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Mariana Haragus: Subharmonic linear dynamics of frequency combs modeled by the Lugiato-Lefever equation

Submitted by Jorge Cisneros on November 19, 2020 - 10:11am
Mariana Haragus

Speaker: Mariana Haragus, Université de Franche-Comté

Date: November 19, 2020

Title: Subharmonic linear dynamics of frequency combs modeled by the Lugiato-Lefever equation

Abstract: The Lugiato-Lefever equation is a nonlinear Schrödinger-type equation with damping, detuning and driving, derived in nonlinear optics by Lugiato and Lefever (1987). While extensively studied in the physics literature, there are relatively few rigorous mathematical studies of this equation. Of particular interest for the physical problem is the formation and the dynamical behavior of Kerr frequency combs (optical signals consisting of a super-position of modes with equally spaced frequencies). The underlying mathematical questions concern the existence and the stability of certain particular steady solutions of the Lugiato-Lefever equation. In this talk, I'll discuss the existence and stability of periodic steady waves. The focus will be on their stability with respect to subharmonic perturbations, i.e., periodic perturbations with periods which are integer multiples of the period of the wave.

YouTube: https://youtu.be/4HKiRLrNoqw

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