Scattering-theory analysis of waveguide-resonator coupling

Using a formalism similar to the quantum scattering theory, we analyze the problem of coupling between optical waveguides and high Q resonators. We gi ve the optical transmission and reflection coefficients as functions of the waveguide-resonator coupling, cavity loss (gain), and cavity resonant freq uency. Based on these results, the recently proposed concept of "critical c oupling" is discussed. Using a matrix formalism based on the scattering ana lysis, we find the dispersion relation of indirectly coupled resonator opti cal waveguides. The coupling between waveguides and multiple cavities is in vestigated and the reflection and transmission coefficients are derived.