Abstract

We study dipole-dipole (d-d) interaction mediated by the whispering gallery modes (WGM) of a dielectric microsphere (with radius a).The dipole A is assumed to be at the north pole on the surface of the microsphere, while the dipole B is at the south pole at a distance dfrom the surface. We consider both normal and tangential to the surface orientations of the dipoles (henceforth referred to as r-orientation and θ-orientation, respectively). The d-d interaction can be calculated using the dyadic Green’s functions¹${}_{\text{G}}^{\Rightarrow }\left({\overrightarrow{r}}_A,{\overrightarrow{r}}_B,\omega \right)$, which can be separated out in the free space and the surface components. The surface components carry the signature of the whispering gallery modes of the microsphere. We assume the WGM to be in resonance with the natural frequency of the dipoles and introduce enhancement factors as $K_{0ij}=\mathrm{Re}\left(-\frac{i{e}^2\omega }{2m{c}^2{\gamma }_0}{\overrightarrow{n}}_A{\stackrel{\Rightarrow }{G}}^{\left(s\right)}\left({\overrightarrow{r}}_A,{\overrightarrow{r}}_B,\omega \right).{\overrightarrow{n}}_B\right)$ (the superscript sdenotes the surface contribution and γ₀gives the dipole decay rate in free space and ${}_n^{\to }$denotes the orientation of the dipole) evaluated at the resonance frequency. The results for the enhancement factors for silica microspheres (refractive index n=l 46) with both the dipoles r-oriented and for two values of a,namely a=5(top) and 200 µm(bottom) are shown in figure. We used the a_39,1and a_2312,167modes, respectively for the two radii. The dramatic enhancement for the larger sphere can be clearly seen from the figure For both the dipoles having θ-orientation the interaction is two orders of magnitude less since the coupling efficiency of the a-mode to θ-oriented dipoles is minimal. For mutually orthogonal orientation of the dipoles there is no coupling.

© 2000 IEEE