Fig. 1. Schematic diagram of the experimental setup for automatic laser frequency stabilization based on an analog-digital hybrid PID controller. FNC, fiber noise cancellation; PM fiber, polarization maintaining optical fiber; AOM, acousto-optic modulator; P₁ and P₂, polarizers; EOM, electro-optic modulator; ISO, optical isolator; λ/4, quarter-wave plate; PD, photo-detector; LPF, low pass filter; ADC, analog to digital converter; CMOS SW, CMOS analog switch; Digi-POT, digital potentiometer; PZT, piezo transducer.

Fig. 2. (a) Logic block diagram of automatic laser frequency locking. (b) The PDH signal and the cavity reflection signal with U_PDH-0 and U_r-0 marked.

Fig. 3. (a) Signal of U_PZT, U_PDH, and U_r when the laser frequency starts to lock. (b) Statistics of laser frequency relocking time.

Fig. 4. (a) Recorded beating frequency between two automatic frequency-locking laser systems at 1064 nm over 22 days. The inset shows the frequency instability of four sub-datasets. (b) The frequency instability of the beat note between two automatic frequency-locking laser systems at 1064 nm (Lasers #1 and #2, blue dots) and between Laser #1 and a cavity-stabilized 578 nm laser (red squares). The black dashed line indicates the thermal noise-limited laser frequency instability for a single 1064 nm laser. (c) Distribution of the linewidth measurement of the beat note between Lasers #1 and #2 measured on an FFT spectrum analyzer with a resolution bandwidth of 122 mHz. The inset shows one of the measurements.