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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.