Degenerate Perturbation Theory Describing the Mixing of Orbital Angular Momentum Modes in Fabry-P\'erot Cavity Resonators

TL;DR

This paper develops an analytic perturbation theory that extends the paraxial approximation to include polarization-dependent mirror effects, revealing how orbital angular momentum degeneracy in optical resonators is lifted at small sizes and high finesse.

Contribution

It introduces a novel perturbation theory that accounts for polarization-dependent reflectivity, providing insight into mode mixing in optical resonators beyond the paraxial approximation.

Findings

Degeneracy of Laguerre-Gauss modes is lifted at small sizes and high finesse.

Eigenmodes exhibit two distinct orbital angular momentum components.

Mirror structure subtly influences the fractional composition of OAM modes.

Abstract

We present an analytic perturbation theory which extends the paraxial approximation for a common cylindrically symmetric stable optical resonator and incorporates the differential, polarization-dependent reflectivity of a Bragg mirror. The degeneracy of Laguerre-Gauss modes with distinct orbital angular momentum (OAM) and polarization, but identical transverse order N, will become observably lifted at sufficiently small size and high finesse. The resulting paraxial eigenmodes possess two distinct OAM components, the fractional composition subtly depending on mirror structure.