Beam Quality Factor of Single-Mode Gain-Guided Fiber Lasers

The beam quality factor M^2 for the fundamental LP01 mode of a step-index fiber 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 M^2 value of a single-mode gain-guided fiber laser can be arbitrary large. The results are important for the interpretation of the beam quality measurements in recent experiments on single-mode gain-guided fiber lasers.