Mode instabilities in Yb:YAG crystalline fiber amplifiers.

Mode instabilities (MI) threshold in the Yb:YAG crystalline fiber amplifier is simulated by a full numerical model. The propagation of signal fields is simulated by the finite-difference beam-propagation method combined with the rate equations, and the time-dependent heat equation is solved by the alternating-direction-implicit method. Considering the strong temperature-dependent laser performance of Yb:YAG, an iterative method is applied to reach the steady state of Yb:YAG, the crystalline fiber amplifier, before the simulation of MI behavior. The simulated MI thresholds in Yb:YAG crystalline fiber amplifiers are found to be at least 28 times of those in Yb-doped silica-glass fiber amplifiers, up to tens of kilowatts. Simulation results show that, in addition to the expected higher thermal conductivity and lower thermo-optic coefficient, strong gain saturation also plays an important role in the high MI threshold of the Yb:YAG crystalline fiber.