# Lorenz curve of a light beam: evaluating beam quality from a mayorization perspective

## TL;DR

This paper presents a new method for assessing laser beam quality using Lorenz curves and majorization theory, offering a criterion independent of traditional beam width definitions.

## Contribution

It introduces the Lorenz curve of a light beam as a novel tool for beam quality evaluation based on majorization theory, unifying various entropy-based measures.

## Key findings

- Lorenz curves provide a comprehensive beam quality assessment.
- Higher Lorenz curves indicate better beam quality across measures.
- Intersecting Lorenz curves require specific criteria for comparison.

## Abstract

We introduce a novel approach for the characterization of the quality of a laser beam that is not based on particular criteria for beam width definition. The Lorenz curve of a light beam is a sophisticated version of the so-called power-in-the-bucket curve, formed by the partial sums of discretized joint intensity distribution in the near and far fields sorted in decreasing order. According to majorization theory, a higher Lorenz curve implies that all measures of spreading in phase space, and, in particular, all R\'enyi (and Shannon) entropy-based measures of the beam width products in near and far fields, are unanimously smaller, providing a strong assessment of a better beam quality. Two beams whose Lorenz curves intersect can only be considered of relatively better or lower quality according to specific criteria, which can be inferred from the plot of the respective Lorenz curves.