Estimation of surface density of molecules adsorbed on a whispering gallery mode resonator: Utility of isotropic polarizability
Iwao Teraoka and Stephen Arnold
J. of Appl. Phys. 102, 076109 (2007)

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.