Three-dimensional vortex solitons in quasi-two-dimensional lattices.

Area of Science:

• Nonlinear optics
• Quantum physics
• Condensed matter physics

Background:

• The study investigates the three-dimensional (3D) Gross-Pitaevskii equation, a model for Bose-Einstein condensates and nonlinear optics.
• A quasi-two-dimensional (2D) square-lattice potential is applied, relevant to optical lattices and photonic crystal fibers.

Purpose of the Study:

• To find and characterize stable 3D solitons with embedded vorticity in a quasi-2D lattice potential.
• To identify novel types of 3D solitons, specifically localized vortices and lattice-supported vortex solitons.

Main Methods:

• Variational approximation was employed to predict soliton properties.
• Numerical simulations were used to confirm the existence and stability of the solitons.

Main Results:

• Stable 3D solitons with embedded vorticity (S=1 and S=2) were found, structured as rhombuses of fundamental solitons.
• Two new species of stable 3D solitons were identified: localized vortices (S>1) and lattice-supported vortex solitons (S≠0).
• Instability scenarios for localized vortices, including collapse and decay, were characterized.

Conclusions:

• The research introduces novel stable 3D soliton solutions in nonlinear systems with lattice potentials.
• These findings expand the understanding of nonlinear light propagation and quantum matter, with implications for optical technologies and fundamental physics.