Phase-bistable pattern formation in oscillatory systems via rocking: application to nonlinear optical systems.

Area of Science:

• Nonlinear dynamics
• Pattern formation
• Optical physics

Background:

• Oscillatory systems exhibit complex behaviors under external forcing.
• Parametric resonance (2:1 resonance) is a known method for pattern formation.
• Rocking (1:1 resonant forcing) is proposed as an alternative to parametric resonance.

Purpose of the Study:

• To review and present new results on a universal forcing method called "rocking."
• To demonstrate rocking's ability to induce phase bistability and associated patterns.
• To explore rocking as an alternative to parametric resonance, particularly in optical systems.

Main Methods:

• Applying a time- or space-modulated forcing with alternating sign (π-phase jumps) to oscillatory systems.
• Analyzing the emergence of phase bistability and pattern formation.
• Investigating a paradigmatic nonlinear optical system (two-level laser).

Main Results:

• Rocking leads to phase bistability and pattern formation, including phase domains, spatial solitons, and bistable extended patterns.
• Rocking is effective when parametric forcing is inefficient, such as in optics.
• In a two-level laser system, rocking replaces ubiquitous vortices with phase domains and dark-ring solitons.

Conclusions:

• Rocking is a versatile forcing technique for controlling pattern formation in oscillatory systems.
• The 1:1 resonant nature and amplitude modulation of rocking offer advantages over traditional parametric resonance.
• Rocking provides a new mechanism for generating specific optical patterns, like phase domains and dark-ring solitons.