Dynamic mode theory of optical resonators undergoing refractive index changes

Abstract

We present a theoretical model describing the dynamics of the electromagnetic field in an optical resonator undergoing refractive index changes. We use an operator formulation of Maxwell’s equations with a standard time-dependent perturbation theory to derive the dynamic mode-amplitude equations that govern the response of a resonator to a perturbing dipole-moment density. We show that in the case of time-dependent changes in the refractive index, a coupling matrix Γkm(t) that appears in the equations accounts for all novel physical processes that can be expected to occur. In particular, the phenomenon of adiabatic wavelength conversion is governed by the diagonal elements of this matrix, and the off-diagonal elements are responsible for the transfer of energy from an excited resonator mode into its neighboring modes. Our model clearly shows that the latter process can occur only when the index changes are spatially nonuniform. We discuss the spatially uniform and nonuniform cases separately and compare the predictions of our model with experimental data available in the literature. The overall good agreement suggests that this model should be useful in the study of dynamic optical resonators. Moreover, since we do not make any assumptions about the type of dielectric cavity used, the width of input pulses, or the speed with which the refractive index is changed, this model should be applicable under most experimental situations.