Higher order Laguerre-Gauss mode degeneracy in realistic, high finesse cavities

TL;DR

This paper analyzes the degeneracy and mode coupling of higher order Laguerre-Gauss beams in realistic high-finesse cavities, relevant for gravitational wave detectors, using new analytical methods and measured mirror surface data.

Contribution

It introduces a new analytical approximation for mode coupling using Zernike polynomials and applies it to realistic LIGO mirror data to understand mode degeneracy effects.

Findings

Identifies mirror distortions causing mode coupling

Quantifies mode distortions due to degeneracy

Derives mirror surface requirements for mode stability

Abstract

Higher order Laguerre-Gauss (LG) beams have been proposed for use in future gravitational wave detectors, such as upgrades to the Advanced LIGO detectors and the Einstein Telescope, for their potential to reduce the effects of the thermal noise of the test masses. This paper details the theoretical analysis and simulation work carried out to investigate the behaviour of LG beams in realistic optical setups, in particular the coupling between different LG modes in a linear cavity. We present a new analytical approximation to compute the coupling between modes, using Zernike polynomials to describe mirror surface distortions. We apply this method in a study of the behaviour of the LG33 mode within realistic arm cavities, using measured mirror surface maps from the Advanced LIGO project. We show mode distortions that can be expected to arise due to the degeneracy of higher order spatial modes within such cavities and relate this to the theoretical analysis. Finally we identify the mirror distortions which cause significant coupling from the LG33 mode into other order 9 modes and derive requirements for the mirror surfaces.