Ultrahigh Q-Frequency product for optomechanical disk resonators with a mechanical shield

We report on optomechanical GaAs disk resonators with ultrahigh quality factor - frequency product Qf. Disks standing on a simple pedestal exhibit GHz breathing modes attaining a Qf of 10^13 measured under vacuum at cryogenic temperature. Clamping losses are found to be the dominant source of dissipation in this configuration. A new type of disk resonator integrating a shield within the pedestal is then proposed and its working principles and performances investigated by numerical simulations. For dimensions compatible with fabrication constraints, the clamping-loss-limited Q reaches 10^7-10^9 corresponding to Qf of 10^16-10^18. This shielded pedestal approach applies to any heterostructure presenting an acoustic mismatch.