# Fast Frequency Acquisition and Phase Locking of Nonplanar Ring Oscillators
## 4 Experimental Results  
The phase locking loop was constructed according to Figure 1. First, the FDCM was turned off, and the initial frequency difference of the two lasers was controlled by adjusting the crystal temperature of the signal laser. At a set frequency difference, as the FDCM was turned on, frequency acquisition and phase locking were tested. In the experiments, the output signal of the loop filter, the PZT driving signal, and the laser beat signal were monitored. The frequency acquisition and phase locking process at an 8 MHz initial frequency difference is shown in Figure 4 with a time scale of 200 ms/div. At 630 ms, the FDCM was turned on, and the feedback control was started. After 80 ms, phase locking was achieved, as indicated by the beat signal (yellow). According to the frequency discrimination and control program, under the control of the FDCM, the local laser generated an initial frequency shift. As the change in frequency difference is measured, the direction of the frequency control and the frequency shift amount were determined. The main function of the initial frequency shift determined the right frequency control direction. After that, the frequency difference decreased to less than \(\Delta f_{c}\), 40 kHz, as indicated by the PZT driving signal (green). For such a small frequency difference, the phase locking time based on the loop filter was quite short, shorter than 1 ms, which is negligible compared to the frequency acquisition time. As the initial frequency difference increased to 164 MHz, the acquisition time was around 440 ms, as shown in Figure 5. As the beat signal was detected via the probe of the oscilloscope, the amplitude of the detected signal varied with the signal frequency in the acquisition process because impedance matching varied at different frequencies. For a higher initial frequency difference, the frequency discrimination and control would go wrong sometimes. The main reason for this is that the machine cycle of the MCU, compared to the divided beat signal period, was so long that the frequency could not be correctly measured. It could be improved by increasing the crystal frequency and the processing speed of the MCU. In order to guarantee the stability of the frequency control process, the local laser frequency shift was set to less than 3 MHz at every control step. For an even higher frequency shift step, the laser frequency would not reach a steady state at the end of the control period, causing inaccurate frequency measuring in the following measuring period, even leading to false control. As the initial frequency difference increased, more control periods were needed, and acquisition time was normally extended. In the frequency acquisition process, when the beat signal frequency was out of the pull-in range of the loop, the loop filter output a constant DC signal. Only as the beat frequency fell into the pull-in range of the loop did the loop filter signal have an obvious response, as shown in the figure by the blue line. According to the measurement of the laser frequency stability, the frequency drift of the beat signal of the two lasers was around 100 MHz in 8 h, under precise temperature control. Figure 4: Frequency acquisition and phase locking process at an 8 MHz initial frequency difference. The frequency acquisition range, 164 MHz, was significantly larger than the frequency drift range, so a stable loop operation was achievable. The frequency acquisition and phase locking time at different initial beat frequencies is shown in Figure 6. According to the frequency discrimination and control program, the theoretical minimum number of control cycles was equal to the initial frequency difference divided by the maximum frequency shift step of a given period, which was set to 3 MHz. As the time of one control cycle was set to 6 ms, minimum acquisition time could be computed. The actual acquisition time was usually longer, and had a certain degree of uncertainty.