Self-focusing length in highly multimode ultra-large-mode-area fibers

Recent theoretical researches reveal that the self-focusing critical power in the fiber waveguide is identical to that in the bulk medium. However, the delivery of peak power much higher than the self-focusing critical power has been demonstrated experimentally in ultra-large-mode-area fiber (ULMAF). And no experimental observation of self-focusing effect has been reported in recent pulsed fiber laser system whose peak power has reached or even exceeded the critical power. In this paper, we try to address this issue by studying the self-focusing length theoretically in the ULMAF which is highly multimode. Nonlinear beam propagation method employing PÁDE(2,2) approximation is applied in the numerical simulation. The results show that the self-focusing length of the fundamental mode is typically a few millimeters which is almost identical to that in the bulk medium. However, the self-focusing length of the summation of numerous modes can be as long as a few meters.