Kumar, S.; Cardoso, W.B.; Malomed, A.B.A. Stable Patterns in the Lugiato–Lefever Equation with a Confined Vortex Pump. Symmetry2024, 16, 470.
Kumar, S.; Cardoso, W.B.; Malomed, A.B.A. Stable Patterns in the Lugiato–Lefever Equation with a Confined Vortex Pump. Symmetry 2024, 16, 470.
Kumar, S.; Cardoso, W.B.; Malomed, A.B.A. Stable Patterns in the Lugiato–Lefever Equation with a Confined Vortex Pump. Symmetry2024, 16, 470.
Kumar, S.; Cardoso, W.B.; Malomed, A.B.A. Stable Patterns in the Lugiato–Lefever Equation with a Confined Vortex Pump. Symmetry 2024, 16, 470.
Abstract
We introduce a model of a passive optical cavity based on the two-dimensional Lugiato-Lefever
equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity.
Up to S = 5, stable vortex-ring states (vortex pixels) are produced by a variational approximation
and in a numerical form. Surprisingly, vast stability areas of the vortex states are found, for
both the self-focusing and defocusing signs of the nonlinearity, in the plane of the pump-strength and
loss parameters. When the vortex-rings are unstable, they are destroyed by azimuthal perturbations
which break the axial symmetry. The results suggest new possibilities for mode manipulations in
nonlinear optical media.
Keywords
soliton; stability; variational approximation; vortex; optical cavity; winding number
Subject
Physical Sciences, Optics and Photonics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
