Transition between self-focusing and self-defocusing in nonlocally nonlinear media

TL;DR

This paper investigates how the focusing or defocusing behavior of optical beams in nonlocal nonlinear media depends on the degree of nonlocality, revealing a transition point and associated soliton solutions.

Contribution

It predicts a novel transition between self-focusing and self-defocusing states based on nonlocality degree, supported by soliton solutions and stability analysis.

Findings

Transition from focusing to defocusing occurs at a critical nonlocality value.

Bright and dark solitons are obtained in respective states.

The phenomenon can be experimentally realized in nematic liquid crystals or quadratic media.

Abstract

We reveal the relevance between the nonlocality and the focusing/defocusing states in nonlocally nonlinear media, and predict a novel phenomenon that the self-focusing/self-defocusing property of the optical beam in the nonlocally nonlinear medium with a sine-oscillation response function depends on its degree of nonlocality. The transition from the focusing nonlinearity to the defocusing nonlinearity of the nonlinear refractive index will happen when the degree of nonlocality of the system goes cross a critical value, and vise verse. Bright and dark soliton solutions are obtained, respectively, in the focusing state and in the defocusing state, and their stabilities are also discussed. It is mentioned that such a phenomenon might be experimentally realized in the nematic liquid crystal with negative dielectric anisotropy or in the quadratic nonlinear medium.