Noise factor of Brillouin amplifiers

Stimulated Brillouin scattering (SBS), an optical nonlinearity arising from photon-phonon interactions, has formed the basis for a large class of optical signal processing devices, including Brillouin amplifiers. A limiting factor of such amplifiers is the noise due to thermal-mechanical fluctuations that the phonons imprint on the optical signal. Prior work has either inferred or experimentally observed a noise factor ($F$) that depends only on the thermal occupation of the phonons ($F\approx 1+n_{th}$). We show that this noise factor results naturally from a Hamiltonian-based spatio-temporal coupled mode treatment in the limit of large Brillouin amplification and when phonon propagation is neglected. Moreover, this theoretical framework allows us to extend our treatment to a much larger and more representative parameter space for emerging SBS systems; specifically, this analysis accounts for the forward or backward nature of the scattering process and the effects of phonon propagation, optical loss, and small Brillouin gains. Our results demonstrate that the noise factor can deviate radically from $F\approx 1+n_{th}$ for a host of modern SBS devices, especially those in which phonon propagation significantly changes the coupled mode dynamics.