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

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.

32 pages, 11 figures

References in corpus (10)

• Stable mode-locked pulses from mid-infrared semiconductor lasers
• Coherent Frequency Combs produced by Self Frequency Modulation in Quantum Cascade Lasers
• Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr
• Semiconductor ring laser frequency combs induced by phase turbulence
• Self-starting harmonic frequency comb generation in a quantum cascade laser
• Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator
• Short pulse generation and mode control of broadband terahertz quantum cascade lasers
• Active mode locking of quantum cascade lasers operating in external ring cavity
• Picosecond pulses from a mid-infrared interband cascade laser
• Laser radio transmitter

Cited by in corpus (5)

• Self-starting Harmonic Comb Emission in THz Quantum Cascade Lasers
• Analytical theory of frequency-modulated combs: generalized mean-field theory, complex cavities, and harmonic states
• Frequency-modulated combs via on-chip field enhancement
• Intensity correlations in quantum cascade laser harmonic frequency combs
• Efficient computation of coherent multimode instabilities in lasers using a spectral approach