Fundamental noise dynamics in cascaded-order Brillouin lasers

The dynamics of cascaded-order Brillouin lasers make them ideal for applications such as rotation sensing, highly coherent optical communications, and low-noise microwave signal synthesis. Remarkably, when implemented at the chip scale, recent experimental studies have revealed that Brillouin lasers can operate in the fundamental linewidth regime where optomechanical and quantum noise sources dominate. To explore new opportunities for enhanced performance, we formulate a simple model to describe the physics of cascaded Brillouin lasers based on the coupled mode dynamics governed by electrostriction and the fluctuation-dissipation theorem. From this model, we obtain analytical formulas describing the steady-state power evolution and accompanying noise properties, including expressions for phase noise, relative-intensity noise, and power spectra for beat notes of cascaded laser orders. Our analysis reveals that cascading can enhance laser noise, resulting in a broader emission linewidth and larger intensity fluctuations with increased power. Consequently, higher-coherence laser emission can be achieved if indefinite cascading can be prevented. In addition, we derive a simple analytical expression that enables the Stokes linewidth to be obtained from spectra of beat notes between distinct cascaded laser orders and their relative powers. We validate our results using stochastic numerical simulations of the cascaded laser dynamics.