Frequency comb generation in quadratic media
Originally conceived for frequency metrology, optical frequency combs of equally spaced frequency lines nowadays are routinely used in a wide range of scientific and technological applications. Ultrafast mode-locked lasers, first used for comb generation, have then been joined by continuously-pumped Kerr microresonators, exploiting the third-order nonlinearity χ<sup>(3)</sup> of the materials.
We have demonstrated generation of optical frequency combs in a continuously-pumped second-order χ<sup>(2)</sup> nonlinear crystal, placed in a pump-resonant optical cavity. The nonlinear cavity, initially conceived for second harmonic generation (SHG), gives rise to a cascaded optical parametric oscillator (OPO), above a given pump threshold, Fig. 1(a). Actually, the onset of a secondary OPO immediately starts a series of multiple cascaded second-order sum-frequency processes, Fig 1(b), possibly leading to the formation of frequency combs.
The SHG system is based on a periodically-poled nonlinear crystal, lithium niobate, placed in a travelling-wave optical cavity, pumped by a 9 W, cw Nd:YAG laser. When the crystal is quasi-phase matched for SHG, we observe the generation of frequency combs (χ<sup>(2)</sup>-combs), with teeth spaced by multiple of the cavity free spectral range (FSR). As the pump power is further increased, secondary parametric oscillations result in the emergence of secondary frequency combs around each primary comb tooth, with secondary teeth spaced by the cavity FSR. When the initial SHG is strongly phase mismatched, a 1-FSR-spaced χ<sup>(2)</sup>-comb directly appears around the fundamental mode and successively broadens up to 10 nm (∼ 5000 teeth), Fig. 2(a). The narrow feature of the intermodal beat notes, Fig. 2(a) and 2(b), at the cavity free-spectral-range indicate a higher degree of correlation between comb teeth.
We have also developed a theoretical model remarkably similar to the description of third-order effects in microresonators. This similarity unveils the possibility to predict and observe most of the effects occurring in Kerr-medium-filled cavities, such as temporal solitons, FWM amplification, intermodal phase coherence and mode-locking, pulsed emission. A χ<sup>(2)</sup>-comb has several advantages with respect to Kerr-combs based on χ<sup>(3)</sup> materials, exploiting the intrinsically higher efficiency of χ<sup>(2)</sup> processes, combined with the ability of spectrally tailoring the nonlinear efficiency of the material. Phase-matching plays a role similar to the material dispersion in χ<sup>(3)</sup> resonators, allowing to change from normal to anomalous ‘dispersive’ regimes by simply varying the phase-matching condition. Hence, in principle, χ<sup>(2)</sup>-combs can be realized all over the transparency range of the nonlinear material without the more severe constraint on the dispersive characteristics of χ<sup>(3)</sup>-based devices.