Noise dynamics in large-mode-volume Brillouin lasers

Photonic integrated Brillouin lasers have emerged as a key tool to realize a wide range of precision applications, including atomic time keeping, low-noise microwave-signal generation, fiber and quantum sensing, and ultrahigh capacity coherent communications. While Brillouin lasers routinely achieve sub-Hz instantaneous linewidths, many of these applications also require exceptional frequency stability and high-power single-mode emission. A recent demonstration showed that extending the resonator length increases the laser power while simultaneously improving the frequency stability through suppression of low-frequency thermorefractive noise. However, as the resonator length scales to larger size, multiple optical resonances can be found within the Brillouin gain bandwidth, greatly complicating the laser dynamics and extending beyond the validity of existing coupled-mode Brillouin laser models. Given the potential to scale lasers of this type to watt-level output powers at sub-mHz linewidths, a theoretical model describing this physics is needed to provide key insights into their performance. Here, we develop a coupled-mode theory of integrated large mode volume Brillouin lasers, accounting for multiple cavity modes with the potential to lase within the gain bandwidth. We obtain expressions for the steady-state dynamics, spontaneous spectrum, relative intensity noise, and frequency noise. Our analysis reveals that the broad gain bandwidth results in atypical Brillouin dynamics, giving rise to distinct features in the noise spectra, and consequently modifications of the standard, single-mode fundamental linewidth of Brillouin lasers. Additionally, these features may be used for a variety of tangential applications, such as phonon spectroscopy or quality-factor enhancement. Furthermore, we find that the linewidth can be significantly impacted by transferred RIN from the external pump in Brillouin lasers that lack ideal phase matching.