanced nonlinear instabilities in photonic circuits with distinctive level degeneracies. Photon. Res. 8, 737–744 (2020).
Miri, M.-A. & Alù, A. Nonlinearity-induced PT-symmetry with out materials achieve. New J. Phys. 18, 065001 (2016).
Shi, Y., Yu, Z. & Fan, S. Limitations of nonlinear optical isolators as a consequence of dynamic reciprocity. Nat. Photon. 9, 388–392 (2015).
Ge, L. & El-Ganainy, R. Nonlinear modal interactions in parity–time (PT) symmetric lasers. Sci. Rep. 6, 24889 (2016).
Khanikaev, A. B. & Shvets, G. Two-dimensional topological photonics. Nat. Photon. 11, 763–773 (2017).
Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).
Yang, Y. et al. Terahertz topological photonics for on-chip communication. Nat. Photon. 14, 446–451 (2020).
Dai, T. et al. Topologically protected quantum entanglement emitters. Nat. Photon. 16, 248–257 (2022).
Midya, B., Zhao, H. & Feng, L. Non-Hermitian photonics guarantees distinctive topology of sunshine. Nat. Commun. 9, 2674 (2018).
Weimann, S. et al. Topologically protected sure states in photonic parity–time-symmetric crystals. Nat. Mater. 16, 433–438 (2017).
Zeuner, J. M. et al. Remark of a topological transition within the bulk of a non-Hermitian system. Phys. Rev. Lett. 115, 040402 (2015).
Pan, M., Zhao, H., Miao, P., Longhi, S. & Feng, L. Photonic zero mode in a non-Hermitian photonic lattice. Nat. Commun. 9, 1308 (2018).
Ni, X. et al. PT section transitions of edge states at PT symmetric interfaces in non-Hermitian topological insulators. Phys. Rev. B 98, 165129 (2018).
Kremer, M. et al. Demonstration of a two-dimensional PT-symmetric crystal. Nat. Commun. 10, 435 (2019).
Ao, Y. et al. Topological section transition within the non-Hermitian coupled resonator array. Phys. Rev. Lett. 125, 013902 (2020).
Wang, Okay. et al. Producing arbitrary topological windings of a non-Hermitian band. Science 371, 1240–1245 (2021).
Zhen, B. et al. Spawning rings of outstanding factors out of Dirac cones. Nature 525, 354–358 (2015).
Yao, S. & Wang, Z. Edge states and topological invariants of non-Hermitian techniques. Phys. Rev. Lett. 121, 086803 (2018).
Track, Y. et al. Two-dimensional non-Hermitian pores and skin impact in an artificial photonic lattice. Phys. Rev. Appl. 14, 064076 (2020).
Weidemann, S. et al. Topological funneling of sunshine. Science 368, 311–314 (2020).
Zhu, X. et al. Photonic non-Hermitian pores and skin impact and non-Bloch bulk-boundary correspondence. Phys. Rev. Res. 2, 013280 (2020).
Zhu, B. et al. Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian pores and skin impact. Phys. Rev. Lett. 129, 013903 (2022).
Cerjan, A. et al. Experimental realization of a Weyl distinctive ring. Nat. Photon. 13, 623–628 (2019).
Harari, G. et al. Topological insulator laser: idea. Science 359, eaar4003 (2018).
Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).
Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017).
Zeng, Y. et al. Electrically pumped topological laser with valley edge modes. Nature 578, 246–250 (2020).
Shao, Z.-Okay. et al. A high-performance topological bulk laser primarily based on band-inversion-induced reflection. Nat. Nanotechnol. 15, 67–72 (2020).
Contractor, R. et al. Scalable single-mode floor emitting laser by way of open-Dirac singularities. Nature 608, 692–698 (2022).
Zhao, H. et al. Non-Hermitian topological mild steering. Science 365, 1163–1166 (2019).
Gorlach, M. A. et al. Far-field probing of leaky topological states in all-dielectric metasurfaces. Nat. Commun. 9, 909 (2018).
Smirnova, D. et al. Third-harmonic era in photonic topological metasurfaces. Phys. Rev. Lett. 123, 103901 (2019).
You, J. W., Lan, Z. & Panoiu, N. C. 4-wave mixing of topological edge plasmons in graphene metasurfaces. Sci. Adv. 6, eaaz3910 (2020).
Park, S. H. et al. Remark of an distinctive level in a non-Hermitian metasurface. Nanophotonics 9, 1031–1039 (2020).
Li, Z. et al. Non-hermitian electromagnetic metasurfaces at distinctive factors. Prog. Electromagn. Res. 171, 1–20 (2021).
Yang, F. et al. Non-Hermitian metasurface with non-trivial topology. Nanophotonics 11, 1159–1165 (2022).
Track, Q., Odeh, M., Zúñiga-Pérez, J., Kanté, B. & Genevet, P. Plasmonic topological metasurface by encircling an distinctive level. Science 373, 1133–1137 (2021).
Smirnova, D., Leykam, D., Chong, Y. & Kivshar, Y. Nonlinear topological photonics. Appl. Phys. Rev. 7, 021306 (2020).
Parto, M., Liu, Y. G. N., Bahari, B., Khajavikhan, M. & Christodoulides, D. N. Non-Hermitian and topological photonics: optics at an distinctive level. Nanophotonics 10, 403–423 (2021).
Xia, S. et al. Nonlinear tuning of PT symmetry and non-Hermitian topological states. Science 372, 72–76 (2021).
Soleymani, S. et al. Chiral and degenerate excellent absorption on distinctive surfaces. Nat. Commun. 13, 599 (2022).
Yulaev, A. et al. Distinctive factors in lossy media result in deep polynomial wave penetration with spatially uniform energy loss. Nat. Nanotechnol. 17, 583–589 (2022).
Li, A. et al. Riemann-encircling distinctive factors for environment friendly uneven polarization-locked units. Phys. Rev. Lett. 129, 127401 (2022).
Hokmabadi, M. P., Nye, N. S., El-Ganainy, R., Christodoulides, D. N. & Khajavikhan, M. Supersymmetric laser arrays. Science 363, 623–626 (2019).
Kang, M., Chen, J. & Chong, Y. D. Chiral distinctive factors in metasurfaces. Phys. Rev. A 94, 033834 (2016).
Ezawa, M. Nonlinear non-Hermitian higher-order topological laser. Phys. Rev. Res. 4, 013195 (2022).
