Abstract
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.
Highlights
Numerical simulations of pulse propagation are an integral part of investigating dispersive and nonlinear effects within optical fibers
The efficiency of simulating the generalized nonlinear Schrödinger equation (GNLSE) using the split-step Fourier method (SSFM) is attributed to the execution speed of the fast Fourier transform (FFT) algorithm
For it to be effective the time-frequency grid is required to be linearly spaced. This constraint can prove detrimental to the execution times when the frequency bandwidth considered is very large. This is adverse to simulating fiber optical parametric amplifiers (FOPA) where the effects that are of interest are concentrated in small frequency bands that can be spaced over large separations [2]
Summary
Numerical simulations of pulse propagation are an integral part of investigating dispersive and nonlinear effects within optical fibers. One of the most popular models used for this is the generalized nonlinear Schrödinger equation (GNLSE), which in combination with the split-step Fourier method (SSFM) provides an accurate and efficient tool for investigating dispersive, Kerr and Raman effects of pulses throughout propagation in optical fibers [1]. The efficiency of simulating the GNLSE using the SSFM is attributed to the execution speed of the fast Fourier transform (FFT) algorithm For it to be effective the time-frequency grid is required to be linearly spaced. The GNLSE is usually split between multiple coupled nonlinear Schrödinger equations (CNLE) that simulate pulse propagation within certain frequency bands [3] These coupled equations usually disregard the Raman effect by setting its fractional contribution to the total nonlinearity to zero.
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