  Soliton microcombs constitute chip-scale optical frequency combs, and have
the potential to impact a myriad of applications from frequency synthesis and
telecommunications to astronomy. The requirement on external driving lasers has
been significantly relaxed with the demonstration of soliton formation via
self-injection locking of the pump laser to the microresonator. Yet to date,
the dynamics of this process has not been fully understood. Prior models of
self-injection locking were not able to explain sufficiently large detunings,
crucial for soliton formation. Here we develop a theoretical model of
self-injection locking to a nonlinear microresonator (nonlinear self-injection
locking) for the first time and show that self- and cross-phase modulation of
the clockwise and counter-clockwise light enables soliton formation. Using an
integrated soliton microcomb of directly detectable 30 GHz repetition rate,
consisting of a DFB laser self-injection-locked to a Si3N4 microresonator chip,
we study the soliton formation dynamics via self-injection locking, as well as
the repetition rate evolution, experimentally. We reveal that Kerr nonlinearity
in microresonator significantly modifies locking dynamics, making laser
emission frequency red detuned. We propose and implement a novel technique for
measurements of the nonlinear frequency tuning curve and concurrent observation
of microcomb states switching in real time.
