Walk-off controlled self-starting frequency combs in χ(2) optical microresonators

Theoretical Analysis of Microcavity Simultons Reinforced by χ^{(2)} and χ^{(3)} Nonlinearities

High-Q microcavities with quadratic and cubic nonlinearities add lots of versatility in controlling microcombs. Here, we study microcavity simulton and soliton dynamics reinforced by both χ^{(2)} and χ^{(3)} nonlinearities in a continuously pumped microcavity. Theoretical analysis based on the Lagrangian approach reveals the soliton peak power and gain-loss balance are impacted by the flat part of the intracavity pump, while the dark-pulse part of the pump leads to a nearly constant soliton group velocity change. We also derived a soliton conversion efficiency upper limit that is fully determined by the coupling condition and the quantum-limited soliton timing jitter in the χ^{(2,3)} system. Numerical simulations confirm the analytical results. Our theory is particularly useful for investigating AlN microcombs and sheds light on the interplay between χ^{(2)} and χ^{(3)} nonlinearities within microcavity simultons.

Soliton based χ(2) combs in high-Q optical microresonators

Investigations of the frequency combs in χ⁽³⁾ microresonators have passed a critical point when the soliton based regimes are well established and realized on different platforms. For χ⁽²⁾ microresonators, where the first harmonic (FH) and second harmonic (SH) envelopes are coupled via the SH generation and optical parametric oscillation, the comb-soliton studies are just starting. Here we report on a vast accessible dual χ⁽²⁾ soliton-comb family in high-Q microresonators with the SH and FH combs centered at the pump frequency ω_p and its half ω_p/2. Vicinity of the point of equal FH and SH group velocities λ_c, available via proper radial poling, is found to be the most advantageous for the generation of spectrally broad dual FH-SH combs. Our predictions as applied to lithium niobate resonators include the dependence of comb and dissipative soliton parameters on the pump power, the deviation λ_p - λ_c, the modal quality factors and frequency detunings, and the necessary parameters of radial poling of the resonator. These predictions form a solid basis for the realization of χ⁽²⁾ frequency combs.

Fine structure of second-harmonic resonances in χ(2) optical microresonators

Owing to the discrete frequency spectrum of whispering gallery resonators (WGRs), the resonance and phase-matching conditions for the interacting waves in the case of second-harmonic generation (SHG) cannot generally be fulfilled simultaneously. To account for this, we develop a model describing SHG in WGRs with non-zero frequency detunings at both the pump and second-harmonic frequencies. Our model predicts strong distortions of the line shape of pump and second-harmonic resonances for similar linewidths at both frequencies; for much larger linewidths at the second-harmonic frequency, this behavior is absent. Furthermore, it describes the SHG efficiency as a function of detuning. Experimentally, one can change the WGR eigenfrequencies, and thus the relative detuning between pump and second-harmonic waves by a number of means, for example electro-optically and thermally. Using a lithium niobate WGR, we show an excellent quantitative agreement for the SHG efficiency between our experimental results and the model. Also, we show the predicted distortions of the pump and second-harmonic resonances to be absent in the lithium niobate WGR but present in a cadmium silicon phosphide WGR, as expected from the linewidths of the resonances involved.