论文标题
基于$ \ cal pt $对称性的基于拓扑拆分谐振器依赖收益和损失
Topological split-ring resonator based metamaterials with $\cal PT$ symmetry relying on gain and loss
论文作者
论文摘要
引入了依赖平衡增益和损失的一维超材料（$ {\ cal pt} $）对称性的一维超物质，包括磁耦合的拆分环谐振器（SRRS）。一种特定的拓扑结合了非平凡的（拓扑）二聚体构型与微不足道的（非探针）二聚体构型，该构造既不是获得增益或损失的中央SRR。通过关注这种拓扑$ {\ cal pt} $莫非材料（PTMM）的动态方面，在数值上证明了在中央SRR上定位的{\ em受拓扑保护的界面状态}的存在。相应的{\ em二次特征值问题的解决方案表明，受保护的状态实际上是拓扑ptmm的强大本本特征，其特征值在两个波段频谱的间隙（中间隙状态）的中间分离出来。直接的数值模拟已被进一步用于确定这些状态在{\ em dimerization强度}和{\ em增益 - 损失系数}的参数空间中的鲁棒性和动态稳定性。
A one-dimensional metamaterial with parity-time (${\cal PT}$) symmetry that relies on balanced gain and loss is introduced, comprising of magnetically coupled split-ring resonators (SRRs). A particular topology that combines a non-trivial (topological) dimer configuration with a trivial (non-topological) dimer configuration which are separated by a central SRR with neither gain or loss, is investigated. By focusing on the dynamical aspects of such a topological ${\cal PT}$ metamaterial (PTMM), the existence of {\em topologically protected interface states} which are localized at the central SRR is demonstrated numerically. The solution of the corresponding {\em quadratic eigenvalue problem} reveals that the protected state is actually a robust eigenmode of the topological PTMM, whose eigenvalue is isolated in the middle of the gap (mid-gap state) of the two-band frequency spectrum. Direct numerical simulations have been further used to determine the robustness and dynamic stability of these states in the parameter space of the {\em dimerization strength} and the {\em gain-loss coefficient}.
