Topological photonics

Nature Photonics

Volumn 8, Issue 11, 2014, Pages 821-829

  Lu, Ling ^a   Joannopoulos, John D ^a   Soljačić, Marin ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL IMPURITIES; INTERFACE STATES;

BACK REFLECTION; CONTINUOUS DEFORMATIONS; COUPLED RESONATOR; STATES OF LIGHT; TOPOLOGICAL EFFECTS; UNDERLYING PRINCIPLES; WAVEVECTOR SPACE;

TOPOLOGY;

EID: 84908470798     PISSN: 17494885     EISSN: 17494893     Source Type: Journal    
DOI: 10.1038/nphoton.2014.248     Document Type: Review

References (98)

1. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045-3067 (2010).
2. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057-1110 (2011).
3. Haldane, F. D. M. Model for a quantum Hall efect without landau levels: Condensed-matter realization of the 'parity anomaly'. Phys. Rev. Lett. 61, 2015-2018 (1988).
4. Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).
5. Raghu, S. & Haldane, F. D. M. Analogs of quantum-Hall-efect edge states in photonic crystals. Phys. Rev. A 78, 033834 (2008).
6. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light 2nd edn (Princeton Univ. Press, 2008).
7. Wang, Z., Chong, Y. D., Joannopoulos, J. D. & Marin Soljačić. Refection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett. 100, 013905 (2008).
8. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić., M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772-775 (2009).
9. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nature Phys. 7, 907-912 (2011).
10. Fang, K., Yu, Z. & Fan, S. Realizing efective magnetic feld for photons by controlling the phase of dynamic modulation. Nature Photon. 6, 782-787 (2012).
11. Khanikaev, A. B. et al. Photonic topological insulators. Nature Mater. 12, 233-239 (2013).
12. Lu, L., Fu, L., Joannopoulos, J. D. & Soljačić, M. Weyl points and line nodes in gyroid photonic crystals. Nature Photon. 7, 294-299 (2013).
13. Skirlo, S. A., Lu, L. & Soljačić, M. Multimode one-way waveguides of large Chern numbers. Phys. Rev. Lett. 113, 113904 (2014).
14. Kraus, Y. E., Lahini, Y., Ringel, Z., Verbin, M. & Zilberberg, O. Topological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett. 109, 106402 (2012).
15. Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196-200 (2013).
16. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nature Photon. 7, 1001-1005 (2013).
17. Sepkhanov, R. A., Nilsson, J. & Beenakker, C. W. J. Proposed method for detection of the pseudospin-1/2 Berry phase in a photonic crystal with a Dirac spectrum. Phys. Rev. B 78, 045122 (2008).
18. Sepkhanov, R. A., Ossipov, A. & Beenakker, C. W. J. Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum. Europhys. Lett. 85, 14005 (2009).
19. Peleg, O. et al. Conical difraction and gap solitons in honeycomb photonic lattices. Phys. Rev. Lett. 98, 103901 (2007).
20. Bahat-Treidel, O. et al. Klein tunneling in deformed honeycomb lattices. Phys. Rev. Lett. 104, 063901 (2010).
21. Rechtsman, M. C. et al. Strain-induced pseudomagnetic feld and photonic landau levels in dielectric structures. Nature Photon. 7, 153-158 (2013).
22. Schomerus, H. & Halpern, N. Y. Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices. Phys. Rev. Lett. 110, 013903 (2013).
23. Rechtsman, M. C. et al. Topological creation and destruction of edge states in photonic graphene. Phys. Rev. Lett. 111, 103901 (2013).
24. Onoda, M., Murakami, S. & Nagaosa, N. Hall efect of light. Phys. Rev. Lett. 93, 083901 (2004).
