# Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator

## TL;DR

This paper investigates how avoided crossings in microresonators influence nonlinear frequency comb generation, revealing conditions for exciting bright solitons and broadband combs using coupled Lugiato-Lefever equations.

## Contribution

It introduces a coupled Lugiato-Lefever model to analyze comb generation at avoided crossings, providing analytical and computational insights into soliton excitation.

## Key findings

- Bright solitons can be excited at avoided crossings.
- Broadband frequency combs are achievable with proper pumping.
- A deterministic path for soliton generation is identified.

## Abstract

Guided-mode coupling in a microresonator generally manifests itself through avoided crossings of the corresponding resonances. This coupling can strongly modify the resonator local effective dispersion by creating two branches that have dispersions of opposite sign in spectral regions that would otherwise be characterized by either positive (normal) or negative (anomalous) dispersion. In this paper, we study, both analytically and computationally, the general properties of nonlinear frequency comb generation at an avoided crossing using the coupled Lugiato-Lefever equation. In particular, we find that bright solitons and broadband frequency combs can be excited when both branches are pumped for a suitable choice of the pump powers and the detuning parameters. A deterministic path for soliton generation is found.