Photon-conserving generalized nonlinear Schrödinger equation for frequency-dependent nonlinearities

Abstract

Pulse propagation in nonlinear waveguides is most frequently modeled by resorting to the generalized nonlinear Schrödinger equation (GNLSE). In recent times, exciting new materials with peculiar nonlinear properties, such as negative nonlinear coefficients and a zero-nonlinearity wavelength, have been demonstrated. Unfortunately, the GNLSE may lead to unphysical results in these cases since, in general, it does not preserve the number of photons and, in the presence of a negative nonlinearity, predicts a blue shift due to Raman scattering. In this paper, we put forth a modified GNLSE that can be used to model the propagation in media with an arbitrary, even negative, nonlinear coefficient. This novel photon-conserving GNLSE (pcGNLSE) ensures preservation of the photon number and can be solved by the same tried and trusted numerical algorithms used for the standard GNLSE. Finally, we compare results for soliton dynamics in fibers with different nonlinear coefficients obtained with the pcGNLSE and the GNLSE.

Octave-Spanning Supercontinuum Generation in As2S3-Silica Hybrid Waveguides Pumped by Thulium-Doped Fiber Laser

“…The n 2 value of As 2 S 3 increases with increasing wavelength and changes the sign in the wavelength range from 600 nm to 1000 nm. Since SC is predominantly generated in the wavelength range of 1 µm to 3 µm in this work, consideration of the complex dependence is not required [31]. The nonlinear coefficient γ as a function of wavelength was calculated by the equation [1]:…”

“…3b). In this case, the calculation cannot be accurately performed and it is necessary to use another model [31]. Thus, for each waveguide, the maximum peak pump pulse power, at which the mathematical model is suitable and the calculation can be performed, is determined.…”

A generic model for the study of supercontinuum generation in graphene-covered nanowires

“…In particular, we extended the pcNLSE to account for TPA in [28]. We must emphasize that the pcNLSE and its modifications [29] have been successfully used to model the propagation of optical pulses in a variety of cases [30][31][32][33][34].…”