Design of waveguides in silicon phoxonic crystal slabs

We consider the problem of designing waveguides in nanostructures presenting simultaneously a phononic and a photonic band gap. We specifically opt for designs in perforated silicon membranes that can be conveniently obtained using silicon-on-insulator technology. Geometrical parameters for simultaneous photonic and phononic band gaps are first chosen, based on the finite element analysis of a perfect phoxonic crystal of circular holes. A plain core waveguide is then defined, and simultaneous slow light and elastic guided modes are identified. Joint confinement of light and elastic waves with group velocities reduced by a factor of approximately 30 is predicted.