On the beam profile and beam quality of gain-guided index-antiguided fibers with finite cladding boundary

The beam quality factor M2 for the fundamental LP01 mode of a step-index fiber with a finite cladding diameter is calculated in the presence of gain, in a closed form, as a function of the complex generalized V number. It is shown that the conventional infinite cladding diameter approximation cannot be used for index-antiguided gain-guided fibers, and the rigorous analysis presented in this paper is required for accurate prediction of the beam quality factor, as reported in recent experimental measurements.