Solitary waves in systems with separated Bragg grating and nonlinearity

Area of Science:

• Nonlinear optics
• Waveguide theory
• Soliton dynamics

Background:

• Investigating optical waveguide behavior is crucial for developing advanced photonic devices.
• Solitons, self-reinforcing wave packets, are key phenomena in nonlinear systems.
• Dual-core waveguides offer unique properties due to coupled light propagation.

Purpose of the Study:

• To explore the existence and stability of solitons in a specific dual-core optical waveguide.
• To analyze the influence of Kerr nonlinearity and Bragg gratings on soliton behavior.
• To determine the conditions for stable soliton propagation in the presence of spectral gaps.

Main Methods:

• Analytical investigation of soliton solutions for zero group velocity (c=0).
• Numerical simulations to test soliton stability for both c=0 and c≠0.
• Exploration of soliton existence in spectral gaps, including those overlapping with continuous spectra.

Main Results:

• Analytical solutions for zero-velocity solitons found, filling three spectral gaps when c=0.
• Numerical analysis revealed stable solitons only in the upper section of the upper gap for c=0.
• For c≠0, unusual stationary solitons were found in the upper gap, with stability confirmed in a specific parameter region; stable moving solitons were also identified.

Conclusions:

• Soliton stability in this dual-core waveguide is highly dependent on spectral gap characteristics and group velocity.
• The study identifies specific conditions and regions within spectral gaps where stable solitons can exist and propagate.
• An analytical framework for understanding the radiative decay of these solitons is presented.