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Topological Edge Modes in One-Dimensional Photonic Artificial Structures (Invited)

By Jiajun Zheng, Zhiwei Guo, Yong Sun, Haitao Jiang, Yunhui Li, and Hong Chen
Progress In Electromagnetics Research, Vol. 177, 1-20, 2023


In recent years, topological states in photonic artificial structures have attracted great attention due to their robustness against certain disorders and perturbations. To readily understand the underlying principles, topological edge modes in one-dimensional (1D) system have been widely investigated, which bring aboutthe discovery of novel optical phenomena and devices. In this article, we review our recent advances in topological edge modes. We introduce the connection between topological orders and effective electromagnetic parameters of photonic artificial structures in band gaps, discuss experimental demonstration of robust topological modes and their potential applications in wireless power transfer, sensing and field of optics, and give a brief introduction of future opportunities in 1D topological photonics.


Jiajun Zheng, Zhiwei Guo, Yong Sun, Haitao Jiang, Yunhui Li, and Hong Chen, "Topological Edge Modes in One-Dimensional Photonic Artificial Structures (Invited)," Progress In Electromagnetics Research, Vol. 177, 1-20, 2023.


    1. Hasan, M. Z. and C. L. Kane, "Colloquium: Topological insulators," Reviews of Modern Physics, Vol. 82, No. 4, 3045-3067, 2010.

    2. Qi, X.-L. and S.-C. Zhang, "Topological insulators and superconductors," Reviews of Modern Physics, Vol. 83, No. 4, 1057-1110, 2011.

    3. Lu, L., J. D. Joannopoulos, and M. Soljacic, "Topological photonics," Nature Photonics, Vol. 8, No. 11, 821-829, 2014.

    4. Haldane, F. D. M. and S. Raghu, "Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry," Physical Review Letters, Vol. 100, No. 1, 013904, 2008.

    5. Wang, Z., Y. D. Chong, J. D. Joannopoulos, and M. Soljacic, "Observation of unidirectional backscattering-immune topological electromagnetic states," Nature, Vol. 461, No. 7265, 772-775, 2009.

    6. Hafezi, M., S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, "Imaging topological edge states in silicon photonics," Nature Photonics, Vol. 7, No. 12, 1001-1005, 2013.

    7. Khanikaev, A. B., et al., "Photonic topological insulators," Nature Materials, Vol. 12, No. 3, 233-239, 2013.

    8. Wu, L. H. and X. Hu, "Scheme for achieving a topological photonic crystal by using dielectric material," Physical Review Letters, Vol. 114, No. 22, 223901, 2015.

    9. Harari, G., M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, "Topological insulator laser: Theory," Science, Vol. 359, No. 6381, eaar4003, 2018.

    10. Bandres, M. A., S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, "Topological insulator laser: Experiments," Science, Vol. 359, No. 5381, eaar4005, 2018.

    11. Rechtsman, M. C., et al., "Photonic Floquet topological insulators," Nature, Vol. 496, No. 7444, 196-200, 2013.

    12. Lin, H. and L. Lu, "Dirac-vortex topological photonic crystal fibre," Light: Science & Applications, Vol. 9, No. 1, 202, 2020.

    13. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed., Princeton University Press, 2008.

    14. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Physical Review Letters, Vol. 58, No. 20, 2059-2062, 1987.

    15. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Physical Review Letters, Vol. 58, No. 23, 2486-2489, 1987.

    16. Zhu, W., X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, "Simultaneous observation of a topological edge state and exceptional point in an open and non-Hermitian acoustic system," Physical Review Letters, Vol. 121, No. 12, 124501, 2018.

    17. Zhu, S. and X. Zhang, "Metamaterials: Artificial materials beyond nature," National Science Review, Vol. 5, No. 2, 131-131, 2018.

    18. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 85, No. 18, 3966-3969, 2000.

    19. Ahn, D., J. Park, C. Kim, J. Kim, Y. Qian, and T. Itoh, "A design of the low-pass filter using the novel microstrip defected ground structure," IEEE Transactions on Microwave Theory and Techniques, Vol. 49, No. 1, 86-93, 2001.

    20. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 5781, 1780-1782, 2006.

    21. Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, No. 5801, 977-980, 2006.

