On the Beam Profile and Beam Quality of Gain-Guided Index-Antiguided   Fibers with Finite Cladding Boundary
  The beam quality factor $M^2$ 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. 
Parisa Gandomkar Yarandi, Krishna Mohan Gundu, and Arash Mafi
physics.optics