[1] Xiao D, Chang M C, Niu Q A. Berry phase effects on electronic properties[J]. Reviews of Modern Physics, 82, 1959-2007(2010).

[2] Hasan M Z, Kane C L. Colloquium: topological insulators[J]. Reviews of Modern Physics, 82, 3045-3067(2010).

[3] Qi X L, Zhang S C. Topological insulators and superconductors[J]. Reviews of Modern Physics, 83, 1057-1110(2011).

[4] Lu L, Joannopoulos J D, Soljačić M. Topological photonics[J]. Nature Photonics, 8, 821-829(2014).

[5] Ozawa T, Price H M, Amo A et al. Topological photonics[J]. Reviews of Modern Physics, 91, 015006(2019).

[6] Chen J F, Liang W Y, Li Z Y. Progress of topological photonic state in magneto-optical photonic crystal[J]. Acta Optica Sinica, 41, 0823015(2021).

[7] Bergholtz E J, Budich J C, Kunst F K. Exceptional topology of non-Hermitian systems[J]. Reviews of Modern Physics, 93, 015005(2021).

[8] El-Ganainy R, Makris K G, Khajavikhan M et al. Non-Hermitian physics and PT symmetry[J]. Nature Physics, 14, 11-19(2018).

[9] Feng L, El-Ganainy R, Ge L. Non-Hermitian photonics based on parity-time symmetry[J]. Nature Photonics, 11, 752-762(2017).

[10] Özdemir Ş K, Rotter S, Nori F et al. Parity–time symmetry and exceptional points in photonics[J]. Nature Materials, 18, 783-798(2019).

[11] Miri M A, Alù A. Exceptional points in optics and photonics[J]. Science, 363, eaar7709(2019).

[12] Guo A, Salamo G J, Duchesne D et al. Observation of PT-symmetry breaking in complex optical potentials[J]. Physical Review Letters, 103, 093902(2009).

[13] Doppler J, Mailybaev A A, Böhm J et al. Dynamically encircling an exceptional point for asymmetric mode switching[J]. Nature, 537, 76-79(2016).

[14] Lafalce E, Zeng Q J, Lin C H et al. Robust lasing modes in coupled colloidal quantum dot microdisk pairs using a non-Hermitian exceptional point[J]. Nature Communications, 10, 561(2019).

[15] Zhu B F, Wang Q A, Leykam D et al. Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect[J]. Physical Review Letters, 129, 013903(2022).

[16] Xu H, Mason D, Jiang L Y et al. Topological energy transfer in an optomechanical system with exceptional points[J]. Nature, 537, 80-83(2016).

[17] Assawaworrarit S, Yu X F, Fan S H. Robust wireless power transfer using a nonlinear parity-time-symmetric circuit[J]. Nature, 546, 387-390(2017).

[18] Liu Q J, Li S Y, Wang B et al. Efficient mode transfer on a compact silicon chip by encircling moving exceptional points[J]. Physical Review Letters, 124, 153903(2020).

[19] Li A D, Chen W J, Wei H et al. Riemann-encircling exceptional points for efficient asymmetric polarization-locked devices[J]. Physical Review Letters, 129, 127401(2022).

[20] Zhong Q, Khajavikhan M, Christodoulides D N et al. Winding around non-Hermitian singularities[J]. Nature Communications, 9, 4808(2018).

[21] Zhou H Y, Peng C, Yoon Y et al. Observation of bulk Fermi arc and polarization half charge from paired exceptional points[J]. Science, 359, 1009-1012(2018).

[22] Zhen B, Hsu C W, Igarashi Y et al. Spawning rings of exceptional points out of Dirac cones[J]. Nature, 525, 354-358(2015).

[23] Cerjan A, Huang S, Wang M H et al. Experimental realization of a Weyl exceptional ring[J]. Nature Photonics, 13, 623-628(2019).

[24] Yao S Y, Wang Z. Edge states and topological invariants of non-Hermitian systems[J]. Physical Review Letters, 121, 086803(2018).