25. Ochiai, T. & Onoda, M. Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states. Phys. Rev. B 80, 155103 (2009).
26. Fang, K., Yu, Z. & Fan, S. Microscopic theory of photonic one-way edge mode. Phys. Rev. B 84, 075477 (2011).
27. Poo, Y., Wu, R.-X., Lin, Z., Yang, Y. & Chan, C. T. Experimental realization of self-guiding unidirectional electromagnetic edge states. Phys. Rev. Lett. 106, 93903 (2011).
28. Liu, K., Shen, L. & He, S. One-way edge mode in a gyromagnetic photonic crystal slab. Opt. Lett. 37, 4110-4112 (2012).
29. Asatryan, A. A., Botten, L. C., Fang, K., Fan, S. & McPhedran, R. C. Local density of states of chiral Hall edge states in gyrotropic photonic clusters. Phys. Rev. B 88, 035127 (2013).
30. He, C. et al. Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal. Appl. Phys. Lett. 96, 111111 (2010).
31. Zang, X. & Jiang, C. Edge mode in nonreciprocal photonic crystal waveguide: manipulating the unidirectional electromagnetic pulse dynamically. J. Opt. Soc. Am. B 28, 554-557 (2011).
32. Fu, J.-X., Liu, R.-J. & Li, Z.-Y. Robust one-way modes in gyromagnetic photonic crystal waveguides with diferent interfaces. Appl. Phys. Lett. 97, 041112 (2010).
33. Fu, J.-X., Lian, J., Liu, R.-J., Gan, L. & Li, Z.-Y. Unidirectional channel-drop flter by one-way gyromagnetic photonic crystal waveguides. Appl. Phys. Lett. 98, 211104 (2011).
34. Qiu, W., Wang, Z. & Soljačić, M. Broadband circulators based on directional coupling of one-way waveguides. Opt. Express 19, 22248-22257 (2011).
35. Yang, Y., Poo, Y., Wu, R.-X., Gu, Y. & Chen, P. Experimental demonstration of one-way slow wave in waveguide involving gyromagnetic photonic crystals. Appl. Phys. Lett. 102, 231113 (2013).
36. Chong, Y. D., Wen, X. G. & Soljačić, M. Efective theory of quadratic degeneracies. Phys. Rev. B 77, 235125 (2008).
37. Yu, Z., Veronis, G., Wang, Z. & Fan, S. One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic feld and a photonic crystal. Phys. Rev. Lett. 100, 23902 (2008).
38. Mittal, S. et al. Topologically robust transport of photons in a synthetic gauge feld. Phys. Rev. Lett. 113, 087403 (2014).
39. Umucalilar, R. O. & Carusotto, I. Artifcial gauge feld for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).
40. Petrescu, A., Houck, A. A. & Le Hur, K. Anomalous Hall efects of light and chiral edge modes on the Kagome lattice. Phys. Rev. A 86, 053804 (2012).
41. Hafezi, M. Measuring topological invariants in photonic systems. Phys. Rev. Lett. 112, 210405 (2014).
42. Liang, G. Q. & Chong, Y. D. Optical resonator analog of a two-dimensional topological insulator. Phys. Rev. Lett. 110, 203904 (2013).
43. Pasek, P. & Chong, Y. D. Network models of photonic Floquet topological insulators. Phys. Rev. B 89, 075113 (2013).
44. Fang, K., Yu, Z. & Fan, S. Photonic Aharonov-Bohm efect based on dynamic modulation. Phys. Rev. Lett. 108, 153901 (2012).
45. Li, E., Eggleton, B. J., Fang, K. & Fan, S. Photonic Aharonov-Bohm efect in photon-phonon interactions. Nature Commun. 5, 3225 (2014).
46. Tzuang, L. D., Fang, K., Nussenzveig, P., Fan, S. & Lipson, M. Non-reciprocal phase shif induced by an efective magnetic fux for light. Nature Photon. 8, 701-705 (2014).
47. Kitagawa, T., Berg, E., Rudner, M. & Demler, E. Topological characterization of periodically driven quantum systems. Phys. Rev. B 82, 235114 (2010).
48. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nature Phys. 7, 490-495 (2011).
49. Kopp, V. I. et al. Chiral fber gratings. Science 305, 74-75 (2004).
50. Jia, S. & Fleischer, J. W. Nonlinear light propagation in rotating waveguide arrays. Phys. Rev. A 79, 041804 (2009).
51. Dalibard, J., Gerbier, F., Juzeliu¯nas, G. & Öhberg, P. Colloquium: Artifcial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523 (2011).
52. Jaksch, D. & Zoller, P. Creation of efective magnetic felds in optical lattices: the Hofstadter butterfy for cold neutral atoms. New J. Phys. 5, 56 (2003).
53. Schmidt, M., Peano, V. & Marquardt, F. Optomechanical metamaterials: Dirac polaritons, gauge felds, and instabilities. Preprint at http://lanl.arxiv.org/ abs/1311.7095 (2013).
54. Jia, N., Sommer, A., Schuster, D. & Simon, J. Time reversal invariant topologically insulating circuits. Preprint at http://lanl.arxiv.org/ abs/1309.0878 (2013).
55. Kong, J. A. Teorems of bianisotropic media. Proc. IEEE 60, 1036-1046 (1972).
56. Jonsson, F. & Flytzanis, C. Photospin-orbit coupling in photonic structures. Phys. Rev. Lett. 97, 193903 (2006).
57. Ma, T., Khanikaev, A. B., Mousavi, S. H. & Shvets, G. Topologically protected photonic transport in bi-anisotropic meta-waveguides. Preprint at http://lanl.arxiv.org/abs/1401.1276 (2014).
58. Chen, W.-J., Jiang, S.-J., Chen, X.-D., Dong, J.-W. & Chan, C. T. Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide. Preprint at http://lanl.arxiv.org/abs/1401.0367 (2014).
59. Gao, W. et al. Chiral hyperbolic metamaterial as a robust photonic topological insulator. Preprint at http://lanl.arxiv.org/abs/1401.5448 (2014).
60. Kraus, Y. E., Ringel, Z. & Zilberberg, O. Four-dimensional quantum Hall efect in a two-dimensional quasicrystal. Phys. Rev. Lett. 111, 226401 (2013).
61. Chen, W.-J. et al. Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking. Phys. Rev. Lett. 107, 023901 (2011).
62. Lu, L., Joannopoulos, J. D. & Soljačić, M. Waveguiding at the edge of a three-dimensional photonic crystal. Phys. Rev. Lett. 108, 243901 (2012).
63. Burkov, A. A., Hook, M. D. & Balents, L. Topological nodal semimetals. Phys. Rev. B 84, 235126 (2011).
64. Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).
65. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).
66. Malkova, N., Hromada, I., Wang, X., Bryant, G. & Chen, Z. Observation of optical Shockley-like surface states in photonic superlattices. Opt. Lett. 34, 1633-1635 (2009).
67. Tan, W., Sun, Y., Chen, H. & Shen, S.-Q. Photonic simulation of topological excitations in metamaterials. Sci. Rep. 4, 3842 (2014).
68. Poshakinskiy, A. V., Poddubny, A. N., Pilozzi, L. & Ivchenko, E. L. Radiative topological states in resonant photonic crystals. Phys. Rev. Lett. 112, 107403 (2014).
69. Xiao, M., Zhang, Z. Q. & Chan, C. T. Surface impedance and bulk band geometric phases in one-dimensional systems. Phys. Rev. X 4, 021017 (2014).
70. Poddubny, A., Miroshnichenko, A., Slobozhanyuk, A. & Kivshar, Y. Topological Majorana states in zigzag chains of plasmonic nanoparticles. ACS Photon. 1, 101-105 (2014).
71. Ling, C. W., Xiao, M., Yu, S. F. & Fung, K. H. Topological edge plasmon modes between diatomic chains of nanoparticles. Preprint at http://lanl.arxiv.org/ abs/1401.7520 (2014).
72. Poli, C., Bellec, M., Kuhl, U., Mortessagne, F. & Schomerus, H. Selective enhancement of topologically induced interface states. Preprint at http://lanl.arxiv.org/abs/1407.3703 (2014).
