Solitary Waves in Optical Fibers Governed by Higher Order Dispersion

TL;DR

This paper presents exact solutions for stable solitary waves in optical fibers considering higher order dispersion effects, with potential applications in communications and laser technologies.

Contribution

It introduces a new exact solitary wave solution for the nonlinear Schrödinger equation with higher order dispersion and analyzes its stability and scaling properties.

Findings

Stable sech2-shaped solitons exist with higher order dispersion.

Stability is proven via operator sign-definiteness and Sobolev integrals.

Scaling relations enable efficient parameter tuning for practical applications.

Abstract

An exact solitary wave solution is presented for the nonlinear Schrodinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The stability of this soliton-like solution with sech2 shape is proven by the sign-definiteness of the operator and an integral of the Sobolev type. The main criteria governing the existence of such stable localized pulses propagating in optical fibers are also formulated. A unique feature of these soliton-like optical pulses propagating in a fiber with higher order dispersion is that their parameters satisfy efficient scaling relations. The main soliton solution term given by perturbation theory is also presented when absorption or gain is included in the nonlinear Schrodinger equation. We anticipate that this type of stable localized pulses could find practical applications in communications, slow-light devices and ultrafast lasers.