Square waves and Bykov T-points in a delay algebraic model for the Kerr-Gires-Tournois interferometer

Area of Science:

• Nonlinear optics
• Cavity quantum electrodynamics
• Theoretical physics

Background:

• Vertically emitting micro-cavities are crucial for optical devices.
• Gires-Tournois resonators with Kerr media exhibit complex dynamics.
• Optical feedback and injection significantly influence cavity behavior.

Purpose of the Study:

• To theoretically investigate the mechanisms of square wave formation.
• To analyze square wave solutions in a micro-cavity with Kerr nonlinearity, delayed feedback, and detuned injection.
• To elucidate the role of homoclinic bifurcations and T-points in generating complex wave patterns.

Main Methods:

• Theoretical analysis of a time-delayed system.
• Application of homoclinic bifurcation theory.
• Investigation of relative homoclinic solutions for large delay limits.
• Analysis of Bykov T-points and Maxwell points.

Main Results:

• Square wave solutions are linked to relative homoclinic solutions.
• The collapsed snaking scenario of square waves is explained.
• Complex-shaped multistable square wave solutions arise from a Bykov T-point.
• The T-point's position correlates with the Maxwell point.

Conclusions:

• Homoclinic bifurcation theory provides a framework for understanding square wave formation.
• Bykov T-points are key to multistable square wave dynamics.
• The study offers insights into controlling optical output in micro-cavities.