Floquet lattice solitons in zigzag modulated waveguide arrays with zero average modulation: Exponential localization...

Area of Science:

• Nonlinear optics
• Condensed matter physics
• Photonic lattices

Background:

• Waveguide arrays with periodic modulations exhibit complex phenomena.
• The Su-Schrieffer-Heeger (SSH) model describes topological insulators and has analogs in photonic systems.
• Kerr nonlinearity introduces nonlinear effects crucial for soliton formation.

Purpose of the Study:

• To investigate the existence and stability of nonlinear localized solutions in waveguide arrays with zigzag modulations.
• To analyze the influence of Floquet band gaps on the localization of these solutions.
• To explore the stability of nonlinear lattice solitons under specific conditions.

Main Methods:

• Utilizing the tight-binding model for waveguide arrays.
• Analyzing the Floquet spectrum of the linearized Su-Schrieffer-Heeger (SSH)-like system.
• Employing numerical continuation to find nonlinear solutions.
• Performing numerical Floquet linear stability analysis.

Main Results:

• Identified spectral gaps in the Floquet spectrum where nonlinear solutions can exist.
• Found exponentially localized Floquet lattice solitons in both bulk and edge states.
• Determined regimes of stability for these solitons.
• Characterized instability scenarios arising from internal mode resonances.

Conclusions:

• Nonlinear localized waves, or Floquet lattice solitons, can be stably realized in waveguide arrays with zigzag modulations.
• The spectral properties of the linearized system dictate the possible locations and localization of these nonlinear solutions.
• Internal mode resonances play a significant role in soliton instability.