Through the fourth order Runge-Kutta formulas, the multimode rate equations, tailored to accommodate different pumping methods, are employed to evaluate the pumping efficiency and the signal power in the multimode fiber amplifier. The effect of the tiny change of fiber length (about millimeter level) on the output beam quality is studied. The beam quality factor varies quasi-periodically with the tiny change of fiber length. And the period is dependent on the propagation constant difference between the eigen modes of the amplifier.
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