Fundamental noise dynamics in cascaded-order Brillouin lasers

TL;DR

This paper develops a theoretical model for cascaded Brillouin lasers, revealing how cascading affects noise properties and linewidth, and provides analytical tools for predicting and measuring laser performance.

Contribution

The authors introduce a simple coupled mode model for cascaded Brillouin lasers, deriving analytical formulas for noise and linewidth that account for cascading effects, validated by simulations.

Findings

Cascading modifies intermediate laser order dynamics and noise properties.

Linewidth depends on coupled order dynamics, broader than single-mode predictions.

Analytical expression for beat note linewidth enables measurement based on relative powers.

Abstract

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. Remark- ably, 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 modifies the dynamics of intermediate laser orders, yielding noise properties that differ from single-mode Brillouin lasers. These modifications lead to a Stokes order linewidth dependency on the coupled order dynamics and a broader linewidth than that predicted with previous single order theories. We also derive a simple analytical expression for the higher order beat notes that enables calculation of the Stokes linewidth based on only the relative measured powers between orders instead of absolute parameters, yielding a method to measure cascaded order linewidth as well as a prediction for sub-Hz operation. We validate our results using stochastic numerical simulations of the cascaded laser dynamics.