Hodographic Vortices

TL;DR

This paper explores the universal nature of vortices as screw phase dislocations in nonlinear optics, analyzing their behavior through geometric optics equations and focusing on Kerr nonlinearities.

Contribution

It introduces a hodograph plane analysis revealing how vortex solutions depend on the specific form of the nonlinear response.

Findings

Vortices are universal solutions in nonlinear optical systems.

Hodograph analysis shows deformation of vortex solutions based on nonlinearity.

Kerr nonlinearity exemplifies the sensitivity of vortex solutions.

Abstract

Vortices are screw phase dislocations associated with helicoidal wave-fronts. In nonlinear optics, vortices arise as singular solutions to the phase-intensity equations of geometric optics. They exist for a general class of nonlinear response functions. In this sense, vortices possess a universal character. Analysis of geometric optics equations on the hodograph plane leads to deformed vortex type solutions that are sensitive to the form of the nonlinearity. The case of a Kerr type nonlinear response is discussed as a specific example.