Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal
National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences & Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Authors to whom correspondence should be addressed.
Received: 6 February 2019 / Revised: 1 March 2019 / Accepted: 2 March 2019 / Published: 7 March 2019
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Time-reversal symmetry (TRS) of electrons is associated with an anti-unitary operator with
, which induces Kramers degeneracy and plays an important role in realizing the quantum spin Hall effect (QSHE). By contrast, TRS of photons is described by
. We point out that due to this difference, TRS is not the necessary condition for the construction of the photonic analogue of the QSHE. Instead, by constructing an artificial pseudo TRS
in a photonic system, one can realize the photonic Kramers degeneracy and a pair of topological protected edge states, a photonic analogue of the QSHE. Specifically, by retrieving the optical parameters of materials with the pseudo TRS, we propose a photonic topological insulator (PTI) utilizing a pair of double-degenerate transverse electric (TE) and transverse magnetic (TM) polarizations to mimic the spin up and down states of the electron. We demonstrate that the unidirectional polarization-dependent transportation of TE and TM edge states can be realized in this system based on computer simulations. For all possible symmetry types, we check the robustness of these topological states by using a complete set of impurities, including three Pauli matrices and one complex conjugate operator. The results show that the PTI is protected by the pseudo TRS
. In general, an arbitrary pair of optical polarizations on the Bloch sphere can be utilized to construct photonic pseudospin states and the PTI. Our findings confirm the physical meaning of the pseudo TRS and may provide guidance for future PTI designs.
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Sun, X.-C.; He, C.; Liu, X.-P.; Zou, Y.; Lu, M.-H.; Hu, X.; Chen, Y.-F. Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal. Crystals 2019, 9, 137.
Sun X-C, He C, Liu X-P, Zou Y, Lu M-H, Hu X, Chen Y-F. Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal. Crystals. 2019; 9(3):137.
Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Zou, Yi; Lu, Ming-Hui; Hu, Xiao; Chen, Yan-Feng. 2019. "Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal." Crystals 9, no. 3: 137.
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