Estimation of surface density of molecules adsorbed on a whispering gallery mode resonator: Utility of isotropic polarizability

A protocol is presented to estimate the surface density and anisotropic polarizability of molecules adsorbed on the surface of a dielectric resonator of uniform refractive index. Measurement of resonance wavelength shift of transverse electric and transverse magnetic whispering gallery modes in the resonator gives the product of the surface density and the polarizability components normal and tangential to the resonator surface. The isotropic mean of the two products is independent of the molecular orientation, allowing us to estimate the surface density with the knowledge of the isotropic polarizability. If the adsorbate consists of anisotropic molecules, one can obtain information on the orientation of the molecules from the polarizability components. We also show that the effect of dipoles induced in nearby adsorbed molecules is in practice negligible up to the highest density in random sequential adsorption.