论文标题
在介电板上具有周期性缸体阵列的Bloch特征码的特殊点
Exceptional points of Bloch eigenmodes on a dielectric slab with a periodic array of cylinders
论文作者
论文摘要
电磁共振状态在开放式介电结构上的特征值问题是非热的，并且可能具有两个或多个特征频率的特征（EP），其中两个或更多的特征频率和相应的特征性函数cocece。光子结构共振状态的EPS产生了许多异常波浪现象，并且具有潜在的重要应用。为具有参数的结构找到一些EPS是相对容易的，但是隔离的EP没有提供有关其参数空间中其形成和变化的信息，并且总是很难确保找到参数空间域中的所有EPS。在本文中，我们分析了EPS的介电板，该介电板包含周期性的圆柱体阵列。通过将周期性结构调整为均匀的平板，并连续遵循EPS，我们能够获得有关限制统一板的精确条件，从而使EPS命令并将EPS分析为轨道，并通过分析确定其端点。发现沿着每个轨道，通过特殊的第四阶EP转换为具有真实频率的特殊三阶EP的谐音状态（具有复杂频率）的二阶EP。我们的研究为参数空间中的EPS提供了清晰而完整的图片，并为其实际应用提供了有用的指导。
Eigenvalue problems for electromagnetic resonant states on open dielectric structures are non-Hermitian and may have exceptional points (EPs) at which two or more eigenfrequencies and the corresponding eigenfunctions coalesce. EPs of resonant states for photonic structures give rise to a number of unusual wave phenomena and have potentially important applications. It is relatively easy to find a few EPs for a structure with parameters, but isolated EPs provide no information about their formation and variation in parameter space, and it is always difficult to ensure that all EPs in a domain of the parameter space are found. In this paper, we analyze EPs for a dielectric slab containing a periodic array of circular cylinders. By tuning the periodic structure towards a uniform slab and following the EPs continuously, we are able to obtain a precise condition about the limiting uniform slab, and thereby order and classify EPs as tracks with their endpoints determined analytically. It is found that along each track, a second order EP of resonant states (with a complex frequency) is transformed to a special kind of third order EP with a real frequency via a special fourth order EP. Our study provides a clear and complete picture for EPs in parameter space, and gives useful guidance to their practical applications.
