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Kelvin-Wave-Inspired Optical Vortex Excitation in Kerr Nonlinear Media

Yosuke Minowa, Nobuhiko Yokoshi, Makoto Tsubota

TL;DR

The paper addresses how to rigorously connect nonlinear optical dynamics in defocusing Kerr media with quantum-fluid vortex dynamics, enabling optical realization of Kelvin-wave excitations on vortex cores. By deriving a (3+1)D nonlinear Schrödinger equation for the optical field and mapping it to the Gross–Pitaevskii framework, it establishes a formal optical–quantum-fluid correspondence. It then introduces a Kelvin-wave analogue via a deformed vortex core, deriving an effective Lagrangian that yields two helical Kelvin-wave branches and a stationary mode, with explicit dispersion relations and field profiles. The work outlines feasible experimental schemes to generate and image these modes, positioning nonlinear optics as a versatile simulator for complex vortex dynamics such as Kelvin-wave cascades and reconnections in quantum fluids.

Abstract

We demonstrate a direct one-to-one correspondence between nonlinear optical fields in defocusing Kerr media and wave functions in weakly interacting Bose-Einstein condensates or quantum fluids. Based on this correspondence, we propose the existence of excitations in an optical vortex beam characterized by a helical deformation of its phase singularity core. These excitations are direct analogues of Kelvin waves known in quantum and classical fluid dynamics. We further show that the excitations exhibit two distinct branches, one of which includes a stationary solution. A feasible experimental scheme for generating these excitations is also discussed.

Kelvin-Wave-Inspired Optical Vortex Excitation in Kerr Nonlinear Media

TL;DR

The paper addresses how to rigorously connect nonlinear optical dynamics in defocusing Kerr media with quantum-fluid vortex dynamics, enabling optical realization of Kelvin-wave excitations on vortex cores. By deriving a (3+1)D nonlinear Schrödinger equation for the optical field and mapping it to the Gross–Pitaevskii framework, it establishes a formal optical–quantum-fluid correspondence. It then introduces a Kelvin-wave analogue via a deformed vortex core, deriving an effective Lagrangian that yields two helical Kelvin-wave branches and a stationary mode, with explicit dispersion relations and field profiles. The work outlines feasible experimental schemes to generate and image these modes, positioning nonlinear optics as a versatile simulator for complex vortex dynamics such as Kelvin-wave cascades and reconnections in quantum fluids.

Abstract

We demonstrate a direct one-to-one correspondence between nonlinear optical fields in defocusing Kerr media and wave functions in weakly interacting Bose-Einstein condensates or quantum fluids. Based on this correspondence, we propose the existence of excitations in an optical vortex beam characterized by a helical deformation of its phase singularity core. These excitations are direct analogues of Kelvin waves known in quantum and classical fluid dynamics. We further show that the excitations exhibit two distinct branches, one of which includes a stationary solution. A feasible experimental scheme for generating these excitations is also discussed.
Paper Structure (4 sections, 32 equations, 3 figures)

This paper contains 4 sections, 32 equations, 3 figures.

Table of Contents

  1. Introduction
  2. (3+1)-dimensional nonlinear Schrödinger equation in Kerr nonlinar media
  3. Kelvin wave analogue excitation in defocusing Kerr media
  4. Discussion

Figures (3)

  • Figure 1: Schematic illustration of optical vortex beams. (a) Phase front of a straight optical vortex beam. (b) Phase front of an optical vortex beam exhibiting a helically deformed phase singularity, analogous to a Kelvin-wave excitation observed on quantized vortices. The entire electric field distribution is helically deformed.
  • Figure 2: Dispersion relation for the Kelvin-wave analogue mode along the vortex beam. Here we assume $\ln\left(R/r_0\right)=5$.
  • Figure 3: Electric field distribution around the vortex core for the straight vortex solution (a--c) and the left-handed stationary Kelvin-wave solution (d--f). Panels (a, d) and (b, e) illustrate the field distribution in the $xz$ and $yz$ planes, respectively. Panels (c, f) show the iso-surface of the normalized electric field magnitude, $|E/E_0|$.