Dual backgrounds and their stability during ${\chi }^{(2)}$ comb generation in microresonators

Abstract

Light states relevant to the ${\chi }^{(2)}$ comb generation in optical microresonators possess typically dual backgrounds for coupled first-harmonic (FH) and second-harmonic (SH) envelopes. Stability and/or instability of these backgrounds is crucial for realization of stable ${\chi }^{(2)}$ combs and also for an efficient SH generation. We explore the properties of the dual backgrounds and their instability for the cases of FH and SH pumping of the resonator. In contrast to the optical parameteric oscillation, the instability is controlled by a 4th-degree characteristic equation for the increment. Coefficients of this equation depend not only on wavenumbers of the perturbations, the pump power, and dispersion parameters, but also on FH-SH group velocity difference (temporal walk-off). Our results include characterization of the regions and conditions of stability for the FH- and SH-pumping cases and different spectral ranges.

arXiv comment10 pages, 8 figures

References in corpus (19)

• Temporal solitons in optical microresonators
• Ultra-efficient frequency comb generation in AlGaAs-on-insulator microresonators
• Nonlinear and Quantum Optics with Whispering Gallery Resonators
• Naturally-phasematched second harmonic generation in a whispering gallery mode resonator
• Pockels Soliton Microcomb
• Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators
• Walk-off-induced modulation instability, temporal pattern formation, and frequency comb generation in cavity-enhanced second-harmonic generation
• Modulation Instability Induced Frequency Comb Generation in a Continuously Pumped Optical Parametric Oscillator
• Frequency comb generation via cascaded second-order nonlinearities in microresonators
• Frequency comb formation in doubly resonant second-harmonic generation
• Quadratic Soliton Combs in Doubly-Resonant Second-Harmonic Generation
• Frequency combs in a microring optical parametric oscillator
• Soliton and quasi-soliton frequency combs due to second harmonic generation in microresonators
• Experimental observation of internally-pumped parametric oscillation and quadratic comb generation in a ${\chi }^{(2)}$ whispering-gallery-mode microresonator
• Frequency comb generation threshold in ${\chi }^{(2)}$ optical microresonators
• Walk-off controlled self-starting frequency combs in ${\chi }^{(2)}$ optical microresonators
• Nonlinear solutions for χ^(2) frequency combs in optical microresonators
• Theory of ${\chi }^{(2)}$-microresonator-based frequency conversion
• Fine structure of second-harmonic resonances in χ^{(2)} optical microresonators