# Far Off-Resonance Laser Frequency Stabilization Technology
## 3 Far Off-Resonance Laser Frequency Stabilization by Using the Faraday Effect
proposed a far off-resonance laser frequency stabilization method by using multipass cells in Rb Faraday rotation spectroscopy [22]. Figure 5 exhibits the setup used by them, demonstrating the far off-resonance frequency stabilization method. A Rb cell with a length of 50 mm and a diameter of 25 mm was placed inside a magnet with the same length. The plate beam splitter split the light into two bunches. The optical path length of the transmitted light was L = 50 mm and that of the reflected light was about 2L = 100 mm. They used a servo controller (model of LB1005) to lock to the zero crossings in the Faraday signal. Experimental results demonstrate that the number of lock points of the reflected light was two more than that of the transmitted light. The red detuning of the first-order zero crossing point of the reflected light is larger than that of the transmitted light. This shows that the detuning of the locking point can be extended to a farther area by increasing the optical path length. Figure 4: Experimental setup. PBS: polarizing beam splitter; \(\lambda/2\): half wave plate; PD: photo detector. (Figure reproduced from [52]). Figure 5: Experimental setup. PBS: polarizing beam splitter; \(\lambda/2\): half wave plate; PD: photo detector; BS: plate beam splitter. (Figure reproduced from [22]). In 2018, [PERSON] et al. presented a far off-resonance laser frequency stabilization method that could adjust the frequency lock points in the range of tens to hundreds of megahertz based on the Faraday rotation spectroscopy [53]. They used the setup shown in Figure 6 to demonstrate the far off-resonance frequency stabilization method. First, the transmitted beam is sent through a half-wave plate and PBS cube, leaving a small proportion of the total output light for the Faraday beam. Then it is combined with the acousto-optic modulator (AOM) to control and move the laser frequency. Furthermore, in order to effectively compensate the deviation from the propagation direction of the first-order diffracted light, a double-pass AOM system is used. In the experiment, they got the Faraday rotation spectra under large detuning by using a cesium (Cs) cell heated to 130 \({}^{\circ}\)C. The AOM-derived radio frequency was 65 MHz. Notably, the Faraday optical rotation spectrum corresponding to the first-order light produced a red shift relative to the original spectrum. Based on this method, the frequency lock point with detuning of \(-6.2\) GHz was precisely shifted by 130 MHz, and they obtained a frequency drift of 3.3 MHz\(\cdot\)h\({}^{-1}\) and an rms fluctuation of 0.6 MHz\(\cdot\)h\({}^{-1}\). As a scheme of using the atomic transition frequency as a reference, the main purpose of the Faraday scheme is to improve the long-term stability of the frequency far away from the resonance. The PDH scheme discussed in Section 2 is to find an optical cavity as a reference. Normally, the linewidth of the reference cavity is very narrow, but its center frequency drift is serious, which means the short-term stability of the PDH scheme can be very high [15]. While the center frequency stability of the atomic transition line as a frequency reference is very high, in theory, the Faraday scheme will have an excellent long-term stability [51]. However, we compared the experimental data in the reference, such as frequency drift and fractional frequency instability, and found that the Faraday scheme is worse than the PDH scheme in terms of its short-term stability and long-term stability. We speculate that the main reason for this phenomenon is that the Faraday scheme has extremely high requirements on temperature and magnetic field stability [52], and its frequency stabilization effect is easily affected by temperature and magnetic field. In addition to being susceptible to temperature and magnetic fields, it is found that the laser frequency stabilization technique in Faraday effect also has other shortcomings.