Coupled mode theory of optical resonant cavities

This paper presents a theory describing coupled optical resonant cavities by means of systems of time-dependent coupled equations for the field amplitudes of standing waves in each resonator. The coupling coefficients entering the theory are derived from first principles. To the author's knowledge, this theory is new. The coupling coefficients can approximately be related to the amplitude transmission coefficients of traveling waves passing between the two resonant cavities. This relationship is checked for an example. Finally, we show that the mode amplitudes of one cavity can be eliminated so that the field in the other cavity becomes coupled to samples of itself taken at earlier times. The coupled-cavity theory applies to cavities with loss or gain. It is here expressed in scalar approximation, but it can easily be extended to vector fields.