Comparison of numerical methods for modeling laser mode locking with saturable gain

The widely used split-step Fourier method has difficulties when solving partial differential equations with saturable gain. Here, we describe a modified split-step Fourier method, and we compare it to several different algorithms for solving the Haus mode-locking equation and related equations that are used to model mode-locked lasers and other optical oscillators and amplifiers with saturable gain. These equations all include the product of a scalar nonlinearity and a stiff nonlinear operator. We find that a modified split-step method is the easiest to program with the same level of reliability and accuracy as the other methods that we investigated.