Surface gap solitons in a nonlinear fractional Schrödinger equation

Area of Science:

• Nonlinear optics
• Condensed matter physics
• Mathematical physics

Background:

• Gap solitons are crucial for optical signal processing.
• Optical lattices create unique bandgap structures.
• Fractional Schrödinger equation models anomalous diffusion and wave propagation.

Purpose of the Study:

• Investigate gap soliton dynamics at uniform media-optical lattice interfaces.
• Explore the influence of fractional diffraction on soliton properties.
• Analyze conditions for soliton stabilization, particularly for multi-peaked solitons.

Main Methods:

• Numerical simulations based on the nonlinear fractional Schrödinger equation.
• Analysis of Floquet-Bloch spectrum for bandgap identification.
• Characterization of soliton families and their stability properties.

Main Results:

• Identified novel gap soliton families in the first and second bandgaps.
• Demonstrated suppression of soliton instability by decreasing the Lévy index.
• Found that multi-peaked solitons can achieve complete stability above a critical power threshold.

Conclusions:

• Fractional diffraction effects significantly influence gap soliton behavior.
• The Lévy index offers a tunable parameter for controlling soliton stability.
• Stable multi-peaked solitons are achievable in fractional dimensions, opening new possibilities for optical devices.