Linking the Quasi-Normal and Natural Modes of an open cavity

TL;DR

This paper establishes a novel link between Quasi-Normal Modes and Natural Modes in open optical cavities, comparing theoretical approaches and analyzing the accuracy of the first-order Born approximation.

Contribution

It introduces the first known connection between QNMs and NMs in classical electrodynamics for 1D open cavities and assesses the Born approximation's impact on QNM eigenfunctions.

Findings

First-order Born approximation causes symmetry breaking in QNM eigenfunctions.

The approximation introduces errors that differ at the cavity's terminal surfaces.

A comparison between eigenfunctions reveals discrepancies near the cavity boundaries.

Abstract

The present paper proposes a comparison between the extinction theorem and the Sturm-Liouville theory approaches for calculating the 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-Perot (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.