孤立非简并共振附近透射和反射谱的近似计算
Approximating transmission and reflection spectra near isolated nondegenerate resonances
摘要：
线性散射问题的入射波和出射波被限制在有限数量的辐射通道，可以精确地描述由频率相关的散射矩阵。散射矩阵的元素作为频率的函数，产生透射谱和反射谱。为了严格地求出散射矩阵，必须数值求解控制相关波的偏微分方程。在本文中，我们考虑一个孤立的非简并谐振模式的复频率$ω_\star$的谐振结构，并表明，对于$ω_0 = \mbox{Re}(ω_\star)$附近的实际频率，透射和反射谱可以近似使用仅在$ω_0$和信息的散射矩阵的谐振模式。我们还提出了一个修订的时间耦合模理论，产生相同的近似公式的透射和反射光谱。给出了平面波对周期结构衍射的数值算例来验证我们的理论。
英文摘要：
A linear scattering problem for which incoming and outgoing waves are restricted to a finite number of radiation channels can be precisely described by a frequency-dependent scattering matrix. The entries of the scattering matrix, as functions of the frequency, give rise to the transmission and reflection spectra. To find the scattering matrix rigorously, it is necessary to solve numerically the partial differential equations governing the relevant waves. In this paper, we consider resonant structures with an isolated nondegenerate resonant mode of complex frequency $ω_\star$, and show that for real frequencies near $ω_0 = \mbox{Re}(ω_\star)$, the transmission and reflection spectra can be approximated using only the scattering matrix at $ω_0$ and information about the resonant mode. We also present a revised temporal coupled-mode theory that produces the same approximate formulas for the transmission and reflection spectra. Numerical examples for diffraction of plane waves by periodic structures are presented to validate our theory.
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