Walk-off-induced modulation instability, temporal pattern formation, and frequency comb generation in cavity-enhanced second-harmonic generation

Abstract

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 behaviour. 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.

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Cited by in corpus (40)

• Nonlinear and Quantum Optics with Whispering Gallery Resonators
• Second-harmonic assisted four-wave mixing in chip-based microresonator frequency comb generation
• Emerging material systems for integrated optical Kerr frequency combs
• Modulation Instability Induced Frequency Comb Generation in a Continuously Pumped Optical Parametric Oscillator
• Frequency comb formation in doubly resonant second-harmonic generation
• Temporal Simultons in Optical Parametric Oscillators
• Super cavity solitons and the coexistence of multiple nonlinear states in a tristable passive Kerr resonator
• Quadratic Soliton Combs in Doubly-Resonant Second-Harmonic Generation
• Soliton and quasi-soliton frequency combs due to second harmonic generation in microresonators
• Single envelope equation modelling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearity
• Frequency comb generation through the locking of domain walls in doubly resonant dispersive optical parametric oscillators
• Optical frequency combs in quadratically nonlinear resonators
• Temporal Walk-off Induced Dissipative Quadratic Solitons
• Towards optical frequency comb generation in continuous-wave pumped titanium indiffused lithium niobate waveguide resonators
• Experimental observation of internally-pumped parametric oscillation and quadratic comb generation in a ${\chi }^{(2)}$ whispering-gallery-mode microresonator
• Localized structures in dispersive and doubly resonant optical parametric oscillators
• Frequency comb generation threshold in ${\chi }^{(2)}$ optical microresonators
• Parametrically tunable soliton-induced resonant radiation by three-wave mixing
• Parametric localized patterns and breathers in dispersive quadratic cavities
• Soliton trapping and comb self-referencing in a single microresonator with ${\chi }^{(2)}$ and ${\chi }^{(3)}$ nonlinearities
• Coupled-mode theory for microresonators with quadratic nonlinearity
• Walk-off controlled self-starting frequency combs in ${\chi }^{(2)}$ optical microresonators
• Nonlinear solutions for χ^(2) frequency combs in optical microresonators
• Localized structures formed through domain wall locking in cavity-enhanced second-harmonic generation
• Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator
• Modulation instability of Kerr optical frequency combs in dual-coupled optical cavities
• Dark quadratic localized states and collapsed snaking in doubly resonant dispersive cavity enhanced second harmonic generation
• Photon-photon polaritons in chi(2) microresonators
• A high-power waveguide resonator second harmonic device with external conversion efficiency up to 75%
• Modulational instability in $\mathcal{P}\mathcal{T}$-symmetric Bragg grating structures with saturable nonlinearity
• Frequency-domain model of optical frequency-comb generation in optical resonators with second- and third-order nonlinearities
• Depletion-limited Kerr solitons in singly-resonant optical parametric oscillators
• Bistable soliton optical frequency combs in a second harmonic generation Kerr cavity
• Modeling of quasi-phase-matched cavity enhanced second harmonic generation
• Dual backgrounds and their stability during ${\chi }^{(2)}$ comb generation in microresonators
• Walk-off induced dissipative breathers and dissipative breather gas in microresonators
• Parametric conversion via second harmonic generation and two-hump solitons in phase-matched microresonators
• Fine structure of second-harmonic resonances in χ^{(2)} optical microresonators
• Modulation instability and frequency-comb generation in hybrid quadratic-cubic resonators with spectral filtering
• Deterministic generation of parametrically driven dissipative Kerr soliton