Frequency-banded nonlinear Schrödinger equation with inclusion of Raman nonlinearity.

The well-established generalized nonlinear Schrödinger equation (GNLSE) to simulate nonlinear pulse propagation in optical fibers and waveguides becomes inefficient if only narrow spectral bands are occupied that are widely separated in frequency/wavelength, for example in parametric amplifiers. Here we present a solution to this in the form of a coupled frequency-banded nonlinear Schrödinger equation (BNLSE) that only simulates selected narrow frequency bands while still including all dispersive and nonlinear effects, in particular the inter-band Raman and Kerr nonlinearities. This allows for high accuracy spectral resolution in regions of interest while omitting spectral ranges between the selected frequency bands, thus providing an efficient and accurate way for simulating the nonlinear interaction of pulses at widely different carrier frequencies. We derive and test our BNLSE by comparison with the GNLSE. We finally demonstrate the accuracy of the BNLSE and compare the computational execution times for the different models.