# Spectral Broadening in a Continuously Pumped Singly Resonant Second-Harmonic Cavity
## 3 Experimental Results and Discussion  
Our experimental study reports on the spectral dynamic properties of a cw-pumped singly resonant cavity implemented with tunable cavity length control that utilizes the quasi-phase-matched second-harmonic process. Essentially, the detuning of the optical cavity resonance was stabilized, not to the pump beam, but to a counter-propagating beam, via an adjustable offset sideband locking that it was scanned across the pump frequency to generate emission in various frequency ranges. The locking point of the PDH servo corresponds to the low-frequency PDH sideband, and the cavity resonance is swept across the optical pump frequency by changing the modulation frequency (f\({}_{M}\)), as shown in Figure 1b. This scheme allowed us to explore a rich variety of spectral regimes by controlling the detuning over several cavity linewidths. The pump frequency and second-harmonic powers were measured at the resonator output to follow their temporal evolution as the frequency detuning changed. Furthermore, the infrared cavity output was monitored via an optical spectrum analyzer and the inter  
Figure 1: (**a**) Scheme of the experimental setup for broad\(-\)bandwidth comb generation including cw\(-\)pumped singly resonant SH cavity with PDH setup for cavity length stabilization. Red and green lines are free\(-\)space infrared and optical beams, respectively, yellow are fibers and blue electric cables. Dichroic mirror (DM), electro\(-\)optic modulator (EOM), fiber coupler (FC), fiber collimator (FCol), local oscillator (LO), optical circulator (OC), optical spectrum analyzer (OSA), periodically poled MgO:LiNbO\({}_{3}\) crystal (PPLN), piezoelectric actuator (PZT), photodiode (PD), half\(-\)wave plate (\(\lambda/2\)), radio\(-\)frequency spectrum analyzer (RF\(-\)SA); (**b**) operating principle of the active frequency detuning control where the pump laser beam is free running, while the cavity is locked on the negative sideband frequency of the PDH error signal, obtained by a counter\(-\)propagating beam that is orthogonally polarized to the pump. modal beat notes were detected by a fast photodetector and measured by a radio-frequency spectrum analyzer. Through suitable changes in the modulation frequency, we expanded the cavity so that the cavity resonance \(\
u_{r}\) could be tuned from higher to lower frequencies across the laser frequency \(\
u_{p}\) (Figure 1b), with the resonance tuned from the blue side of the pump to the red side accordingly. Specifically, we observe that by increasing the cavity length, as \(\
u_{r}\) moves towards \(\
u_{p}\), the onset of thermal effects leads to a measured fringe broadening over several cold cavity linewidths. When \(\
u_{r}\) is lower than \(\
u_{p}\), the intracavity power rapidly decreases and shows a triangular asymmetric fringe shape [34; 35]. The measured hot-cavity frequency detuning results are shown in Figure 2 for a pump power of 2 W.  
Here, we investigate comb formation under an adiabatic cavity length scan with \(\
u_{r}>\
u_{p}\) and resonator-pump frequency detuning \(\Delta=\
u_{p}-\
u_{r}<0\) (blue-side). The optothermal dynamics produce a self-stabilizing effect that allows us to record the comb spectra during the cavity length scan. Figure 2 displays the pump and second-harmonic cavity output power as a function of the frequency shift of the cold-cavity frequency detuning \(\Delta^{c}\) defined by \(\Delta^{c}{}_{p}=\
u_{0}-\
u_{r}\) and \(\Delta^{c}{}_{sh}=2\cdot\Delta^{c}{}_{p}\). Here, \(\
u_{0}\) is the cold cavity resonance frequency measured at 10 mW input power. Figure 2: Measured output power when the cavity resonance scans across the pump from smaller to larger frequency. Panels show evolution of the power spectral density (PSD) during the laser scan in four transmission profiles. \(\Delta^{c}\) can be estimated by measuring the f\({}_{\text{M}}\) changes, while the effective frequency detuning \(\Delta\) is such that \(\Delta\leq\Delta^{c}\) under normal operating conditions.