New expression of coupling coefficient between resonators based on overlap integral of EM field

The coupled mode theory is applied to analyze the coupling between resonators. According to the theory, the coupling coefficient is, in principle, described by adding the overlap integral of the electric field of the two resonators and the magnetic counterpart regardless of the configurations. But, depending on the configurations, such as two dielectric resonators, one dielectric resonator with degenerate modes, two metallic resonators or one metallic resonator with degenerate modes, simpler expressions are obtained that is useful for numerical calculations and physical interpretations. The present paper derives the general coupling equation based on the coupled mode theory and shows some numerical results for two dielectric resonators using a derived simple overlap integral expression.