Based on the intensity model of few-mode erbium-doped fiber amplifiers (FM-EDFAs), we put forward a semianalytic method for efficiently calculating the signal mode gains by solving the analytical expression for the average population inversion over each fiber segment. Our studies show that, the semi-analytic method can offer a desirable calculation accuracy, very close to that of the full approach method. According to the length dependency of the overlap integral between the normalized transverse distribution of population inversion and the signal modal field, a large iterative step size is verified to be feasible for the semi-analytic method, which is helpful for greatly reducing the iterative times. We also take the example of designing FM-EDFA's overall gain using the semi-analytic method. The semi-analytic method is not only suitable for the FM-EDFAs with complex erbium-ion doping profile, the cladding pumping scheme and the cascaded FM-EDFAs, but also helpful for greatly improving the optimization efficiency of FM-EDFAs in combination with relevant optimization algorithms.
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