Revisiting Soliton Dynamics in Fiber Optics Under Strict Photon-Number Conservation

We revisit the complex interplay between the Raman-induced frequency shift (RIFS) and the effect of self-steepening (SS) in the propagation of solitons, and in the framework of an equation that ensures strict conservation of the number of photons. The generalized nonlinear Schrödinger equation (GNLSE) is shown to severely fail in preserving the number of photons for sub-100-fs solitons, leading to a large overestimation of the frequency shift. Furthermore, when considering the case of a frequency-dependent nonlinear coefficient, the GNLSE also fails to provide a good estimation of the time shift experienced by the soliton. We tackle these shortcomings of the GNLSE by resorting to the recently introduced photon-conserving GNLSE (pcGNLSE) and study the interplay between the RIFS and self-steepening. As a result, we make apparent the impact of higher-order nonlinearities on short-soliton propagation and propose an original and direct method for the estimation of the second-order nonlinear coefficient.