Quantifying fundamental mode purity with <i>M</i> ² -measurements

Abstract Beam quality is a fundamental aspect for evaluating the performance of laser sources. M 2 -measurements serve as the gold standard for beam quality assessment since the 1990s. The measured M 2 -parameter indicates similarity to the pure fundamental Gaussian mode, characterized by the ideal M 2 = 1, by describing a beams’ divergence. M 2 -values close to 1 are considered to correspond to nearly fundamental sources. However, in terms of the higher-order mode contribution of a laser, it does not permit a quantitative statement. Here, we introduce a framework to assess the fundamental mode content of a laser beam using M 2 -measurements and establish a direct link between beam quality and its mode composition by deriving a lower and upper bound to the fundamental mode’s power in dependence of the measured M 2 -values. This result significantly enhances the utility of M 2 -measurements in evaluating laser sources, coupling efficiencies, focusing performance, and long-distance propagation, yielding a novel approach for characterization of light sources in fields like atomic, molecular and optical physics, quantum optics and the photonics industry. Given that the M 2 formalism underlies the international beam-characterization standard ISO 11146-1, our results may help guide future improvements of the standard toward mode-purity-based beam quality specifications.