# Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr

## TL;DR

This paper develops a theoretical framework for frequency modulated (FM) combs in lasers, revealing how spatial hole burning, dispersion, and Kerr effects cause linear frequency chirps, and compares predictions with experimental observations.

## Contribution

It introduces a master equation for FM combs that captures the effects of spatial hole burning, dispersion, and Kerr, providing new insights into phase-locking mechanisms in lasers.

## Key findings

- Linear frequency chirp arises from combined effects of spatial hole burning, dispersion, and Kerr.
- The theory explains observed chirp behavior in semiconductor lasers.
- Chirp is a general feature of self-starting FM combs.

## Abstract

Frequency modulated (FM) frequency combs constitute an exciting alternative to generate equidistant spectra. The full set of Maxwell-Bloch equations is reduced to a single master equation for FM combs with fast dynamics to provide insight into the governing mechanisms behind phase-locking. It reveals that the recently observed linear frequency chirp is caused by the combined effects of spatial hole burning, group velocity dispersion and Kerr due to asymmetric gain. The comparison to observation in various semiconductor lasers suggests that the linear chirp is general to self-starting FM combs.