[25] Song W G, Sun W Z, Chen C et al. Breakup and recovery of topological zero modes in finite non-Hermitian optical lattices[J]. Physical Review Letters, 123, 165701(2019).

[26] Weimann S, Kremer M, Plotnik Y et al. Topologically protected bound states in photonic parity-time-symmetric crystals[J]. Nature Materials, 16, 433-438(2017).

[27] Poli C, Bellec M, Kuhl U et al. Selective enhancement of topologically induced interface states in a dielectric resonator chain[J]. Nature Communications, 6, 6710(2015).

[28] Zhao H, Miao P, Teimourpour M H et al. Topological hybrid silicon microlasers[J]. Nature Communications, 9, 981(2018).

[29] Parto M, Wittek S, Hodaei H et al. Edge-mode lasing in 1D topological active arrays[J]. Physical Review Letters, 120, 113901(2018).

[30] Fu T, Wang Y F, Wang X Y et al. Microstructure lasers based on parity-time symmetry and supersymmetry[J]. Chinese Journal of Lasers, 48, 1201005(2021).

[31] Weidemann S, Kremer M, Helbig T et al. Topological funneling of light[J]. Science, 368, 311-314(2020).

[32] Li Y H, Liang C, Wang C Y et al. Gain-loss-induced hybrid skin-topological effect[J]. Physical Review Letters, 128, 223903(2022).

[33] Luo X W, Zhang C W. Higher-order topological corner states induced by gain and loss[J]. Physical Review Letters, 123, 073601(2019).

[34] Ao Y T, Hu X Y, You Y L et al. Topological phase transition in the non-Hermitian coupled resonator array[J]. Physical Review Letters, 125, 013902(2020).

[35] Guo Z W, Wu X, Sun Y et al. Anomalous broadband Floquet topological metasurface with pure site rings[J]. Advanced Photonics Nexus, 2, 016006(2023).

[36] Hui S Y R, Ho W C. A new generation of universal contactless battery charging platform for portable consumer electronic equipment[J]. IEEE Transactions on Power Electronics, 20, 620-627(2005).

[37] Urzhumov Y, Smith D R. Metamaterial-enhanced coupling between magnetic dipoles for efficient wireless power transfer[J]. Physical Review B, 83, 205114(2011).

[38] Wu Q, Li Y H, Gao N et al. Wireless power transfer based on magnetic metamaterials consisting of assembled ultra-subwavelength meta-atoms[J]. EPL (Europhysics Letters), 109, 68005(2015).

[39] Song M Z, Baryshnikova K, Markvart A et al. Smart table based on a metasurface for wireless power transfer[J]. Physical Review Applied, 11, 054046(2019).

[40] Chen Y Q, Guo Z W, Wang Y Q et al. Experimental demonstration of the magnetic field concentration effect in circuit-based magnetic near-zero index media[J]. Optics Express, 28, 17064-17075(2020).

[41] Cannon B L, Hoburg J F, Stancil D D et al. Magnetic resonant coupling as a potential means for wireless power transfer to multiple small receivers[J]. IEEE Transactions on Power Electronics, 24, 1819-1825(2009).

[42] Sample A P, Meyer D T, Smith J R. Analysis, experimental results, and range adaptation of magnetically coupled resonators for wireless power transfer[J]. IEEE Transactions on Industrial Electronics, 58, 544-554(2011).

[43] Wang B N, Teo K H, Nishino T et al. Experiments on wireless power transfer with metamaterials[J]. Applied Physics Letters, 98, 254101(2011).

[44] Kim J W, Son H C, Kim K H et al. Efficiency analysis of magnetic resonance wireless power transfer with intermediate resonant coil[J]. IEEE Antennas and Wireless Propagation Letters, 10, 389-392(2011).

[45] Ho J S, Yeh A J, Neofytou E et al. Wireless power transfer to deep-tissue microimplants[J]. Proceedings of the National Academy of Sciences of the United States of America, 111, 7974-7979(2014).

[46] Mei H, Irazoqui P P. Miniaturizing wireless implants[J]. Nature Biotechnology, 32, 1008-1010(2014).

