Modification of the split-step method for modeling multicore fiber with saturated gain

We report an efficient noniterative numerical algorithm for solving a system of linearly coupled nonlinear Schrödinger equations (NLSE) describing the propagation of light pulses in multicore optical fibers, with optical losses and saturated gain taken into account. The method can also be used in the case of a single scalar NLSE. The proposed algorithm is based on the split-step Fourier method and has the second order of accuracy in the evolutionary variable and the exponential order of accuracy in time. To solve the system of coupled NLSEs, we propose to approximate the matrix exponential using the Pade approximation.