Engineering multiple GHz mechanical modes in optomechanical crystal cavities

Optomechanical crystal cavities (OMCCs) are fundamental nanostructures for a wide range of phenomena and applications. Usually, optomechanical interaction in such OMCCs is limited to a single optical mode and a unique mechanical mode. In this sense, eliminating the single mode constraint - for instance, by adding more mechanical modes - should enable more complex physical phenomena, giving rise to a context of multimode optomechanical interaction. However, a general method to produce in a controlled way multiple mechanical modes with large coupling rates in OMCCs is still missing. In this work, we present a route to confine multiple GHz mechanical modes coupled to the same optical field with similar optomechanical coupling rates - up to 600 kHz - by OMCC engineering. In essence, we increase the number of unit cells (consisting of a silicon nanobrick perforated by a circular holes with corrugations at its both sides) in the adiabatic transition between the cavity center and the mirror region. Remarkably, the mechanical modes in our cavities are located within a full phononic bandgap, which is a key requirement to achieve ultra high mechanical Q factors at cryogenic temperatures. The multimode bevavior in a full phononic bandgap and the easiness of realization using standard silicon nanotechnology make our OMCCs highly appealing for applications in the classical and quantum realms.