# Generation of very high-order high purity Gaussian modes via spatial light modulation

## TL;DR

This paper demonstrates experimentally converting a fundamental laser mode into high-order Hermite-Gaussian modes with high purity using a spatial light modulator, with potential applications in precision measurement and cold atom physics.

## Contribution

It introduces a method to generate high-order Hermite-Gaussian modes with high purity via spatial light modulation and cavity filtering, expanding capabilities for optical applications.

## Key findings

- Achieved mode purities of 96%, 93%, and 78% for specific high-order modes.
- Measured conversion efficiencies of 6.6%, 3.7%, and 1.7%.
- Demonstrated potential applications in optical clocks, gravitational wave detectors, and cold atom physics.

## Abstract

We experimentally demonstrate the conversion of a fundamental $\text{TEM}_{00}$ laser mode at 1064\,nm to higher order Hermite-Gaussian modes (HG) of arbitrary order via a commercially available liquid crystal Spatial Light Modulator (SLM). We particularly studied the $\text{HG}_{5,5}/\text{HG}_{10,10}/\text{HG}_{15,15}$ modes. A two-mirror plano-spherical cavity filters the higher-order modes spatially. We analyze the cleaned modes via a three-mirror diagnosis cavity and measure a mode purity of 96/93/78\% and a conversion efficiency of 6.6\%/3.7\%/1.7\% respectively. The generated high-purity Hermite-Gaussian modes can be employed for the mitigation of mirror thermal noise in optical cavities for both optical clocks and gravitational wave (GW) detectors. HG modes are then converted into high order LG modes which can be of particular interest in cold atom physics.