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Using a formalism similar to the quantum scattering theory, we analyze the problem of coupling between optical waveguides and high Q resonators. We give the optical transmission and reflection coefficients as functions of the waveguide-resonator coupling, cavity loss (gain), and cavity resonant frequency. Based on these results, the recently proposed concept of "critical coupling" is discussed. Using a matrix formalism based on the scattering analysis, we find the dispersion relation of indirectly coupled resonator optical waveguides. The coupling between waveguides and multiple cavities is investigated and the reflection and transmission coefficients are derived.
Xu et al. (Wed,) studied this question.