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, leading to a dramatic decrease in size, weight, power, and cost 1 . In particular, photonic integrated ultra-narrow linewidth lasers are a critical component for applications including coherent communications 2 , metrology 3-5 , microwave photonics 6 , spectroscopy 7 , and optical synthesizers 1 . Stimulated Brillouin scattering (SBS) lasers, through their unique linewidth narrowing properties 8 , are an ideal candidate to create highly-coherent waveguide integrated sources. In particular, cascaded-order Brillouin lasers show promise for multi-line emission 14 , low-noise microwave generation 6 and other optical comb applications. To date, compact, very-low linewidth SBS lasers have been demonstrated using discrete, tapered-fiber coupled chip-scale silica 9,10 or CaF2 11 microresonators. Photonic integration of these lasers can dramatically improve their stability to environmental and mechanical disturbances, simplify their packaging, and lower cost through wafer-scale photonics foundry processes. While single-order silicon 12 and cascade-order chalcogenide 13 waveguide SBS lasers have been demonstrated, these lasers produce modest emission linewidths of 10-100 kHz and are not compatible with waferscale photonics foundry processes. Here, 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 (< 0.5 dB/m) 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. By using a theory for cascaded-order Brillouin laser dynamics 14 , 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 of these high performance lasers to the visible and near-IR wavebands is possible due to the low optical loss of silicon nitride waveguides from 405 nm to 2350 nm 15 , paving the way to photonic-integrated sub-Hz lasers for visible-light applications including atomic clocks and precision spectroscopy.

Integrated optical resonators are key building blocks for an ever-increasing range of applications including optical communications, sensing, and navigation. A challenge to today's photonics integration is realizing circuits and functions that require ultralow loss waveguides on-chip while balancing the waveguide loss with device function and footprint. Incorporating Si 3 N 4 /SiO 2 waveguides into a photonic circuit requires tradeoffs between waveguide loss, device footprint, and desired device specifications. In this paper, we focus on the design of resonator based circuits in the silicon nitride platform and the balancing of desired properties like quality factor Q, free spectral range, finesse, transmission shape with waveguide design, and footprint. The design, fabrication, and characterization of two resonator-based circuit examples operating at 1550 nm are described in detail. The first design is a thin core, large mode-volume bus-coupled resonator, with a 2.72 GHz free spectral range and a measured intrinsic Q of 60 million and loaded Q on the order of 30 Million, representing the highest reported loaded Q for a large mode volume resonator with a deposited upper cladding. The second circuit is a thicker core, smaller footprint, low loss flat passband third-order resonator filter with an ultrahigh extinction ratio of 80 dB tunable over 100% of the free spectral range and insertion loss under 1.3 dB.

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