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.