标题： 周期性介质结构的电磁 Siegert 状态 显示英文标题

标题： Electromagnetic Siegert states for periodic dielectric structures

摘要： Siegert态的形式主义用于描述量子理论中的共振散射，被扩展到电磁波在周期性电介质阵列上的共振散射。 通过入射波包激发电磁Siegert态及其衰减过程被研究。 该形式主义被应用于发展一种耦合电磁共振的理论，这种共振出现在两个这样的阵列之间相距2h（或一般情况下，当散射阵列的物理性质依赖于实数耦合参数h）的电磁散射问题中。 通过正则摄动定理，建立了Siegert态作为耦合参数h函数的解析性质，该定理是Kato-Rellich定理在当前情况下的扩展。 借助该定理，证明了如果散射结构在某个耦合参数h的值下在辐射连续谱中存在束缚态，则结构中总存在某些区域，其近场可以通过调整h的值被放大到任意程度。这建立了一种相当普遍的机制，用于控制和放大具有非线性电介质极化率的周期性平面结构中的光学非线性效应。 显示英文摘要

摘要： The formalism of Siegert states to describe the resonant scattering in quantum theory is extended to the resonant scattering of electromagnetic waves on periodic dielectric arrays. The excitation of electromagnetic Siegert states by an incident wave packet and their decay is studied. The formalism is applied to develop a theory of coupled electromagnetic resonances arising in the electromagnetic scattering problem for two such arrays separated by a distance 2h (or, generally, when the physical properties of the scattering array depend on a real coupling parameter h). Analytic properties of Siegert states as functions of the coupling parameter h are established by the Regular Perturbation Theorem which is an extension the Kato-Rellich theorem to the present case. By means of this theorem, it is proved that if the scattering structure admits a bound state in the radiation continuum at a certain value of the coupling parameter h, then there always exist regions within the structure in which the near field can be amplified as much as desired by adjusting the value of h. This establishes a rather general mechanism to control and amplify optical nonlinear effects in periodically structured planar structures possessing a nonlinear dielectric susceptibility.