  Thermodynamic noise places a fundamental limit on the frequency stability of
dielectric optical resonators. Here, we present the characterization of
thermo-refractive noise in photonic-chip-based silicon nitride microresonators
and show that thermo-refractive noise is the dominant thermal noise source in
the platform. We employed balanced homodyne detection to measure the
thermo-refractive noise spectrum of microresonators of different diameters. The
measurements are in good agreement with theoretical models and finite element
method simulations. Our characterization sets quantitative bounds on the
scaling and absolute magnitude of thermal noise in photonic chip-based
microresonators. An improved understanding of thermo-refractive noise can prove
valuable in the design considerations and performance limitations of future
photonic integrated devices.
