周期介质结构的电磁Siegert态
Electromagnetic Siegert states for periodic dielectric structures
摘要：
将量子理论中描述共振散射的Siegert态形式推广到电磁波在周期介质阵列上的共振散射。研究了入射波包对电磁Siegert态的激发及其衰减。的形式主义是应用于开发的电磁散射问题中产生的耦合电磁谐振的理论，两个这样的阵列分开的距离2 h（或，一般来说，当散射阵列的物理特性取决于一个真正的耦合参数h）。Siegert态作为耦合参数h的函数的解析性质由正则微扰定理建立，正则微扰定理是Kato-Rellich定理到目前情况的推广。利用这一定理，证明了如果散射结构在耦合参数h的某一值处允许辐射连续谱中存在束缚态，那么在散射结构中总存在这样一个区域，在该区域中，通过调节h的值，可以使近场放大到所希望的程度。这建立了一个相当普遍的机制，以控制和放大光学非线性效应的周期性结构的平面结构，具有非线性介电极化率。
英文摘要：
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.
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