The Relation Between Optical beams Propagation in Free Space and in Strongly Nonlocal Nonlinear Media

TL;DR

This paper establishes a direct mathematical correspondence between optical beam propagation in strongly nonlocal nonlinear media and free space, enabling transfer of solutions and properties, and introduces an efficient numerical method for SNN media analysis.

Contribution

It demonstrates a one-to-one correspondence between propagation in SNN media and free space, providing new analytical and numerical tools for studying wave evolution in these media.

Findings

Propagation properties in SNN media can be directly derived from free space solutions.

The method simplifies the analysis of solitons and breathers in SNN media.

The approach applies to other wave evolution contexts like Bose-Einstein condensates.

Abstract

The relation between optical beams propagation in strongly nonlocal nonlinear (SNN) media and {propagation} in free space is {demonstrated using} the technique of variable transformation. The governing equation, integral and analytical solutions, and propagation properties in free space can be directly transferred to their counterparts in SNN media through a one-to-one correspondence. The one-to-one correspondence together with the Huygens-Fresnel integral yields an efficient numerical method to describe SNN propagation. The existence conditions and possible structures of solitons and breathers in SNN media are described in a unified manner by comparing propagation properties in SNN media with those in free space. The results can be employed in other contexts in which the governing equation for the evolution of waves is equivalent to that in SNN media, such as for quadratic graded-index media, or for harmonically trapped Bose-Einstein condensates in the noninteracting limit.