# Far Off-Resonance Laser Frequency Stabilization Technology
## 1 Introduction  
In 1958, [PERSON] and [PERSON] took the first step on the road to the laser by establishing general physical conditions for light amplification by the stimulated emission of radiation (LASER) [1]. In the 1960s, [PERSON] ushered in a new age by crossing the threshold of laser oscillation and demonstrated the construction of the world's first laser [2]. Since then, different types of lasers and laser control technologies have been developed rapidly. Frequency stabilization is an important indicator of lasers, as it is required for high precision. Frequency-stable laser sources are central to several applications, such as gravitational wave detection [3], low-phase-noise microwave generation [4], precision spectroscopy [5], and quantum computation [6]. The essence of frequency stabilization is to maintain the stability of the optical path length of the resonant cavity. Based on the dependence of frequency stabilization on an external reference frequency source, frequency stabilization is divided into passive frequency stabilization and active frequency stabilization. Passive frequency stabilization refers to the maintenance of the cavity length to stabilize the laser frequency by controlling temperature, using complementary cavity materials, and vibration isolation. With poor reproducibility, lasers operating in the passive frequency stabilization mode are generally used in situations where the frequency stabilization and accuracy are not too high. In contrast, active frequency stabilization refers to the selection of a stable frequency reference point. The frequency discriminator provides an error signal when the frequency of the laser deviates from the reference frequency. Then the error signal is fed back into the laser system using the servo system in order to achieve stability. Generally, there are two purposes for locking laser frequency to reference according to the applications. Improving the short-term stability of the laser suppressing the phase noise andreducing the linewidth is one of the two aims. The other is to obtain long-term stability calibrating the frequency of the laser. Notably, many established active frequency stabilization techniques are available for locking close to an atomic resonance, including frequency-modulation spectroscopy [7], saturated absorption spectroscopy [8], polarization spectroscopy [9], dichroic atomic vapor laser locking (DAVLL) [10], and Sagnac interferometry [11]. Light-atomic interactions offer grand promise for broad range of applications, such as atomic magnetometer [12], cold atoms [13], atomic gyroscopes [14], and other precision measurement and metrology; however, sometimes the frequency of the probe beam should be locked on the detuning as far as several tens of gigahertz away from atomic resonance line. Unfortunately, frequency stabilization at such a large detuning cannot be achieved via the above-mentioned methods. For several applications, highly stable Fabry-Perot (F-P) cavity is selected as the reference. F-P cavities and similar resonant optical cavities exhibit excellent frequency discrimination performance, and thus are widely used for the frequency stabilization and tuning of lasers. Common resonant optical cavity-based frequency stabilization techniques include Pound-Drever-Hall (PDH) technique [15; 16; 17] and tilt-locking [18; 19; 20]. Moreover, a laser locking technique based on the transfer of the frequency stability from an F-P cavity is useful for applications that require stabilization of lasers at a large-detuned atomic-reference frequency [21]. Like a one-step reduction gear, the optical frequency combs can connect optically to different frequencies. Based on this, frequency transfer using optical frequency combs is also an excellent method for far off-resonance laser stabilization. Recently, the Faraday effect was used for the stabilization of a laser frequency at large detuning from the atomic reference line [22].