Calculating the Fine Structure of a Fabry-Perot Resonator using Spheroidal Wave Functions

TL;DR

This paper introduces a new mathematical approach using spheroidal wave functions to accurately compute the fine structure of eigenmodes in Fabry-Perot resonators, accounting for effects beyond the paraxial approximation.

Contribution

It develops a novel set of vector solutions to Maxwell's equations in spheroidal coordinates, enabling precise calculation of first-order corrections in resonator eigenmodes and frequencies.

Findings

Predicts mode splitting due to angular momentum coupling

Shows degeneracy lifting beyond paraxial approximation

Provides a framework for analyzing resonator mode structures

Abstract

A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the complete first-order corrections in the short-wavelength limit to eigenmodes and eigenfrequencies in a Fabry-Perot resonator with perfectly conducting mirrors. Experimentally relevant effects are predicted. Modes which are degenerate according to the paraxial approximation are split according to their total angular momentum. This includes a splitting due to coupling between orbital angular momentum and spin angular momentum.