  Self-injection locking techniques for stabilizing lasers have been developed
using passive cavities to increase the effective lifetime of the laser cavity,
thereby reducing the linewidth of the laser. We propose and demonstrate a new
technique based on nonlinear self-injection locking (N-SIL) which we implement
via feedback from the gain-narrowed Stokes mode of a fiber Brillouin
oscillator. By blue-shifting the Stokes field back to its pump frequency with
an electro-optic modulator we realize recursive linewidth reduction that
eliminates the phase drift caused by spontaneous emission noise. The
fundamental linewidth limit is set by the spontaneous emission limit of the
nonlinear oscillator, far lower than the spontaneous emission limit of a
semiconductor laser. We demonstrate the power of this approach by achieving
sub-hertz fundamental linewidth from the output of a commercial DFB laser and
noise performance that significantly exceeds that of conventional SIL. We also
and propose alternative fully-integrated designs in CMOS-compatible photonic
platforms that allow for highly compact and robust implementations.
