Theory of cascaded forward brillouin scattering

Brillouin Scattering (SBS) is the scattering of light from acoustic vibrations in matter and manifests in three different configurations (see Fig. 1a): The first case is when light is back-scattered and is referred to as stimulated Brillouin scattering (SBS) in the strict sense. The second case is when light is forward-scattered into a different optical mode. This inter-modal scattering process has many similarities with (backward) SBS. The third case is when light is forward-scattered into the same optical mode, which is known as intra-mode forward Brillouin scattering (FBS). In bulk and bulk-like systems, backward SBS is self-amplifying and a promising mechanism for the implementation of applications ranging from novel light sources such as Brillouin lasers or on-chip frequency combs to microwave photonics [1]. However, recent studies [2,3] conducted in nano-scale waveguides showed that FBS can exhibit opto-mechanical coupling in excess of backward SBS and for this reason it has attracted considerable attention. So far, the analysis of many FBS experiments has been based on theory developed for backward SBS. Unfortunately, this turns out not to be applicable. The most striking discrepancy is that simple backward SBS theory predicts exponential growth of Stokes and sound wave, while FBS without optical dispersion does not exhibit any growth at all of the sound wave and oscillatory behaviour in the Stokes signals. The reason for this very different behavior is that in intra-mode FBS and unlike in backward SBS all Stokes orders are coupled by the same acoustic mode and therefore the scattering process can cascade very efficiently [4].