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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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Vortex lattice solitons supported by localized gain.

Yaroslav V Kartashov¹, Vladimir V Konotop, Victor A Vysloukh

¹Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain.

|October 5, 2010

Summary

Localized gain enables dissipative vortex solitons in periodic Kerr media with two-photon absorption. Symmetry between gain and refractive index is crucial for vortex soliton formation, preventing transformation into multipoles.

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Area of Science:

Nonlinear optics
Photonics
Condensed matter physics

Background:

Dissipative solitons are self-organized structures in open systems.
Kerr media exhibit intensity-dependent refractive indices.
Two-photon absorption introduces nonlinear loss.

Purpose of the Study:

To investigate the existence and stability of vortex solitons in periodic Kerr media with localized gain and two-photon absorption.
To determine the conditions for exciting vortex solitons.

Main Methods:

Numerical simulations of nonlinear Schrödinger equations.
Analysis of lattice spectrum and propagation constants.
Investigation of symmetry conditions for soliton formation.

Main Results:

Localized gain supports dissipative vortex solitons in focusing and defocusing Kerr media.
Vortex solitons exist with propagation constants from semi-infinite or finite spectral gaps.
Coincident discrete rotational symmetries of gain and refractive index are necessary for vortex soliton excitation.

Conclusions:

Dissipative vortex solitons can be generated and sustained in engineered periodic optical lattices.
Symmetry breaking leads to the formation of stable dissipative multipoles instead of vortex solitons.