Neutral delay differential equation Kerr cavity model

TL;DR

This paper introduces a neutral delay differential equation model for Kerr cavities with external injection, capturing complex dynamics including dissipative solitons and resonance overlaps, extending the Lugiato-Lefever framework.

Contribution

The paper develops a generalized NDDE model for Kerr cavities that incorporates higher-order dispersion and mode overlaps, surpassing the capabilities of existing LLE-based models.

Findings

The model admits dissipative soliton solutions.

It describes resonance overlaps in Kerr cavities.

Solitons are destroyed by Cherenkov radiation beyond certain limits.

Abstract

A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second and higher order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.