Based on the intensity model of few-mode erbium-doped fiber amplifiers (FM-EDFAs), we put forward a semi-analytic 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.

基于少模掺fiber光纤放大器（FM-EDFA）的强度模型，我们提出了一种半解析方法，通过求解每个光纤段上平均种群反转的解析表达式来有效地计算信号模式增益。我们的研究表明，半解析方法可以提供理想的计算精度，非常接近于完全方法。根据总体反演归一化横向分布与信号模态场之间重叠积分的长度依赖性，证明了较大的迭代步长对于半解析方法是可行的，这有助于大大减少迭代时间。我们还以使用半解析法设计FM-EDFA的整体增益为例。