Square Waves and Bykov T-points in a Delay Algebraic Model for the Kerr-Gires-Tournois Interferometer

TL;DR

This paper investigates the formation and bifurcation mechanisms of square wave solutions in a Kerr-Gires-Tournois interferometer with delayed feedback, revealing complex multistability and the role of T-points in the system.

Contribution

It introduces a novel theoretical approach linking delay differential equations to homoclinic bifurcation theory to analyze square wave solutions.

Findings

Square wave solutions can be analyzed as relative homoclinic solutions in the large delay limit.

The study uncovers the collapsed snaking scenario of square waves.

It identifies the role of Bykov T-points in multistability and complex solution structures.

Abstract

We study theoretically the mechanisms of square wave formation of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a Kerr medium and that is subjected to strong time-delayed optical feedback and detuned optical injection. We show that in the limit of large delay, square wave solutions of the time-delayed system can be treated as relative homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of square wave solutions. In particular, we unveil the mechanisms behind the collapsed snaking scenario of square waves and explain the formation of complex-shaped multistable square wave solutions through a Bykov T-point. Finally we relate the position of the T-point to the position of the Maxwell point in the original time-delayed system.