Efficient simulation of multimodal nonlinear propagation in step-index fibers

A numerical approach to nonlinear propagation in waveguides based on real-space Gaussian quadrature integration of the nonlinear polarization during propagation is investigated and compared with the more conventional approach based on expressing the nonlinear polarization by a sum of mode overlap integrals. Using the step-index fiber geometry as an example, it is shown that the Gaussian quadrature approach scales linearly or at most quadratically with the number of guided modes and that it can account for mode profile dispersion without additional computational overhead. These properties make it superior for multimode nonlinear simulations extending over wide frequency ranges. (C) 2017 Optical Society of America