Transverse mode distribution in multimode diode-pumped Raman fiber laser

Raman lasers based on multimode graded-index fibers may generate high-quality (M2~2) Stokes beams when pumped by highly multimode (M2>30) laser diodes. Here we, examine, both experimentally and theoretically, the energy distribution of the output Stokes beam across the principal quantum mode number n in a bent multimode fiber operating well above the Raman threshold. In contrast to Kerr spatial beam cleaning, leading to a Rayleigh–Jeans mode power distribution, in a multimode Raman fiber laser, we find that the output mode powers approach an exponential distribution. We introduce a coupled-mode equations model, including random linear coupling between neighboring mode groups, and obtain a good agreement between numerical simulations and experimental results. The model shows that, for typical mode coupling coefficients, the randomization of the mode power distribution is compensated by both nonlinear (Raman and Kerr) effects and linear filtering from the fs-inscribed fiber Bragg grating, both acting on the Stokes beam over successive round trips. When random coupling becomes the dominating factor, the mode power distribution of the Stokes beam tends to equipartition, similar to what is observed with large-size highly multimode beams of low intensity (and nonlinearity) in the absence of any filtering.