[47] Patil D, McDonough M K, Miller J M et al. Wireless power transfer for vehicular applications: overview and challenges[J]. IEEE Transactions on Transportation Electrification, 4, 3-37(2018).

[48] Krasnok A, Baranov D G, Generalov A et al. Coherently enhanced wireless power transfer[J]. Physical Review Letters, 120, 143901(2018).

[49] Saha C, Anya I, Alexandru C et al. Wireless power transfer using relay resonators[J]. Applied Physics Letters, 112, 263902(2018).

[50] Badowich C, Markley L. Idle power loss suppression in magnetic resonance coupling wireless power transfer[J]. IEEE Transactions on Industrial Electronics, 65, 8605-8612(2018).

[51] Zhou J L, Zhang B, Xiao W X et al. Nonlinear parity-time-symmetric model for constant efficiency wireless power transfer: application to a drone-in-flight wireless charging platform[J]. IEEE Transactions on Industrial Electronics, 66, 4097-4107(2019).

[52] Wu L H, Zhang B, Zhou J L. Efficiency improvement of the parity-time-symmetric wireless power transfer system for electric vehicle charging[J]. IEEE Transactions on Power Electronics, 35, 12497-12508(2020).

[53] Lerosey G. Wireless power on the move[J]. Nature, 546, 354-355(2017).

[54] Assawaworrarit S, Fan S H. Robust and efficient wireless power transfer using a switch-mode implementation of a nonlinear parity–time symmetric circuit[J]. Nature Electronics, 3, 273-279(2020).

[55] Li H C, Li J, Wang K P et al. A maximum efficiency point tracking control scheme for wireless power transfer systems using magnetic resonant coupling[J]. IEEE Transactions on Power Electronics, 30, 3998-4008(2015).

[56] Sakhdari M, Hajizadegan M, Chen P Y. Robust extended-range wireless power transfer using a higher-order PT-symmetric platform[J]. Physical Review Research, 2, 013152(2020).

[57] Zeng C, Guo Z W, Zhu K J et al. Efficient and stable wireless power transfer based on the non-Hermitian physics[J]. Chinese Physics B, 31, 010307(2022).

[58] Song M Z, Jayathurathnage P, Zanganeh E et al. Wireless power transfer based on novel physical concepts[J]. Nature Electronics, 4, 707-716(2021).

[59] Zhong W X, Lee C K, Hui S Y R. General analysis on the use of tesla’s resonators in domino forms for wireless power transfer[J]. IEEE Transactions on Industrial Electronics, 60, 261-270(2013).

[60] Su W P, Schrieffer J R, Heeger A J. Solitons in polyacetylene[J]. Physical Review Letters, 42, 1698-1701(1979).

[61] Jiang J, Guo Z W, Ding Y Q et al. Experimental demonstration of the robust edge states in a split-ring-resonator chain[J]. Optics Express, 26, 12891-12902(2018).

[62] Jiang J, Ren J E, Guo Z W et al. Seeing topological winding number and band inversion in photonic dimer chain of split-ring resonators[J]. Physical Review B, 101, 165427(2020).

[63] Smirnova D, Leykam D, Chong Y D et al. Nonlinear topological photonics[J]. Applied Physics Reviews, 7, 021306(2020).

[64] Ota Y, Takata K, Ozawa T et al. Active topological photonics[J]. Nanophotonics, 9, 547-567(2020).

[65] Song J A, Yang F Q, Guo Z W et al. Wireless power transfer via topological modes in dimer chains[J]. Physical Review Applied, 15, 014009(2021).

[66] Kurs A, Karalis A, Moffatt R et al. Wireless power transfer via strongly coupled magnetic resonances[J]. Science, 317, 83-86(2007).

[67] Karalis A, Joannopoulos J D, Soljačić M. Efficient wireless non-radiative mid-range energy transfer[J]. Annals of Physics, 323, 34-48(2008).

[68] Guo Z W, Jiang H T, Li Y H et al. Enhancement of electromagnetically induced transparency in metamaterials using long range coupling mediated by a hyperbolic material[J]. Optics Express, 26, 627-641(2018).

