# Hermite-Gaussian Mode Detection via Convolution Neural Networks

## TL;DR

This paper presents a convolution neural network approach to accurately identify the first twenty-one Hermite-Gaussian laser modes, enhancing optical communication and cavity tuning through machine vision.

## Contribution

The study introduces a CNN-based method trained on extensive simulated and experimental data for high-accuracy HG mode detection.

## Key findings

- Achieved over 99% accuracy in HG mode classification.
- Developed a comprehensive dataset for training and testing.
- Demonstrated effectiveness on both simulated and real data.

## Abstract

Hermite-Gaussian (HG) laser modes are a complete set of solutions to the free-space paraxial wave equation in Cartesian coordinates and represent a close approximation to physically-realizable laser cavity modes. Additionally, HG modes can be mode-multiplexed to significantly increase the information capacity of optical communication systems due to their orthogonality. Since, both cavity tuning and optical communication applications benefit from a machine vision determination of HG modes, convolution neural networks were implemented to detect the lowest twenty-one unique HG modes with an accuracy greater than 99%. As the effectiveness of a CNN is dependent on the diversity of its training data, extensive simulated and experimental datasets were created for training, validation and testing.