# Far Off-Resonance Laser Frequency Stabilization Technology
## 4 Far Off-Resonance Laser Frequency Stabilization Using Transfer Cavities
at the State Key Laboratory of Quantum Optics and Quantum Optics Devices of Shanxi University locked the 852 nm laser to the Fg = 4-Fe = 4, 5 transition of Cs atom, and then locked the reference cavity as a bridge to the stabilized frequency. Then the lasers at 830 and 908 nm were locked to the other longitudinal modes of the reference cavity. The two lasers resonated with the reference cavity at the same time, which realized the stabilization of multiple lasers at different wavelengths through the optical cavity [62]. During the same year, [PERSON] et al. stabilized a transfer cavity using a Radio Frequency (RF) current-modulated diode laser which is injection locked to a 780 nm reference diode laser. A Ti:sapphire ring laser at 960 nm was locked on the optical transfer cavity. The RF modulation frequency could be changed for precise scanning, thereby changing the detuning frequency [63]. In 2011, [PERSON] et al. at the Chinese Academy of Sciences used an ultra-stable laser at 729 nm locked via PDH technology as a reference laser and a scanned F-P cavity as the transmission medium to achieve long-term locking of a 397 nm semiconductor laser. After frequency stabilization, the drift of the 397 nm laser within 1 h was less than 1 MHz, and the Allan variance of 100 s was less than \(1\times 10^{-10}\)[64]. In 2014, [PERSON] at the State Key Laboratory of Precision Spectroscopy at East China Normal University realized laser frequency stabilization of an optical transfer cavity based on PDH technology. Figure 8 presents the block diagram of the experimental device. The part in the dotted frame is the F-P cavity locked on the laser at 780 nm. The main aim of the part outside the dotted frame is to achieve the frequency locking of the dye laser (718.6 nm) on the F-P cavity [65]. Figure 7: Scheme of the narrow linewidth laser setup. EOM: electro–optic modulator; PBS: polarizing beam splitter; PD: photo detector; PZT: piezoelectric transducer. (Figure reproduced from [61]). In 2019, [PERSON] et al. at NIST stabilized lasers at 556 and 798 nm through optical cavities [66]. For a fixed cavity length, the distance between the transmission peaks corresponds to the free spectral range (FSR). The optical cavity is scanned in the range slightly larger than the FSR to obtain three peaks, with the master-slave-master (M-S-M') sequence. The frequency of the laser was correlated with the arrival time of the peak and a signal capable of stabilizing the average cavity length, and the slave laser frequency was obtained. In the same year, [PERSON] et al. at the School of Instrumentation and Optoelectronic Engineering proposed a transfer cavity method to transfer laser frequency stability, realizing the far off-resonance of 150 GHz, and the laser frequency drift after stabilization was 1 \(MHz\)-\(h^{-1}\)[67]. The technical block diagram is illustrated in Figure 9. Two lasers were used, one of which was locked on the saturation absorption peak of the \({}^{87}\)Rb atom D2 line. The magnitude and direction of the deviation was identified by the control system with the modulation and demodulation algorithm and a DC voltage was output. The PZT was adjusted to control the cavity length. After the stabilization of the cavity length, the target laser was locked by the dither-lock method. Based on this, during the same year, [PERSON] et al. studied the effect of the length of the 50 and 30 mm F-P cavity on the frequency stability. When the cavity length was shorter, the cavity and the control system were less sensitive to external vibration. Moreover, when the cavity length decreased by 40%, the frequency stability of the system increased by approximately one order of magnitude. Figure 8: Schematic illustration of the frequency stabilization system with a transfer cavity. EOM: electro–optic modulator; AOM: acousto–optic modulator; PBS: polarizing beam splitter; PD: photo detector; PZT: piezoelectric transducer. (Figure reproduced from [65]). Figure 9: Block diagram of frequency stabilization experimental system.