73. Kitaev, A. Periodic table for topological insulators and superconductors. AIP Conf. Proc. 1134, 22 (2009).
74. Schnyder, A. P., Ryu, S., Furusaki, A. & Ludwig, A. W. W. Classifcation of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008).
75. Fu, L. Topological crystalline insulators. Phys. Rev. Lett. 106, 106802 (2011).
76. Yannopapas, V. Gapless surface states in a lattice of coupled cavities: A photonic analog of topological crystalline insulators. Phys. Rev. B 84, 195126 (2011).
77. De Nittis, G. & Lein, M. On the role of symmetries in the theory of photonic crystals. Ann. Phys. 350, 568-587 (2014).
78. Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604-1606 (2012).
79. Umucalilar, R. O. & Carusotto, I. Fractional quantum Hall states of photons in an array of dissipative coupled cavities. Phys. Rev. Lett. 108, 206809 (2012).
80. Hafezi, M., Lukin, M. D. & Taylor, J. M. Non-equilibrium fractional quantum Hall state of light. New J. Phys. 15, 063001 (2013).
81. Lumer, Y., Plotnik, Y., Rechtsman, M. C. & Segev, M. Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111, 243905 (2013).
82. Yuen-Zhou, J., Saikin, S. K., Yao, N. Y. & Aspuru-Guzik, A. Topologically protected excitons in porphyrin thin flms. Nature Mater. http://dx.doi.org/10.1038/nmat4073 (2014).
83. Jacqmin, T. et al. Direct observation of Dirac cones and a fatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).
84. Karzig, T., Bardyn, C.-E., Lindner, N. & Refael, G. Topological polaritons from quantum wells in photonic waveguides or microcavities. Preprint at http://lanl.arxiv.org/abs/1406.4156 (2014).
85. Prodan, E. & Prodan, C. Topological phonon modes and their role in dynamic instability of microtubules. Phys. Rev. Lett. 103, 248101 (2009).
86. Kane, C. L. & Lubensky, T. C. Topological boundary modes in isostatic lattices. Nature Phys. 10, 39-45 (2013).
87. Shindou, R., Matsumoto, R. & Murakami, S. Topological chiral magnonic edge mode in a magnonic crystal. Phys. Rev. B 87, 174427 (2013).
88. Zhen, B., Hsu, C. W., Lu, L., Stone, A. D. & Soljačić, M. Topological nature of bound states in the radiation continuum. Preprint at http://lanl.arxiv.org/ abs/1408.0237 (2014).
89. Koch, J., Houck, A. A., Le Hur, K. & Girvin, S. M. Time-reversal-symmetry breaking in circuit-QED-based photon lattices. Phys. Rev. A 82, 043811 (2010).
90. Aspuru-Guzik, A., Demler, E. & White, A. G. Observation of topologically protected bound states in photonic quantum walks. Nature Commun. 3, 882 (2012).
91. Jalas, D. et al. What is and what is not an optical isolator. Nature Photon. 7, 579-582 (2013).
92. Nakahara, M. Geometry, topology, and physics (CRC, 2003).
93. Xiao, D., Chang, M.-C. & Niu, Q. Berry phase efects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010).
94. Fukui, T., Hatsugai, Y. & Suzuki, H. Chern numbers in discretized Brillouin zone: Efcient method of computing (spin) Hall conductances. J. Phys. Soc. Japan 74, 1674-1677 (2005).
95. Pancharatnam, S. Generalized theory of interference, and its applications. Proc. Indiana Acad. Sci. A44, 247-262 (1956).
96. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond A 392, 45-57 (1984).
97. Tomita, A. & Chiao, R. Y. Observation of Berry's topological phase by use of an optical fber. Phys. Rev. Lett. 57, 937 (1986).
98. Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall efect. Phys. Rev. Lett. 95, 146802 (2005).