Skin effect that all eigenmodes within a frequency range become edge states is dictated by the topological properties of complex eigenvalues unique in non-Hermitian systems. The prevailing attempts to realize such a fascinating effect are confined to either one-dimensional or nonreciprocal systems exhibiting asymmetric couplings. Here, inspired by a recent model Hamiltonian theory, we propose a realistic reciprocal two-dimensional (2D) photonic crystal (PhC) system that shows the desired skin effect. Specifically, we establish a routine for designing such non-Hermitian systems via revealing the inherent connections between the nontrivial eigenvalue topology of order-2 exceptional points (EPs) and the skin effects. Guided by the proposed strategy, we successfully design a 2D PhC that possesses the EPs with nonzero eigenvalue winding numbers. The spectral area along a specific wavevector direction is then formed by leveraging the symmetry of the macroscopic geometry and the unit cell. The projected-band-structure calculations are performed to demonstrate that the desired skin effect exists at the specific crystalline interfaces. We finally employ time-domain simulations to vividly illustrate this phenomenon by exciting a pulse at the center of a finite-sized PhC. Our results form a solid basis for further experimental confirmations and applications of the skin effect.

中文翻译：

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互易光子晶体中几何相关的趋肤效应

频率范围内的所有本征模式都变成边缘状态的趋肤效应是由拓扑性质决定的复杂的唯一的特征值非厄米特系统。实现这种迷人效果的主流尝试仅限于表现出不对称耦合的一维或非互易系统。在这里，受最近模型哈密顿理论的启发，我们提出了一种现实的倒易二维 (2D) 光子晶体 (PhC) 系统，该系统显示出所需的趋肤效应。具体来说，我们通过揭示 2 阶异常点 (EP) 的非平凡特征值拓扑与集肤效应之间的内在联系，建立了设计此类非厄米系统的例程。在所提出的策略的指导下，我们成功地设计了一个具有非零特征值绕组数的 EP 的二维 PhC。然后通过利用宏观几何和晶胞的对称性形成沿特定波矢量方向的光谱区域。执行投影能带结构计算以证明所需的集肤效应存在于特定的晶体界面。我们最终采用时域模拟，通过在有限大小的 PhC 中心激发脉冲来生动地说明这一现象。我们的结果为进一步的实验确认和趋肤效应的应用奠定了坚实的基础。