Phase-stable frequency combs have been instrumental in advancing state-of-the-art metrology and high-precision measurements. Extending the combs toward shorter wavelengths in the ultraviolet and X-ray regimes has pushed ultrafast science to the attosecond level and revolutionized atomic physics. While there has not been much development on comb extension toward longer wavelengths, it is nevertheless important for applications that require critical optical phase control in the middle to far-infrared regime, such as vacuum-based laser-driven particle acceleration. Furthermore, the synthesis of phase-locked combs at longer wavelengths would establish absolute optical frequency standards in the IR regime and enable highly precise spectroscopy at wavelengths unavailable to conventional solid-state lasers.;To realize frequency combs in the mid-IR, we decided to exploit second-order nonlinear processes for down-conversion to longer wavelengths. Additionally, we took advantage of the fixed phase relationship between pump, signal, and idler in optical parametric oscillation (OPO). We predicted that a mode-locked OPO operating at frequency degeneracy would exhibit phase-locking because the signal and idler combs experience mutual injection locking to become phase-coherent with the pump. Furthermore, the carrier-envelope offset (CEO) frequency of the signal/idler comb would be exactly half of that of the pump in this case. To this end, we demonstrated the first self-phase-locked synchronously pumped OPO (SPOPO) as a sub-harmonic generator. The pump source was a mode-locked Ti:sapphire laser that generated an 80-MHz train of 180-fs pulses at 775 nm. The nonlinear gain element used was a 1-mm-long, type I (e-ee) phase-matched, 5% MgO-doped periodically poled LiNbO3 crystal. Under degenerate operation, the SPOPO formed a broad, continuous spectrum centered at 1550 nm with a bandwidth of 50 nm (200 cm-1), which had a comb broadening factor of almost 3 compared to the pump spectrum. The degenerate output pulses were transform-limited with a duration of 70 fs.;To confirm phase-coherence between the pump input and signal/idler output, we interfered the frequency-doubled SPOPO output with the pump at a low angle between the beams to generate a stable fringe pattern with high contrast that would indicate coherence. The interference was also set collinearly to observe potential satellite beat notes in the RF spectrum that would imply unlocked combs with mismatched CEO frequencies. In another method to verify phase-locking, we employed an independent CW laser as an external phase reference and beat it with the pump and SPOPO separately. We showed that the SPOPO beat note tracked the pump beat note at half the latter's value, thus demonstrating the proper CEO frequency ratio for phase-locking.;We also measured the frequency locking range of the degenerate SPOPO state and showed that it monotonically increased with higher pump power (i.e., larger parametric gain) and more output coupling (i.e., lower cavity Q). Using the degenerate nonlinear coupled wave equations and simple perturbation analysis, we developed a heuristic model for the locking range that shared the same functional form of the locking range definition derived from steady-state injection locking and showed that our simple model fit the measured data reasonably well with the number of times above pump threshold and the cavity decay rate as parameters.;The SPOPO consistently exhibited well-behaved and stable operation at degeneracy, contrary to prior misperception that degenerate type I systems were unstable and impractical. Despite the lack of active stabilization, the self-phase-locking would routinely recover after slight intentional perturbations had ceased. The degenerate SPOPO operated stably for nearly an hour when there were minimal environmental noise stimuli.
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