Riemann problem for the photon fluid: self-steepening effects

TL;DR

This paper analyzes the complex wave structures arising from the Riemann problem in photon fluids within optical fibers, incorporating self-steepening effects, and provides a comprehensive classification of possible wave evolutions.

Contribution

It introduces a detailed classification of wave structures for the photon fluid Riemann problem considering self-steepening effects, extending the understanding beyond the standard NLS equation.

Findings

Rich dynamics compared to standard NLS equation

Complete classification of wave structures for all jump conditions

Identification of new wave phenomena due to self-steepening

Abstract

We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear Schroedinger (NLS) equation with self-steepening term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. It is shown that evolution dynamics in this case is much richer than that for the NLS equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity.