Discontinuous spirals of stability in an optically injected semiconductor laser

Area of Science:

• Nonlinear dynamics
• Optically injected semiconductor lasers
• Complex cubic dynamics

Background:

• Optically injected semiconductor lasers exhibit complex dynamics.
• Previous models identified fish-like and cuspidal-like structures as normal forms of cubic dynamics.

Purpose of the Study:

• To report a novel discontinuous spiral structure in the parameter space of an optically injected semiconductor laser model.
• To characterize the tridimensional structure and periodic orbits of this new spiral.
• To investigate the relationship between spiral traversal and laser intensity peaks.

Main Methods:

• Analysis of an optically injected semiconductor laser model.
• Identification and characterization of complex cubic dynamics, including fish-like and cuspidal-like structures.
• Investigation of parameter space, focusing on the linewidth enhancement factor (α).

Main Results:

• A new discontinuous spiral with stable periodic orbits was identified.
• The spiral possesses a tridimensional structure with multiple rolling directions.
• Laser intensity shows a specific increase in peaks when turning along the spiral, but not at discontinuities.
• Discontinuities are formed or destroyed via disaggregation or collapses from/into shrimp-like structures as the linewidth enhancement factor (α) is varied.

Conclusions:

• The discovered discontinuous spiral represents a novel phenomenon in laser dynamics.
• The spiral's behavior, particularly the intensity peak changes, warrants further theoretical and experimental investigation.
• Understanding the origin and relationship of these spirals to homoclinic spirals is a key future direction.