Maxwell equations, coupled mode theory and coupling coefficient

Three different equations to obtain coupling coefficient between 2 resonators are derived based on the coupled mode theory. Since the present method starts from Maxwell equations, it can discriminate the magnetic and electric couplings by overlap integral expressions between magnetic and electric fields of coupled 2 resonators, respectively. In addition, it gives a physically acceptable expression by energy exchange in the time domain. Though similar expressions were given by one of the present authors a few years ago, more detailed derivation, expanded application range for asymmetric cases, and examples for wider applications are described this time.