    22. Fang, N., H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science, Vol. 308, No. 5721, 534-537, 2005.

    23. Cui, T. J., M. Q. Qi, X.Wan, J. Zhao, and Q. Cheng, "Coding metamaterials, digital metamaterials and programmable metamaterials," Light: Science & Applications, Vol. 3, e218, 2014.

    24. Liu, W., Z. N. Chen, and X. Qing, "Metamaterial-based low-profile broadband mushroom antenna," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 3, 1165-1172, 2014.

    25. Hao, J., Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, "Manipulating electromagnetic wave polarizations by anisotropic metamaterials," Physical Review Letters, Vol. 99, No. 6, 063908, 2007.

    26. Cai, T., et al., "High-efficiency and full-space manipulation of electromagnetic wave fronts with metasurfaces," Physical Review Applied, Vol. 8, No. 3, 034033, 2017.

    27. Su, W. P., J. R. Schrieffer, and A. J. Heeger, "Solitons in polyacetylene," Physical Review Letters, Vol. 42, No. 25, 1698-1701, 1979.

    28. Malkova, N., I. Hromada, X. Wang, G. Bryant, and Z. Chen, "Observation of optical Shockley-like surface states in photonic superlattices," Optics Letters, Vol. 34, No. 11, 1633-1635, 2009.

    29. Tan, W., Y. Sun, H. Chen, and S.-Q. Shen, "Photonic simulation of topological excitations in metamaterials," Scientific Reports, Vol. 4, 3842, 2014.

    30. Poshakinskiy, A. V., A. N. Poddubny, L. Pilozzi, and E. L. Ivchenko, "Radiative topological states in resonant photonic crystals," Physical Review Letters, Vol. 112, No. 10, 107403, 2014.

    31. Xiao, M., Z. Q. Zhang, and C. T. Chan, "Surface impedance and bulk band geometric phases in one-dimensional systems," Physical Review X, Vol. 4, No. 2, 021017, 2014.

    32. Poddubny, A., A. Miroshnichenko, A. Slobozhanyuk, and Y. Kivshar, "Topological Majorana states in zigzag chains of plasmonic nanoparticles," ACS Photonics, Vol. 1, No. 2, 101-105, 2014.

    33. Ling, C. W., M. Xiao, S. F. Yu, and K. H. Fung, "Topological edge plasmon modes between diatomic chains of nanoparticles," Optics Express, Vol. 23, No. 3, 2021-2031, 2015.

    34. Poli, C., M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, "Selective enhancement of topologically induced interface states," Nature Communications, Vol. 6, 6710, 2015.

    35. Shen, S. Q., Topological Insulators: Dirac Equation in Condensed Matter, 2nd Ed., Springer, 2017.

    36. Guan, G., H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Applied Physics Letters, Vol. 88, No. 21, 211112, 2006.

    37. Guo, J., H. Chen, H. Li, and Y. Zhang, "Effective permittivity and permeability of one dimensional dielectric photonic crystal within a band gap," Chinese Physics B, Vol. 17, No. 7, 2544-2552, 2008.

    38. Shi, X., C. Xue, H. Jiang, and H. Chen, "Topological description for gaps of one-dimensional symmetric all-dielectric photonic crystals," Optics Express, Vol. 24, No. 16, 18580-18581, 2016.

    39. Huang, Q., Z. Guo, J. Feng, C. Yu, H. Jiang, Z. Zhang, Z. Wang, and H. Chen, "Observation of a topological edge state in the X-ray band," Laser & Photonics Reviews, Vol. 13, No. 6, 1800339, 2019.

    40. Wang, Q., M. Xiao, H. Liu, S. N. Zhu, and C. T. Chan, "Measurement of the Zak phase of photonic bands through the interface states of a metasurface/photonic crystal," Physical Review B, Vol. 93, No. 4, 041415, 2016.

    41. Lemoult, F., N. Kaina, M. Fink, G. Lerosey, and , "Wave propagation control at the deep subwavelength scale in metamaterials," Nature Physics, Vol. 9, No. 1, 55-60, 2013.

    42. Fan, L., W. W. Yu, S. Y. Zhang, H. Zhang, and J. Ding, "Zak phases and band properties in acoustic metamaterials with negative modulus or negative density," Physical Review B, Vol. 94, No. 17, 174307, 2016.

