Tuning of whispering gallery modes of spherical resonators using an external electric field.

In this paper we investigate the electrostriction effect on the whispering gallery modes (WGM) of polymeric microspheres and the feasibility of a WGM-based microsensor for electric field measurement. The electrostriction is the elastic deformation (strain) of a dielectric material under the force exerted by an electrostatic field. The deformation is accompanied by mechanical stress which perturbs the refractive index distribution in the sphere. Both strain and stress induce a shift in the WGM of the microsphere. In the present, we develop analytical expressions for the WGM shift due to electrostriction for solid and thin-walled hollow microspheres. Our analysis indicates that detection of electric fields as small as ~500V/m may be possible using water filled, hollow solid polydimethylsiloxane (PDMS) microspheres. The electric field sensitivities for solid spheres, on the other hand, are significantly smaller. Results of experiments carried out using solid PDMS spheres agree well with the analytical prediction.