Integral equation analysis of propagation in a dielectric waveguide coupled to an infinite periodic sequence of ring resonators

Periodic sequences of resonators coupled to dielectric waveguides have recently attracted the significant theoretical and experimental interest. The article presented in this paper aims to aid the analysis of the structure, proposing a rigorous integral equation approach that treats the problem of propagation as a fully electromagnetic one and has no theoretical limitation in its application. A fully-wave integral equation method is also developed to analyze the problem of a planar waveguide coupled to an infinite sequence of resonators. The formulation is applicable to many similar periodic structures, such as gratings or direct-coupled resonator waveguides, where a rigorous analysis of coupling is needed.