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

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 Schrodinger 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 finite gain bandwidth and linewidth enhancment in fast gain media. 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. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Automated summary

In this study, we conducted a comprehensive analysis of FM combs in order to calculate their significant properties. The analysis was based on the development of a general procedure for constructing mean-field theories. Our findings showed that the FM chirp of arbitrary Fabry-Perot cavities, which is crucial for realistic lasers, is affected by finite gain bandwidth and linewidth enhancement in fast gain media. Additionally, we demonstrated that an eigenvalue formulation of the laser's dynamics can be useful for characterizing all stable states of the laser.