    43. Zhu, W., Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, "Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials," Physical Review B, Vol. 97, No. 19, 195307, 2018.

    44. Fan, C., X. Shi, F. Wu, Y. Li, H. Jiang, Y. Sun, and H. Chen, "Photonic topological transition in dimerized chains with the joint modulation of near-field and far-field couplings," Photonics Research, Vol. 10, No. 1, 41-49, 2022.

    45. Verbin, M., O. Zilberberg, Y. E. Kraus, Y. Lahini, and Y. Silberberg, "Observation of topological phase transitions in photonic quasicrystals," Physical Review Letters, Vol. 110, No. 7, 076403, 2013.

    46. Lang, L., X. Cai, and S. Chen, "Edge states and topological phases in one-dimensional optical superlattices," Physical Review Letters, Vol. 108, No. 21, 220401, 2012.

    47. Kraus, Y. E., Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, "Topological states and adiabatic pumping in quasicrystals," Physical Review Letters, Vol. 109, No. 10, 106402, 2012.

    48. Feng, L., Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, "Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies," Nature Materials, Vol. 12, No. 2, 108-113, 2013.

    49. Shi, X., Y. Sun, C. Xue, and X. Hu, "Prediction of interface states in liquid surface waves with one-dimensional modulation," Physics Letters A, Vol. 383, No. 17, 2106-2109, 2019.

    50. Zhang, D., J. Ren, T. Zhou, and B. Li, "Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling," New Journal of Physics, Vol. 21, 093033, 2019.

    51. Jiang, J., Z. W. Guo, Y. Q. Ding, Y. Sun, Y. H. Li, H. T. Jiang, and H. Chen, "Experimental demonstration of the robust edge states in a split-ring-resonator chain," Optics Express, Vol. 26, No. 10, 12891-12902, 2018.

    52. Bellec, M., U. Kuhl, G. Montambaux, and F. Mortessagne, "Tight-binding couplings in microwave artificial graphene," Physical Review B, Vol. 88, No. 11, 115437, 2013.

    53. Atala, M., M. Aidelsburger, J. T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, and I. Bloch, "Direct measurement of the Zak phase in topological Bloch bands," Nature Physics, Vol. 9, No. 12, 795-800, 2013.

    54. Xiao, M., G. Ma, Z. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan, "Geometric phase and band inversion in periodic acoustic systems," Nature Physics, Vol. 11, No. 3, 240-244, 2015.

    55. Jiang, J., J. Ren, Z. W. Guo, W. W. Zhu, Y. Long, H. T. Jiang, and H. Chen, "Seeing topological winding number and band inversion in photonic dimer chain of split-ring resonators," Physical Review B, Vol. 101, No. 16, 165427, 2020.

    56. Ashcroft, N. W. and N. D. Mermin, Solid State Physics, Saunders College Publishing, 1976.

    57. Guo, Z. W., J. Jiang, H. T. Jiang, J. Ren, and H. Chen, "Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators," Physical Review Research, Vol. 3, No. 1, 013122, 2021.

    58. Guo, Z. W., H. T. Jiang, Y. Sun, Y. H. Li, and H. Chen, "Asymmetric topological edge states in a quasiperiodic Harper chain composed of split-ring resonators," Optics Letters, Vol. 43, No. 20, 5142-5145, 2018.

    59. Hafezi, M., E. A. Delmer, M. D. Lukin, and J. M. Taylor, "Robust optical delay lines with topological protection," Nature Physics, Vol. 7, No. 11, 907-912, 2011.

    60. Song, J., F. Yang, Z. Guo, X.Wu, K. Zhu, J. Jiang, Y. Sun, Y. Li, H. Jiang, and H. Chen, "Wireless power transfer via topological modes in dimer chains," Physical Review Applied, Vol. 15, No. 1, 014009, 2021.

    61. Zhang, L., et al., "Demonstration of topological wireless power transfer," Science Bulletin, Vol. 66, No. 10, 974-980, 2021.

    62. Zeng, C., Y. Sun, G. Li, Y. Li, H. Jiang, Y. Yang, and H. Chen, "Enhanced sensitivity at high-order exceptional points in a passive wireless sensing system," Optics Express, Vol. 27, No. 20, 27562-27572, 2019.

