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

Abstract

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.

Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications

“…We are preparing a manuscript for the TE and TM shifts that take into account the dipolar fields by neighboring particles explicitly at different surface densities of the particles. 17…”

Whispering-gallery modes in a microsphere coated with a high-refractive index layer: polarization-dependent sensitivity enhancement of the resonance-shift sensor and TE-TM resonance matching

“…The magnitude of the downward and upward swings is greater for a layer of a higher RI. The initial decrease in the ratio parallels the decrease of the shift ratio in adsorption of spherical particles to form a layer; 18 The shift ratio decreases with an increasing surface density of adsorbed particles, especially when the RI of the particles is high. It is interesting to note that at particular values of t, the ratio is equal to unity.…”

Optical Microspherical Resonators for Biomedical Sensing

“…More detailed discussions about first order perturbation theory for obtaining the shift can be found in [41,42]. One can assume that the field of a particular biomolecule is not influenced by its neighbors [43] and take into account that the lowest surface density that can be detected depends on the resonance line width δλ (or a fraction F of the linewidth), which in turn depends on the quality factor Q = λ/δλ [11]. Accordingly, the LOD of surface density may be given by [11,21]: ${\sigma }_{\mathrm{italicLOD}}={\epsilon }_0{R}_0 \frac{\left(N_s{}^2-N_m{}^2\right)F}{{\alpha }_{\mathrm{italicex}}Q}$…”