Abstract

Monochromatic pumping of ${\chi ^{\!(2)}}$ microresonators is promising for frequency comb generation. Two main generation schemes refer to pumping into the phase-matched first harmonic (FH) and second harmonic (SH)—FH and SH pumping. The phase matching can be natural or artificial (employing periodic poling). Also, minimization of the FH and SH group velocity difference (temporal walk-off) is needed for effective comb generation. So far, perspective soliton-comb regimes were predicted for SH pumping in lithium niobate (LN)-based resonators at a special poling. Here we explore, analytically and numerically, the possibilities for realizing the ${\chi ^{\!(2)}}$ comb generation for the remaining options of pumping as applied to LN microresonators. This includes the FH pumping case for the pump wavelength ${\lambda _p} \simeq 2698\;{\rm nm} $ in radially poled resonators and also FH and SH pumping schemes at natural phase matching, ${\lambda _p} \simeq 1664$ and 832 nm. It is found that the nonlinear regimes are substantially different and less efficient here as compared to the primary SH pumping case. This is caused by a profound difference between the FH and SH excitation schemes and also by different combinations of signs of the dispersion coefficients for FH and SH resonator modes.

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