  We report disk-shaped silicon optomechanical resonators with frequency up to
1.75 GHz in the ultrahigh frequency band. Optical transduction of the thermal
motion of the disks' in-plane vibrational modes yields a displacement
sensitivity of 4.1 \times 10^(-17) m/Hz^(1/2). Due to the reduced clamping
loss, these disk resonators possess high mechanical quality factors (Q), with
the highest value of 4370 for the 1.47 GHz mode measured in ambient air.
Numerical simulation on the modal frequency and mechanical Q for disks of
varying undercut shows modal coupling and suggests a realistic pedestal size to
achieve the highest possible Q.
