# Far Off-Resonance Laser Frequency Stabilization Technology
## 3 Far Off-Resonance Laser Frequency Stabilization by Using the Faraday Effect  
In 1845, [PERSON] added a piece of glass consisting of a pair of magnetic poles, and interestingly found that the polarization plane of the incident light in the direction of the applied magnetic field was transmitted through the glass. This phenomenon was later called the Faraday effect [48]. The Faraday effect is a magneto-optical phenomenon, in which an electromagnetic wave propagates through a medium and gets affected by the presence of quasi-static magnetic field. This effect can be exploited in alkali metal media. As Figure 3 shows, when a heated alkali metal vapor cell is placed in an axial magnetic field, the magnetic field causes the atoms to undergo Zeeman splitting. The atoms respond differently to left and right circularly polarized components of the linearly polarized light, which results in a rotation of linearly polarized light entering the cell. The rotation angle of the linear polarization plane changes with the laser frequency. We can use the phenomenon described above to stabilize the laser frequency on the large detuning away from the resonance. Here is a brief description. When the [PERSON] effect occurs in the alkali metal vapor cell. There is rotation of linearly polarized light in the central frequency band of the atomic resonance region, but the incident light cannot finally pass through the gas cell due to strong resonance absorption. However, in the frequency band far away from resonance, there is both light rotation and incomplete absorption. We can obtain these transmitted lights with different frequencies through the design of the optical path. The peak points of these transmitted light signals are always based on the frequency of the atomic transition line, which can be used as a stable reference. We can lock the laser frequency to these transmission peak frequencies away from the resonance region. Moreover, when the strength of the axial magnetic field or the temperature of the gas chamber increase, the transmission peak will be farther away from the atomic transition line, which means the detuning will increase. Based on the above principles, far off-resonance laser frequency stabilization can be achieved by using the Faraday effect in the alkali metal vapor cell. In 2009, [PERSON] et al. studied and analyzed the off-resonance absorption and dispersion of Doppler-broadened atomic media and made approximate calculations to the electric susceptibility of atomic media [49]. On the large detuning away from the resonance, the relative absorption of dispersion dominates the atom-light interaction [50]. In 2011, [PERSON] et al. proposed an analytical model of off-resonant Faraday rotation in hot alkali metal vapors [51]. The far off-resonant Faraday rotation angle can be determined by using the temperature of the cell and the optical path length. And they proposed a simple model to predict the detuning of the locking points. Furthermore, in 2011, [PERSON] et al. proposed a simple technique for stabilization of a laser frequency off resonance by using the Faraday effect in a heated rubidium (Rb) vapor cell with an applied magnetic field [52]. They used the setup shown in Figure 4 to produce the Faraday signal. Figure 3: Rotation of polarization plane of light, as it travels through a heated alkali metal vapor cell placed in a magnetic field. In order to lock to a zero crossing in the Faraday signal, they used a home-built locking servo. Finally, they demonstrated stabilization of a 780 nm laser detuned up to 14 GHz from the \({}^{85}\)Rb \(D_{2}\)\(5^{2}S_{1/2}F=2\) to \(5^{2}P_{3/2}F^{\prime}=3\) transition. The locking of the \(\sim\)6-14 GHz red and blue detuned from resonance can be achieved by adjusting the temperature of the vapor cell and the magnetic field. They obtained a root mean square (rms) fluctuation of 7 MHz over 1 h without stabilization of the cell temperature or magnetic field. In 2016, [PERSON] et al.