Unraveling the origin of frequency modulated combs using active cavity mean-field theory

TLDR

In many laser systems, frequency‑modulated combs can form, producing light whose frequency sweeps linearly, yet a compact description of the core physics has remained elusive. The study aims to demonstrate that active‑cavity lasers can be modeled by a nonlinear Schrödinger equation with a potential proportional to the phase of the electric field. The equation can be solved analytically, yielding a field with quasi‑constant intensity and piecewise quadratic phase, which we term extendons that describe both fundamental FM combs and harmonic states. The theory explains the ubiquity of FM combs across many lasers and unifies numerous experimental observations.

Abstract

In many laser systems, frequency combs whose output is frequency-modulated (FM) can form, producing light whose frequency sweeps linearly. While this intriguing result has been replicated experimentally and numerically, a compact description of the core physics has remained elusive. By creating a mean-field theory for active cavities analogous to the Lugiato–Lefever equation, we show that these lasers are described by a nonlinear Schrödinger equation with a potential proportional to the phase of the electric field. This equation can be solved analytically and produces a field with quasi-constant intensity and piecewise quadratic phase. We refer to these nondispersive waves as extendons , and they describe both fundamental FM combs and harmonic states. Our results apply to many lasers, explaining the ubiquity of this phenomenon, and our new theory unifies many experimental observations.