Walk-Off-Induced Modulation Instability, Temporal Pattern Formation, and Frequency Comb Generation in Cavity-Enhanced Second-Harmonic Generation

• Published in: Physical review letters Vol. 116; no. 3; p. 033901
• Main Authors: Leo, F, Hansson, T, Ricciardi, I, De Rosa, M, Coen, S, Wabnitz, S, Erkintalo, M
• Format: Journal Article
• Language: English
• Published: United States 22-01-2016
• Subjects: Computer simulation; Dynamical systems; Instability; Mathematical models; Modulation; Nonlinear dynamics; Nonlinearity; Spectra
• ISSN: 0031-9007; 1079-7114; 1079-7114
• DOI: 10.1103/physrevlett.116.033901

We derive a time-domain mean-field equation to model the full temporal and spectral dynamics of light in singly resonant cavity-enhanced second-harmonic generation systems. We show that the temporal walk-off between the fundamental and the second-harmonic fields plays a decisive role under realistic conditions, giving rise to rich, previously unidentified nonlinear behavior. Through linear stability analysis and numerical simulations, we discover a new kind of quadratic modulation instability which leads to the formation of optical frequency combs and associated time-domain dissipative structures. Our numerical simulations show excellent agreement with recent experimental observations of frequency combs in quadratic nonlinear media [Phys. Rev. A 91, 063839 (2015)]. Thus, in addition to unveiling a new, experimentally accessible regime of nonlinear dynamics, our work enables predictive modeling of frequency comb generation in cavity-enhanced second-harmonic generation systems. We expect our findings to have wide impact on the study of temporal and spectral dynamics in a diverse range of dispersive, quadratically nonlinear resonators.