Full-vectorial multimode nonlinear simulations on a real-space Fourier–Gauss grid

A numerical approach for nonlinear propagation in multimode waveguides based on real-space integration of the nonlinear polarization is developed for full-vectorial simulations. The real-space integrations are performed on a Fourier–Gauss quadrature grid in accordance with an earlier scalar formulation. The method is benchmarked against an alternative approach based on summation of mode overlap integrals, which is efficient for few-mode fibers but scales unfavorably with the number of modes. For silica nanowires and birefringent step-index fibers with weak index contrast, the Fourier–Gauss method is found to be comparable or superior to the mode overlap method when 12 modes (three mode groups) are included in the simulations without accounting for mode profile dispersion.