Beam quality factor of higher order modes in a step-index fiber

The beam quality factor (or M
²
-parameter) for linearly polarized (LP)-modes of a step-index fiber is calculated in a closed form, as a function of the fiber V-number. It is shown that M
²
sharply peaks for all fiber modes when they are close to cutoff. Particularly simple expressions are derived in the limit Vrarrinfin. Two practically important coherent superpositions of modes are considered for which the degree of degradation of the beam quality due to the higher order mode content is calculated. The reported results can be useful for designing large-core high-power fiber lasers, amplifiers, and fiber-based beam delivery systems, when preservation of the spatial beam quality is important