Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal
Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal
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DOI：
10.3390/cryst9030137
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发表时间：
2019-03
期刊：
影响因子：
2.7
通讯作者：
Xiao-Chen Sun;Cheng He;Xiao-ping Liu;Yi Zou;Ming-Hui Lu;Xiao Hu;Yan-Feng Chen
中科院分区：
文献类型：
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作者：
Xiao-Chen Sun;Cheng He;Xiao-ping Liu;Yi Zou;Ming-Hui Lu;Xiao Hu;Yan-Feng Chen
电子的时间反演对称性（TRS）与T2 = − 1的反幺正算符有关，它诱导Kramers简并，在实现量子自旋霍尔效应（QSHE）中起着重要作用。相比之下，光子的TRS由T B 2 = 1描述。我们指出，由于这一差别，TRS不是构造QSHE光子模拟的必要条件。相反，通过在光子系统中构造一个人工伪TRS Tp，使得Tp 2 = − 1，人们可以实现光子Kramers简并和一对拓扑保护边缘态，这是QSHE的光子模拟。具体地说，通过用伪TRS反演材料的光学参数，提出了一种利用双简并横电（TE）和横磁（TM）极化来模拟电子自旋上下态的光子拓扑绝缘体（PTI），并证明了单向极化-基于计算机模拟，在该系统中可以实现TE和TM边缘态的相关输运。对于所有可能的对称类型，我们检查这些拓扑状态的鲁棒性，通过使用一套完整的杂质，包括三个泡利矩阵和一个复共轭算子。结果表明，PTI受到伪TRS Tp的保护.一般来说，布洛赫球上的任意一对光学偏振都可以用来构造光子赝自旋态和PTI。我们的研究结果证实了伪TRS的物理意义，并可能为未来的PTI设计提供指导。
Time-reversal symmetry (TRS) of electrons is associated with an anti-unitary operator with T 2 = − 1 , 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 T b 2 = 1 . 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 T p with T p 2 = − 1 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 T p . 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.