  Photonic systems and technologies traditionally relegated to table-top
experiments are poised to make the leap from the laboratory to real-world
applications through integration. Stimulated Brillouin scattering (SBS) lasers,
through their unique linewidth narrowing properties, are an ideal candidate to
create highly-coherent waveguide integrated sources. In particular,
cascaded-order Brillouin lasers show promise for multi-line emission, low-noise
microwave generation and other optical comb applications. Photonic integration
of these lasers can dramatically improve their stability to environmental and
mechanical disturbances, simplify their packaging, and lower cost. While
single-order silicon and cascade-order chalcogenide waveguide SBS lasers have
been demonstrated, these lasers produce modest emission linewidths of 10-100
kHz. We report the first demonstration of a sub-Hz (~0.7 Hz) fundamental
linewidth photonic-integrated Brillouin cascaded-order laser, representing a
significant advancement in the state-of-the-art in integrated waveguide SBS
lasers. This laser is comprised of a bus-ring resonator fabricated using an
ultra-low loss Si3N4 waveguide platform. To achieve a sub-Hz linewidth, we
leverage a high-Q, large mode volume, single polarization mode resonator that
produces photon generated acoustic waves without phonon guiding. This approach
greatly relaxes phase matching conditions between polarization modes, and
optical and acoustic modes. Using a theory for cascaded-order Brillouin laser
dynamics, we determine the fundamental emission linewidth of the first Stokes
order by measuring the beat-note linewidth between and the relative powers of
the first and third Stokes orders. Extension to the visible and near-IR
wavebands is possible due to the low optical loss from 405 nm to 2350 nm,
paving the way to photonic-integrated sub-Hz lasers for visible-light
applications.
