Eigenmode in a misaligned triangular optical cavity

TL;DR

This paper derives analytical relationships between small misalignments and eigenmode changes in a common triangular optical cavity, providing a practical tool for visualization and validation of cavity behavior in laser interferometry.

Contribution

It presents a novel analytical method linking misalignments to eigenmode changes in triangular cavities, validated by numerical comparison, applicable to typical laser interferometry setups.

Findings

Excellent agreement between analytical and numerical results.

Method applicable to isosceles triangular cavities with specific geometries.

Provides an intuitive visualization tool for cavity eigenmodes.

Abstract

We derive relationships between various types of small misalignments on a triangular Fabry-Perot cavity and associated geometrical eigenmode changes. We focus on the changes of beam spot positions on cavity mirrors, the beam waist position, and its angle. A comparison of analytical and numerical results shows excellent agreement. The results are applicable to any triangular cavity close to an isosceles triangle, with the lengths of two sides much bigger than the other, consisting of a curved mirror and two flat mirrors yielding a waist equally separated from the two flat mirrors. This cavity shape is most commonly used in laser interferometry. The analysis presented here can easily be extended to more generic cavity shapes. The geometrical analysis not only serves as a method of checking a simulation result, but also gives an intuitive and handy tool to visualize the eigenmode of a misaligned triangular cavity.