Analytical theory of frequency-modulated combs: generalized mean-field theory, complex cavities, and harmonic states

Abstract

Frequency-modulated (FM) combs with a linearly-chirped frequency and nearly constant intensity occur naturally in certain laser systems; they can be most succinctly described by a nonlinear Schrödinger equation with a phase potential. In this work, we perform a comprehensive analytical study of FM combs in order to calculate their salient properties. We develop a general procedure that allows mean-field theories to be constructed for arbitrary sets of master equations, and as an example consider the case of reflective defects. We derive an expression for the FM chirp of arbitrary Fabry-Perot cavities$-$important for most realistic lasers$-$and use perturbation theory to show how they are affected by gain curvature. Lastly, we show that an eigenvalue formulation of the laser's dynamics can be useful for characterizing all of the stable states of the laser: the fundamental comb, the continuous-wave solution, and the harmonic states.

22 pages, 8 figures, submitted to Optics Express

References in corpus (5)

• Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillator
• Self-starting Harmonic Comb Emission in THz Quantum Cascade Lasers
• Coherent multi-mode dynamics in a Quantum Cascade Laser: Amplitude and Frequency-modulated Optical Frequency Combs
• Harmonic frequency combs in quantum cascade lasers: time-domain and frequency-domain theory
• Engineering the spectral bandwidth of quantum cascade laser frequency combs

Cited by in corpus (4)

• Planarized THz quantum cascade lasers for broadband coherent photonics
• Multi-mode Dynamics of Terahertz Quantum Cascade Lasers: spontaneous and actively induced generation of dense and harmonic coherent regimes
• Fundamental scaling limits and bandwidth shaping of frequency-modulated combs
• Broadband surface-emitting THz laser frequency combs with inverse-designed integrated reflectors