Evaluating Laguerre-Gaussian beams with an invariant parameter

TL;DR

This paper introduces a new parameter, $Q^{l}_{p}$, for evaluating and distinguishing Laguerre-Gaussian beams, which is easier to measure than traditional mode quality parameters and correlates well with them.

Contribution

The paper defines a novel mode-specific parameter $Q^{l}_{p}$ for LG beams, providing a simpler and effective way to evaluate beam quality.

Findings

$Q^{l}_{p}$ correlates with $M^{2}$ for beam quality assessment.

$Q^{l}_{p}$ is easier to measure than $M^{2}$.

Theoretical and experimental validation of $Q^{l}_{p}$.

Abstract

We define a new parameter about Laguerre-Gaussian (LG) beams, named $Q^{l}_{p}$, which is only related to mode indices $p$ and $l$. This parameter is able to both evaluate and distinguish LG beams. The $Q^{l}_{p}$ values are first calculated theoretically and then measured experimentally for several different LG beams. Another mode quality parameter, $ M^{2} $ value, is also measured. The comparison between $Q^{l}_{p}$ and $ M^{2}$ shows same trend for the quality of LG mode, while the measurement of $Q^{l}_{p}$ is much easier than $ M^{2}$.