Picometer Level Dimensional Sensing Using Microspherical Glass Shell Whispering Gallery Mode Resonators

We present sub-picometer displacement measurement using a high quality-factor (Q) whispering gallery mode (WGM) borosilicate glass microspherical resonators. Calibrating the expansion of the WGM resonator using a laser Doppler vibrometer (LDV) upon absorption of thermal radiation, 3.7 pm of dimensional change can be experimentally resolved using a 1 mm diameter and
$8.4\ \mu \mathrm{m}$
thick glass microspherical shell resonator. COMSOL models presented show that an unprecedented displacement resolution of 89 fm is possible for a microspherical shell resonator with a diameter of 2 mm and a thickness of
$2\ \mu \mathrm{m}$
.