M-2 factor for evaluating fiber lasers from large mode area few-mode fibers

Evaluating the laser quality accurately is one of the most important and fundamental physical issues for laser sources, and the beam quality of lasers from the large mode area few-mode fibers have been haunted by the presence of high order mode for many years. This paper presents a modification to the M-2 factor, which can be used to evaluate the mode content of fiber lasers accurately and efficiently, no matter whether the fiber modes are superposited coherently or incoherently. By mathematical derivation, the origin of the influence of relative phase on the M-2 factor has been determined mathematically. A modification to the second moment of the beam intensity profile has been proposed, which eliminates the impact of uncontrollable relative phase on the second moment, and subsequently restores the one-to-one mapping between mode content and M-2 factor even for coherent superposition cases. Also presented are the results of numerical simulations, which support the validity of the modified M-2 factor to evaluate the mode content of the high power fiber lasers. With modified M-2 factor being less than 1.1, the power fraction of LP11 mode content is unique and determined to be less than 3%.