Linking Quasi-Normal and Natural Modes of an open cavity

Abstract

The present paper proposes a comparison between the extinction theorem and the Sturm–Liouville theory approaches for calculating the electromagnetic (e.m.) field inside an optical cavity. We discuss for the first time to the best of our knowledge, in the framework of classical electrodynamics, a simple link between the quasi normal modes (QNMs) and the natural modes (NMs) for one-dimensional (1D), two-sided, open cavities. The QNM eigenfrequencies and eigenfunctions are calculated for a linear Fabry–Pe´rot (FP) cavity. The first-order Born approximation is applied to the same cavity in order to compare the first-order Born approximated and the actual QNM eigenfunctions of the cavity. We demonstrate that the first-order Born approximation for an FP cavity introduces symmetry breaking: in fact, each Born approximated QNM eigenfunction produces values below or above the actual QNM eigenfunction value on the terminal surfaces of the same cavity. Consequently, the two error-functions for an approximated QNM are not equal in proximity to the two terminal surfaces of the cavity.