  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.
