## 3 Results and Discussion  
### Frequency Control of Division-by-Three OPO  
When the optical parametric oscillator is operating, the frequencies of signal and idler are \(2\omega+\Delta\omega\) and \(\omega-\Delta\omega\) where \(\Delta\omega\) is the deviation in frequency from the fundamental (idler) of the exact division-by-three frequency of the SRO where the pump is at 3\(\omega\). Ideally \(\Delta\omega\) is to be equal to zero. For the SRO, zeroing \(\Delta\omega\) is done by adjusting the temperature of the gain crystal, the intracavity etalon, and the length of the cavity. The primary source of non-zero \(\Delta\omega\) is thermal and mechanical fluctuation of the SRO cavity length. Therefore it is necessary to track and stabilize the cavity length. Here a cavity stabilization feedback circuit is introduced to control the free spectral range of the SRO cavity to eliminate or minimize the frequency deviation. In our experiment, the frequency deviation is deduced from the interference beat signal between the frequency-doubled idler wave and the signal wave. This beat signal is equal to \(\{2\omega+\Delta\omega\) minus \(2\times(\omega-\Delta\omega)\}\) to give 3\(\Delta\omega\). According to standard practice in cavity stabilization, we give this beat signal an offset frequency \(\Omega_{\mathrm{AOM}}\) of +54 MHz by passing the SRO signal beam through an acousto-optic modulator before mixing with the idler's second harmonic. With this offset it is then possible to track the deviation \(\Delta\omega\) on both sides of \(\Delta\omega=0\) readily. The main ICs employed in our phase detection circuit are two ultrafast comparators (Analog Device AD96685), one phase discriminator (Analog Device AD9901) and one differential receiver amplifier (Analog Device AD8130). The error signal from our phase detection circuit is sent into the high-speed proportional integrating controller. Finally, the PZT driver adjusts a PZT (mounted on M3) in accordance to output from the proportional controller.  
The quality of the stabilization control is monitored by recording the beat signal thus produced using a radio frequency (RF) spectrum analyzer (Rohde & Schwarz FSL3) with 100 kHz resolution bandwidth. The frequency of the recorded beat signal is \(3\Delta\omega+\Omega_{\mathrm{AOM}}\). Histograms of the recorded frequency deviation over a 30 min period are shown in Figure 2 with and without cavity stabilization when the temperature of the OPO crystal was set to 92.8 \({}^{\circ}\)C to achieve phase-matching in the frequency division-by-three cw SRO. Figure 2a shows the frequency deviation, \(\Delta\
u=\Delta\omega/2\pi\), without cavity stabilization. The recorded deviation \(\Delta\omega\) centers at 131.8 MHz with a \(\pm\)14.7-MHz random drift (one standard deviation). With the stabilization circuit turned on, the frequency deviation is reduced to centering at \(-\)76 kHz with a \(\pm\)437-kHz random drift. The solid red lines in Figure 2a,b are Gaussian fits of the distribution indicating that the source of the drifts are randomly distributed. The drift width in Figure 2b of 437 kHz is comparable to the frequency stability of the seed DFB diode laser of the fiber amplifier, implying that the seed laser's drifts may be determining the width of the stabilized source. This result shows that by locking the seed laser to a stabilized reference-frequency comb linked to a primary frequency standard \(\Delta\omega\) can be reduced to less than one Hz and phase-stabilized eventually for waveform synthesis.  
Figure 2: The histograms of frequency deviation from 30-min beat-wave signal recording by a radio frequency (RF) spectrum analyzer. The solid red line is fitting curve based on Gaussian distribution (**a**) without cavity stabilization. The frequency deviation centers at 131.8 MHz with a 14.7-MHz standard deviation; (**b**) with cavity stabilized feedback circuit functioning properly. The center is at \(-\)76 kHz with a 437-kHz standard deviation.