[69] Chen X, Wang Y Q, Guo Z W et al. Significant enhancement of magnetic shielding effect by using the composite metamaterial composed of mu-near-zero media and ferrite[J]. EPJ Applied Metamaterials, 8, 13(2021).

[70] Chen X, Guo Z W, Jiang J et al. Ultra-broadband near-field magnetic shielding realized by the Halbach-like structure[J]. Applied Physics Letters, 120, 192201(2022).

[71] Budhia M, Covic G A, Boys J T. Design and optimization of circular magnetic structures for lumped inductive power transfer systems[J]. IEEE Transactions on Power Electronics, 26, 3096-3108(2011).

[72] Kim J, Kim J, Kong S et al. Coil design and shielding methods for a magnetic resonant wireless power transfer system[J]. Proceedings of the IEEE, 101, 1332-1342(2013).

[73] Batra T, Schaltz E. Passive shielding effect on space profile of magnetic field emissions for wireless power transfer to vehicles[J]. Journal of Applied Physics, 117, 17A739(2015).

[74] Park H H, Kwon J H, Kwak S I et al. Effect of air-gap between a ferrite plate and metal strips on magnetic shielding[J]. IEEE Transactions on Magnetics, 51, 9(2015).

[75] Guo Z W, Long Y, Jiang H T et al. Anomalous unidirectional excitation of high-k hyperbolic modes using all-electric metasources[J]. Advanced Photonics, 3, 036001(2021).

[76] Feis J, Stevens C J, Shamonina E. Wireless power transfer through asymmetric topological edge states in diatomic chains of coupled meta-atoms[J]. Applied Physics Letters, 117, 134106(2020).

[77] Zhang L, Yang Y H, Jiang Z et al. Demonstration of topological wireless power transfer[J]. Science Bulletin, 66, 974-980(2021).

[78] Guo Z W, Jiang J, Jiang H T et al. Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators[J]. Physical Review Research, 3, 013122(2021).

[79] Huang Q S, Guo Z W, Feng J T et al. Observation of a topological edge state in the X-ray band[J]. Laser & Photonics Reviews, 13, 1800339(2019).

[80] Yang F Q, Song J A, Guo Z W et al. Actively controlled asymmetric edge states for directional wireless power transfer[J]. Optics Express, 29, 7844-7857(2021).

[81] Guo Z W, Jiang H T, Sun Y et al. Asymmetric topological edge states in a quasiperiodic Harper chain composed of split-ring resonators[J]. Optics Letters, 43, 5142-5145(2018).

[82] Liu X L, Agarwal G S. The new phases due to symmetry protected piecewise berry phases; enhanced pumping and non-reciprocity in trimer lattices[J]. Scientific Reports, 7, 45015(2017).

[83] Kartashov Y V, Arkhipova A A, Zhuravitskii S A et al. Observation of edge solitons in topological trimer arrays[J]. Physical Review Letters, 128, 093901(2022).

[84] Guo Z W, Wu X A, Ke S L et al. Rotation controlled topological edge states in a trimer chain composed of meta-atoms[J]. New Journal of Physics, 24, 063001(2022).

[85] Peterson C W, Li T H, Benalcazar W A et al. A fractional corner anomaly reveals higher-order topology[J]. Science, 368, 1114-1118(2020).

[86] Chen Y F, Meng F, Kivshar Y et al. Inverse design of higher-order photonic topological insulators[J]. Physical Review Research, 2, 023115(2020).

[87] Wang H X, Lin Z K, Jiang B et al. Higher-order Weyl semimetals[J]. Physical Review Letters, 125, 146401(2020).

[88] Ji C Y, Zhang Y Y, Liao Y H et al. Fragile topologically protected perfect reflection for acoustic waves[J]. Physical Review Research, 2, 013131(2020).

[89] Chen H Z, Liu T, Luan H Y et al. Revealing the missing dimension at an exceptional point[J]. Nature Physics, 16, 571-578(2020).

[90] Liu T, An S W, Gu Z M et al. Chirality-switchable acoustic vortex emission via non-Hermitian selective excitation at an exceptional point[J]. Science Bulletin, 67, 1131-1136(2022).