    63. Yang, F., et al., "Actively controlled asymmetric edge states for directional wireless power transfer," Optics Express, Vol. 29, No. 5, 7844-7857, 2021.

    64. Hodaei, H., A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, "Enhanced sensitivity at higher-order exceptional points," Nature, Vol. 548, No. 7666, 187-191, 2017.

    65. Chen, W. J., S. K. Ozdemir, G. M. Zhao, J. Wiersig, and L. Yang, "Exceptional points enhance sensing in an optical microcavity," Nature, Vol. 548, No. 7666, 192-196, 2017.

    66. Chen, P. Y. and R. El-Ganainy, "Exceptional points enhance wireless readout," Nature Electronics, Vol. 2, 323-324, 2019.

    67. Guo, Z. W., T. Zhang, J. Song, H. Jiang, and H. Chen, "Sensitivity of topological edge states in a non-Hermitian dimer chain," Photonics Research, Vol. 9, No. 4, 574-582, 2021.

    68. Wu, J., F. Wu, K. Lv, Z. Guo, H. Jiang, Y. Sun, Y. Li, and H. Chen, "Giant Goos-Hanchen shift with a high reflectance assisted by interface states in photonic heterostructures," Physical Review A, Vol. 101, No. 5, 053838, 2020.

    69. Wang, Q., M. Xiao, H. Liu, S. Zhu, and C. T. Chan, "Optical interface states protected by synthetic weyl points," Physical Review X, Vol. 7, No. 3, 031032, 2017.

    70. Dong, L., H. Jiang, H. Chen, and Y. Shi, "Enhancement of Faraday rotation effect in heterostructures with magneto-optical metals," Journal of Applied Physics, Vol. 107, No. 9, 093101, 2010.

    71. Du, G., H. Jiang, Z. Wang, and H. Chen, "Optical nonlinearity enhancement in heterostructures with thick metallic film and truncated photonic crystals," Optics Letters, Vol. 34, No. 5, 578-580, 2009.

    72. Bergholtz, E. J., J. C. Budich, and F. K. Kunst, "Exceptional topology of non-Hermitian systems," Review of Modern Physics, Vol. 93, No. 1, 015005, 2021.

    73. Yao, S. Y. and Z. Wang, "Edge states and topological invariants of non-Hermitian systems," Physical Review Letters, Vol. 121, No. 8, 086803, 2018.

    74. Lee, T. E., "Anomalous edge state in a non-Hermitian lattice," Physical Review Letters, Vol. 116, No. 13, 133903, 2016.

    75. Xiong, Y., "Why does bulk boundary correspondence fail in some non-Hermitian topological models," Journal of Physics Communications, Vol. 2, No. 3, 035043, 2018.

    76. Helbig, T., et al., "Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits," Nature Physics, Vol. 16, No. 7, 747, 2020.

    77. Okuma, N. and M. Sato, "Hermitian zero modes protected by nonnormality: Application of pseudospectra," Physical Review B, Vol. 102, No. 1, 014203, 2020.

    78. Budich, J. C. and E. J. Bergholtz, "Non-Hermitian topological sensors," Physical Review Letters, Vol. 125, No. 18, 180403, 2020.

    79. Li, J., R. Chu, J. Jain, and S.-Q. Shen, "Topological anderson insulator," Physical Review Letters, Vol. 102, No. 13, 136806, 2009.

    80. Zhang, Z., B. Wu, J. Song, and H. Jiang, "Topological anderson insulator in electric circuits," Physical Review B, Vol. 100, No. 18, 184202, 2019.

    81. Stutzer, S., et al., "Photonic topological Anderson insulators," Nature, Vol. 560, 461-465, 2018.

    82. Liu, G., e al., "Topological Anderson insulator in disordered photonic crystals," Physical Review Letters, Vol. 125, No. 13, 133603, 2020.

    83. Meier, E. J., F. A. An, A. Dauphin, M. Maffei, P. Massignan, T. L. Hughes, and B. Gadway, "Observation of the topological Anderson insulator in disordered atomic wires," Science, Vol. 362, 929, 2018.

    84. Lin, Q., T. Lin, L. Xiao, K. Wang, W. Yi, and P. Xue, "Observation of non-Hermitian topological Anderson insulator in quantum dynamics," Nature Communications, Vol. 13, 3229, 2022.