Dielectric property of particles at interface in random sequential adsorption and its application to whispering gallery mode resonance-shift sensors

Dielectric properties of particles adsorbed onto a planar interface between two dielectric media are considered, taking into account the dipolar fields created by polarization induced in nearby particles as well as by their image dipoles. The use of a dipolar approximation allowed us to derive a self-consistent expression for the effective field experienced by each particle. The expression uses the pair correlation function of the particle distribution and is presented in a close form for normal and tangential directions of the applied field. To obtain the correlation function for the distribution of irreversibly adsorbed particles and calculate the effective field, a computer simulation of random sequential adsorption was carried out at prefixed particle densities and until placing the next particle became extremely difficult. The effective field was also calculated for hexagonal closest packing. Results of these calculations were then used to estimate resonance wavelength shifts of whispering gallery modes in a dielectric microsphere when it adsorbs dielectric particles. A gradual change was seen from the shifts for isolated particles at low densities to those for a packed layer.