Cascaded forward Brillouin scattering to all Stokes orders

TL;DR

This paper develops a Hamiltonian model for cascaded Brillouin scattering across all Stokes orders, analyzing intra-mode forward Brillouin scattering in various waveguides, revealing phase modulation effects and connections to quantum optics.

Contribution

It introduces a unified Hamiltonian formalism for cascaded Brillouin scattering applicable to quantum and classical regimes, with analytical solutions and novel insights into phase modulation and waveguide phenomena.

Findings

Cascaded intra-mode FBS results in pure phase modulation.

Exact analytical solution for dispersionless waveguides.

Connection between FBS and quantum optics phenomena.

Abstract

Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we show that cascaded intra-mode FBS results in a pure phase modulation and discuss how this necessitates specific experimental methods for the observation of fibre-based and integrated FBS. Further, we discuss how the descriptions that have been established in these two classes of waveguides connect to each other and to the broader context of cavity opto-mechanics and Raman scattering. Finally, we draw an unexpected striking similarity between FBS and discrete diffraction phenomena in waveguide arrays, which makes FBS an interesting candidate for future research in quantum-optics.