Approximation of mode profile dispersion in the generalized nonlinear Schrödinger equation superior to the constant overlap approach for weakly guiding fibers

An efficient numerical approach to nonlinear propagation in waveguides based on an approximation of the overlap integrals' frequency dependence is proposed. Two test cases are studied: A weakly guiding step-index fiber and a weakly guiding parabolic-index fiber, where the approximation is compared to the standard approach of neglecting the frequency dependence and calculating the overlaps at a center wavelength λ0, and benchmarked against a Gaussian quadrature approach, whose accuracy can be increased systematically. We believe that the combined accuracy and efficiency of the proposed approximation make it superior to the other two approaches in few-mode simulations.