# Far Off-Resonance Laser Frequency Stabilization Technology
## 4 Far Off-Resonance Laser Frequency Stabilization Using Transfer Cavities  
The principle of far off-resonance frequency stabilization with a transfer cavity involves locking the length of the F-P cavity with a reference laser that has been stabilized. Then the F-P cavity transmission peak is used to perform laser detuning and frequency stabilization. Noteworthy, by selecting different transmission peaks, the laser can be locked at different detuned frequencies. This method mainly uses the transmissivity of the F-P cavity. Before the frequency stabilization with the transfer cavity, the method of frequency offset locking is reviewed [56; 57]. [PERSON] et al. used an F-P cavity and method of dither locking to stabilize the frequency of a dye laser with a frequency instability at the order of \(10^{-10}\)[58]. In the dither-lock method, the frequency at the F-P cavity transmission peak was selected as the reference frequency, the different slopes on both sides as the criterion, and the laser frequency was locked with the reference frequency. However, the shortcoming of this method is obvious, i.e., it cannot distinguish between the power jitter and the frequency jitter of the laser, and the former can result in the change of transmitted light intensity. At the same time, the feedback circuit considers it to be a frequency jitter and makes a wrong feedback regulation. In order to reduce the influence of the power jitter on the frequency stabilization, a frequency offset locking method was proposed. The maximum slope point should theoretically be the lock point; however, the frequency corresponding to half the maximum of the transmitted light intensity is usually selected as the frequency standard because of convenience and similarity [59]. The hypotenuse of the detected transmission curve of the laser passing through the F-P cavity can convert frequency to amplitude. Two photodetectors were used to prevent the laser power jitter from affecting the frequency stabilization. One was used to detect the transmitted light of the selected frequency behind the cavity and the other detected the partial beam of the laser. The input of the servo amplifier corresponded to differential signal between the outputs of two detectors. When the frequency was at the target frequency, the two photocurrents were close to each other. When the frequency was far from the target frequency, the detector outputs were not equal. Thereby, the laser frequency could be controlled to be constant. In 2009, [PERSON] et al. at the State Key Laboratory of Precision Spectroscopy proposed a peak-seeking servo-controlled technology which can be used in laser cavity-enhanced spectroscopy experiments. When the laser frequency is scanned, it can be uninterruptedly locked with resonant frequency of the cavity [60]. In 2012, [PERSON] et al. at Tsinghua University used a high-finesse F-P cavity to suppress laser phase noise, and its technical block diagram is illustrated in Figure 7. In particular, at the Fourier frequency of 17 kHz (approximately the linewidth of the F-P reference cavity), the laser phase noise was significantly suppressed by more than 92 dB. The full width at half maximum linewidth of the laser was reduced from 7 MHz to 4.4 Hz. In Lorentz fitting, its instantaneous linewidth was 220 MHz [61]. With the development of quantum sensing, stabilization of the laser frequency on the fixed frequency point has been inadequate to meet the requirements. For example, in the spin-exchange relaxation-free atomic magnetometer, the inert gas is filled in the atomic cell. Affected by this pressure, the frequency of pumping light should deviate from the resonance frequency by several GHz. Besides, in order to prevent the ultra-high optical thickness from affecting the detection of the signal-to-noise ratio, far off-resonance of more than 100 GHz is often required [12; 22]. Such a large range of detuning cannot be achieved using an AOM or an EOM. Thus, the approach to stabilize far off-resonance frequency via a transfer cavity was explored. In 2006, [PERSON] et al.