论文标题
近似于隔离的非分类共振附近的传输和反射光谱
Approximating transmission and reflection spectra near isolated nondegenerate resonances
论文作者
论文摘要
将传入和传出波仅限于有限数量的辐射通道的线性散射问题，可以通过频率依赖性散射矩阵来精确描述。作为频率的函数，散射矩阵的条目产生了传递和反射光谱。为了严格地找到散射矩阵，有必要以数值来求解相关波的偏微分方程。 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.我们还提出了经过修订的时间耦合模式理论，该理论为传输和反射光谱产生相同的近似公式。提出了通过周期性结构衍射平面波的数值示例，以验证我们的理论。
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.
