An auto-locking ultra-stable laser with sub-hertz linewidth

We report in detail the design process and performance of an auto-locking ultra-stable laser with sub-hertz linewidth at the first time. The laser frequency is automatically stabilized to an optical reference cavity with a home-made controller, which is based on a combination of digital circuit and analog circuit. The digital circuit is used for diagnosing and manipulating the state of the ultra-stable laser, and the analog circuit is used for demodulating the discriminate signal and servo control. A method of searching the transmission signal in the closed-loop state instead of the open-loop state is proposed to reduce the locking time and improve the reliable of the auto-locking ultra-stable laser. The median time of 16.6s is obtained after 157 times of relocking, and the probability of less than 20 s is more than 86%. The median linewidth of 1.08 Hz is obtained, and the fractional frequency instability is less than 3.4E-15 at integration time between 0.1 and 100 s. The performance of this system demonstrates that will be used as an important subsystem to transfer the optical clock signal.