Designing of strongly confined short-wave Brillouin phonons in silicon waveguide periodic lattices.

We propose a feasible waveguide design optimized for harnessing Stimulated Brillouin Scattering with long-lived phonons. The design consists of a fully suspended ridge waveguide surrounded by a 1D phononic crystal that mitigates losses to the substrate while providing the needed homogeneity for the build-up of the optomechanical interaction. The coupling factor of these structures was calculated to be G/Q = 0.54 (W m) for intramodal backward Brillouin scattering with its fundamental TE-like mode and G/Q = 4.5 (W m) for intramodal forward Brillouin scattering. The addition of the phononic crystal provides a 30 dB attenuation of the mechanical displacement after only five unitary cells, possibly leading to a regime where the acoustic losses are only limited by fabrication. As a result, the total Brillouin gain, which is proportional to the product of the coupling and acoustic quality factors, is nominally equal to the idealized fully suspended waveguide.