科研之友
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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. Near a resonance, the temporal coupled-mode theory (TCMT) gives a model for the scattering matrix, and it is often quite accurate. In this paper, we consider resonant structures with an isolated nondegenerate resonant mode of complex frequency ?????, and derive an approximation to the exact scattering matrix for real frequencies near ??0 = Re(?????). The approximate scattering matrix depends on the exact scattering matrix at ??0, and gives the same approximate transmission and reflection spectra as the TCMT. Numerical examples for diffraction of plane waves by periodic structures are presented to validate our theory.
