  The stabilization and manipulation of laser frequency by means of an external
cavity are nearly ubiquitously used in fundamental research and laser
applications. While most of the laser light transmits through the cavity, in
the presence of some back-scattered light from the cavity to the laser, the
self-injection locking effect can take place, which locks the laser emission
frequency to the cavity mode of similar frequency. The self-injection locking
leads to dramatic reduction of laser linewidth and noise. Using this approach,
a common semiconductor laser locked to an ultrahigh-$Q$ microresonator can
obtain sub-hertz linewidth, on par with state-of-the-art fiber lasers.
Therefore it paves the way to manufacture high-performance semiconductor lasers
with reduced footprint and cost. Moreover, with high laser power, the optical
nonlinearity of the microresonator drastically changes the laser dynamics,
offering routes for simultaneous pulse and frequency comb generation in the
same microresonator. Particularly, integrated photonics technology, enabling
components fabricated via semiconductor CMOS process, has brought increasing
and extending interest to laser manufacturing using this method. In this
article, we present a comprehensive tutorial on analytical and numerical
methods of laser self-injection locking, as well a review of most recent
theoretical and experimental achievements.
