Dynamical properties of lasers coupled face to face

Area of Science:

• * Physics, Optics, and Photonics
• * Nonlinear Dynamics and Complex Systems

Background:

• * Modeling coupled laser systems is crucial for understanding complex optical phenomena.
• * Existing models often lack analytical tractability for specific configurations like face-to-face coupling.

Purpose of the Study:

• * To derive and analyze a reduced model for two identical, face-to-face coupled lasers.
• * To investigate the steady-state and periodic solutions of the coupled electric field amplitudes.
• * To classify and determine the stability of these solutions.

Main Methods:

• * Derivation of a reduced model from Maxwell-Bloch equations using adiabatic elimination and large-distance approximations.
• * Analytical and numerical investigation of the resulting coupled delay differential equations.
• * Stability analysis of identified steady and periodic solutions.

Main Results:

• * A reduced model of two coupled delay differential equations with cross-coupling and nonlinearity was established.
• * Identified symmetric, antisymmetric, and asymmetric solutions for electric fields in both steady and periodic states.
• * Stability analysis revealed a homoclinic point associated with asymmetric periodic solutions.

Conclusions:

• * The derived reduced model provides a tractable framework for studying coupled homogeneously broadened lasers.
• * The classification of solutions (symmetric, antisymmetric, asymmetric) offers insights into the dynamics of coupled laser systems.
• * The presence of a homoclinic point highlights complex dynamical behaviors in asymmetric periodic states.