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Light states relevant to the χ ( 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 χ ( 2 ) combs and also for 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 optical parameteric oscillation, the instability is controlled by a fourth-degree characteristic equation for the increment. Coefficients of this equation depend not only on wavenumbers of the perturbations, 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.

Microresonator frequency combs based on the $\chi^{(3)}$ nonlinearity are nowadays well understood and making their way into different applications. Recently, microresonator frequency combs based on the $\chi^{(2)}$ nonlinearity are receiving increasing attention, as they promise certain benefits, but still require further study. Here, we demonstrate the generation of a $\chi^{(2)}$ frequency comb, initiated via optical parametric oscillation (OPO) in a lithium niobate mm-sized microresonator. By pumping at 532 nm with 30 $\mu$W of power, we observe 1-THz-wide comb spectra around 1064 nm with degenerate and non-degenerate states. We also show that comb generation requires signal and idler waves to be degenerate in mode numbers and how the fulfillment of this condition can be identified from the temperature tuning curves. The results demonstrate the potential to directly generate frequency combs via OPO beyond 3 $\mu$m wavelengths in the mid-IR by puming in the near-IR region., Comment: 8 pages, 7 figures

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.

Frequency combs in χ ( 2 ) optical microresonators caused by cascaded second-order nonlinear processes currently attract great research interest. In contrast to χ ( 3 ) resonators, two light amplitudes relevant to the first and second harmonics (FH and SH), two dispersion coefficients, and a considerable difference of the FH and SH group velocities (the walk-off) must be taken into account to investigate localized coherent structures (solitons) propagating with a common velocity. Finding such comb solutions taking into account external pumping is a crucial step toward the χ ( 2 ) combs. We report on two new families of driven soliton-comb solutions for χ ( 2 ) microresonators. They are strongly localized, corresponding to spectrally broad combs, and possess well-defined FH and SH frequency detunings, propagation velocities, and, generally, nonzero spatial backgrounds.