[91] Wiersig J. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection[J]. Physical Review Letters, 112, 203901(2014).

[92] Hodaei H, Hassan A U, Wittek S et al. Enhanced sensitivity at higher-order exceptional points[J]. Nature, 548, 187-191(2017).

[93] Chen W J, Kaya Özdemir Ş, Zhao G M et al. Exceptional points enhance sensing in an optical microcavity[J]. Nature, 548, 192-196(2017).

[94] Dong Z Y, Li Z P, Yang F Y et al. Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point[J]. Nature Electronics, 2, 335-342(2019).

[95] Zhong Q, Ren J, Khajavikhan M et al. Sensing with exceptional surfaces in order to combine sensitivity with robustness[J]. Physical Review Letters, 122, 153902(2019).

[96] Xiao Z C, Li H N, Kottos T et al. Enhanced sensing and nondegraded thermal noise performance based on PT-symmetric electronic circuits with a sixth-order exceptional point[J]. Physical Review Letters, 123, 213901(2019).

[97] Zhang Y J, Kwon H, Miri M A et al. Noninvasive glucose sensor based on parity-time symmetry[J]. Physical Review Applied, 11, 044049(2019).

[98] Park J H, Ndao A, Cai W et al. Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing[J]. Nature Physics, 16, 462-468(2020).

[99] Zeuner J M, Rechtsman M C, Plotnik Y et al. Observation of a topological transition in the bulk of a non-Hermitian system[J]. Physical Review Letters, 115, 040402(2015).

[100] Zangeneh-Nejad F, Fleury R. Topological Fano resonances[J]. Physical Review Letters, 122, 014301(2019).

[101] Gao W, Hu X Y, Li C et al. Fano-resonance in one-dimensional topological photonic crystal heterostructure[J]. Optics Express, 26, 8634-8644(2018).

[102] Imhof S, Berger C, Bayer F et al. Topolectrical-circuit realization of topological corner modes[J]. Nature Physics, 14, 925-929(2018).

[103] Jia N Y, Owens C, Sommer A et al. Time- and site-resolved dynamics in a topological circuit[J]. Physical Review X, 5, 021031(2015).

[104] Albert V V, Glazman L I, Jiang L A. Topological properties of linear circuit lattices[J]. Physical Review Letters, 114, 173902(2015).

[105] Liu S, Ma S J, Zhang Q A et al. Octupole corner state in a three-dimensional topological circuit[J]. Light: Science & Applications, 9, 145(2020).

[106] Wang Y, Price H M, Zhang B L et al. Circuit implementation of a four-dimensional topological insulator[J]. Nature Communications, 11, 2356(2020).

[107] Lee C H, Imhof S, Berger C et al. Topolectrical circuits[J]. Communications Physics, 1, 39(2018).

[108] Lustig E, Segev M. Topological photonics in synthetic dimensions[J]. Advances in Optics and Photonics, 13, 426-461(2021).

[109] Liu H, Yan Z W, Xiao M et al. Recent progress in synthetic dimension in topological photonics[J]. Acta Optica Sinica, 41, 0123002(2021).

[110] Guo Z W, Xue H R, Long Y et al. Editorial: non-Hermitian and topological photonics[J]. Frontiers in Physics, 11, 1177898(2023).

[111] Guo Z W, Lu C C, Lin X A et al. Editorial: optical hyperbolic metamaterials[J]. Frontiers in Materials, 9, 1115744(2022).

[112] Guo Z W, Zhang T Z, Song J A et al. Sensitivity of topological edge states in a non-Hermitian dimer chain[J]. Photonics Research, 9, 574-582(2021).

[113] Zanganeh E, Evlyukhin A, Miroshnichenko A et al. Anapole meta-atoms: nonradiating electric and magnetic sources[J]. Physical Review Letters, 127, 096804(2021).

[114] Hernández-Sarria J J, Oliveira O N, Mejía-Salazar J R. Toward lossless infrared optical trapping of small nanoparticles using nonradiative anapole modes[J]. Physical Review Letters, 127, 186803(2021).