Harmonic frequency combs in quantum cascade lasers: time-domain and frequency-domain theory

TL;DR

This paper combines numerical simulations and analytical theory to explain how harmonic frequency combs form and remain stable in quantum cascade lasers, highlighting the role of frequency modulation and sideband instabilities.

Contribution

It introduces a frequency-domain linearized theory for analyzing harmonic comb stability and demonstrates the potential for self-supported harmonic states in QCLs.

Findings

Harmonic states exhibit frequency-modulated wave nature.

Instability of single modes can lead to harmonic side modes growth.

Harmonic states can be stable and self-supported under certain conditions.

Abstract

Harmonic frequency combs, in which the lasing modes are separated by a period of tens of free spectral ranges from each other, have been recently discovered in quantum cascade lasers (QCLs). There is an ongoing debate how the harmonic combs can be formed and stable under continuous pumping. Here we reproduce the harmonic state of lasing in QCLs by space-time-domain numerical simulations and show that the corresponding optical wave has a frequency-modulated (FM) nature, with the fundamental beat note in the electron population being suppressed. To understand the physics behind the formation and stability of the harmonic state, we develop a frequency-domain linearized analytic theory which analyzes the stability of single mode lasing with respect to the harmonic state formation and the instabilities of the resulting harmonic state. Our analysis shows how the instability of a single lasing mode can result in the growth of harmonic side modes. The coupling between the two side modes leads to opposite gains for FM and amplitude-modulated (AM) waves, and the FM gain is enhanced as compared to the AM gain. The dependence of the sideband gain spectrum on group velocity dispersion is also studied. While the instability gain of a single lasing mode does not prove that the harmonic state can be self-starting, we analyze the sideband instability gain in the presence of three strong harmonic modes and demonstrate that the harmonic state can be stable and self-supported.