A PhoXonic crystal: Photonic and phononic bandgaps in a 1D optomechanical crystal

Recent years have witnessed the increase of interest in cavity optomechanics, which exploits the confinement and coupling of optical waves and mechanical vibrations at the nanoscale. Amongst the different physical implementations, optomechanical (OM) crystals built on semiconductor slabs would enable the integration and manipulation of multiple OM elements in a single chip and provide GHz phonons suitable for coherent phonon manipulation. Different demonstrations of coupling of infrared photons and GHz phonons in cavities created by inserting defects on OM crystals have been performed. However, the considered structures do not show a complete phononic bandgap at the frequencies of interest, which in principle should allow longer dephasing time, since acoustic leakage is minimized. In this work we discuss the excitation of acoustic modes in a 1D OM crystal properly designed to display a full phononic bandgap for acoustic modes at about 4 GHz. The confined phonons have an OM coupling ranging from the kHz to the MHz range with contributions from moving interfaces and the photoelastic effect that add constructively for many of them. The modes inside the complete bandgap are designed to have high mechanical Q factors and invariant to fabrication imperfections, what would allow several coherent phonon manipulations at moderate cryogenic temperatures.