Theory of dispersive shock waves induced by the Raman effect in optical fibers

TL;DR

This paper develops an analytical theory for dispersive shock waves in optical fibers influenced by the Raman effect, using Whitham modulation equations to predict wave profiles that match numerical simulations.

Contribution

It introduces a novel theoretical framework for dispersive shock waves in optical fibers considering the Raman effect, deriving new analytical relations and validating them with numerical solutions.

Findings

Analytical shock wave profiles match numerical simulations.

Derived Rankine-Hugoniot-like conditions for optical shock waves.

The Raman effect stabilizes shock wave profiles during long-distance propagation.

Abstract

We develop the theory of dispersive shock waves in optical fibers for the case of long-distance propagation of optical pulses, when the small Raman effect stabilizes the profile of the shock. The Whitham modulation equations are derived as the basis for the Gurevich-Pitaevskii approach to the analytical theory of such shocks. We show that the wave variables at both sides of the shock are related by the analogue of the Rankine-Hugoniot condition that follows from the conservation laws of the Whitham equations. Solutions of the Whitham equations yield the profiles of the wave variables that agree very well with the exact numerical solution of the generalized nonlinear Schroedinger equation for propagation of optical pulses.