Solitons in non-paraxial optics

TL;DR

This paper derives a new analytical soliton solution for the generalized nonlinear amplitude equation (GNAE) in non-paraxial optics and compares it with the classical NSE solution, revealing phase differences that affect pulse evolution.

Contribution

It introduces a novel analytical soliton solution for GNAE and analyzes its differences from the NSE solution, especially in phase and multisoliton dynamics.

Findings

New soliton solution for GNAE derived

Significant phase differences found between GNAE and NSE solutions

Different multisoliton evolution behavior observed

Abstract

The well-known (1+1D) nonlinear Schr\"odinger equation (NSE) governs the propagation of narrow-band pulses in optical fibers and others one-dimensional structures. For exploration the evolution of broad-band optical pulses (femtosecond and attosecond) it is necessary to use the more general nonlinear amplitude equation (GNAE) which differs from NSE with two additional non-paraxial terms. That is way, it is important to make clear the difference between the solutions of these two equations. We found a new analytical soliton solution of GNAE and compare it with the well-known NSE one. It is shown that for the fundamental soliton the main difference between the two solutions is in their phases. It appears that, this changes significantly the evolution of optical pulses in multisoliton regime of propagation and admits a behavior different from that of the higher-order NSE solitons.