Analytical calculation of Hermite-Gauss and Laguerre-Gauss modes on a bullseye photodiode

TL;DR

This paper analytically derives the response of bullseye detectors to optical beats between higher-order Hermite-Gauss and Laguerre-Gauss modes, comparing with numerical results and demonstrating application in mode mismatch sensing.

Contribution

It provides the first analytical expressions for bullseye detector responses to these specific optical modes, enhancing understanding and simulation capabilities.

Findings

Analytical beat coefficients match numerical calculations.

Derived formulas enable improved mode mismatch sensing.

Application demonstrated in Fabry-Perot cavity simulation.

Abstract

This note describes the analytical derivation of the response of bullseye detectors to optical beats between higher-order spatial modes of the Laguerre-Gauss form, and subsequently the Hermite-Gauss form. Also included is a comparison with numerically calculated beat coefficients, and a simple example of the use of the resulting beat coefficients in simulating a mode mismatch sensor for a Fabry-Perot cavity.