Symmetry breaking in linearly coupled dynamical lattices

Area of Science:

• Nonlinear physics
• Optical lattices
• Soliton dynamics

Background:

• Discrete nonlinear Schrödinger (DNLS) models are crucial for understanding light propagation in optical lattices.
• Investigating symmetry breaking in these systems is key to controlling soliton behavior.
• Previous studies often focused on one-dimensional systems or lacked detailed stability analysis.

Purpose of the Study:

• To investigate symmetry breaking in 1D and 2D DNLS lattice models.
• To analyze the emergence and stability of asymmetric soliton states.
• To explore the dynamical consequences of symmetry breaking in these systems.

Main Methods:

• Analysis of ground states in linearly coupled DNLS lattices.
• Identification of pitchfork bifurcations (subcritical and supercritical).
• Numerical simulations of unstable solution branches to study dynamics.

Main Results:

• Observed a symmetry-breaking phenomenon in 2D DNLS lattices beyond a critical total power.
• Identified asymmetric states emerging via pitchfork bifurcations.
• Demonstrated dynamical manifestations of symmetry breaking through simulations of unstable states.

Conclusions:

• Presented the first example of spontaneous symmetry breaking in 2D lattice solitons.
• Highlighted the absence of this phenomenon in the continuum limit due to collapse instability.
• The findings offer new insights into controlling and understanding nonlinear wave phenomena in discrete systems.