Fig. 1. Schematic of PDH locking method based on double modulation depths and double error signals with phase matching. (a) Optical layout unit; (b) signal processing unit

Fig. 2. Simulation results of the PDH error signal and its derivative signal under different phase delay. (a) PDH error signal; (b) derivative of PDH error signal

Fig. 3. PDH error signal demodulation with the phase delay extraction and matching based on the quadrature demodulation

Fig. 4. Simulation analysis and comparison of the LDR of error signals S_PDH and S_pre. (a) (b) signals P_tran, S_PDH, and S_pre with β=1.08 rad; (c) (d) error signals of S_PDH and S_pre with β=1.08, 1.8, 2.5 rad

Fig. 5. Schematic of the signal processing and control for adaptive PDH locking based on double modulation depths and double error signals

Fig. 6. Schematic of the relationship between the signals Spre,SPDH, and Ptran with the adaptive PDH locking mechanism based on double modulation depths and error signals

Fig. 7. Experimental setup of the F-P cavity locking to the reference laser frequency

Fig. 8. Measured amplitude of Ptran, SPDH, and Spre under two different modulation depths. (a1)-(a3) β=1.08 rad; (b1)-(b3) β=1.80 rad

Fig. 9. Capture and lock performance comparisons by using SPDH with small modulation depth and Spre with large modulation depth. (a1)-(a4) β=1.08 rad and the input signal of PID controller is SPDH; (b1)-(b4) β=1.80 rad and the input signal of PID controller is Spre

Fig. 10. System anti-interference test results under two locking states. (a) β=1.08 rad and the input signal of PID controller is SPDH; (b) β=1.80 rad and the input signal of PID controller is Spre

Fig. 11. Adaptive locking experimental result with double phase modulation depths and double error signals

Fig. 12. Experimental results of F-P cavity locking within 3 h. (a) Control signal of PZT; (b) amplitude of transmission power signal Ptran; (c) amplitude of error signal SPDH