Frequency dependence of the coupling coefficients and resonant frequency detuning in a nanophotonic waveguide-cavity system

Waveguide-cavity interactions may find important applications in future nanophotonic devices. This paper provides a detailed derivation of the evolution equation of the amplitude of a cavity mode coupled to a waveguide, starting from Maxwell´s equations and using the reciprocity relations. The analysis applies to both constant cross-section and periodic waveguides as well. Unlike previous studies, the analysis enables the estimation of the frequency dependence of the coupling coefficients. It is also confirmed that the waveguide-cavity coupling causes a detuning of the resonant frequency of the cavity mode. The detuning is estimated in the case of a photonic crystal waveguide-cavity system and it is shown that it can be significant especially if the structure is intended for filtering applications. The analysis is generalized to the case of a multimode or multiple cavities and provides a useful tool in the analysis of devices based on coupled cavities