Lumped Circuit Modeling at Nanoscale (Part-II: Coupling Between Two Nanospheres)

The equivalent circuit of a nanosphere illuminated by an em wave at optical frequencies can be obtained using the quasi-static analysis. In the companion paper fields, external and internal to a nanosphere were provided in case of a general anisotropic nanosphere as well as a gyroelectric nanosphere biased by a dc magnetic field. In this part, we shall first review how one might derive an equivalent circuit for an isolated nanosphere of small radius and extend the discussion to determine the coupling between two nanospheres in general made of anisotropic materials and provide an equivalent circuit for this arrangement. Note that the derivation in an earlier paper by Alu et al. involving isotropic nanospheres had a minor mathematical oversight, which is fixed in the present paper, and the correct expressions for the fields internal and external to the nanospheres and those coupling from one nanosphere to the other are provided. Further note that the present paper assumes anisotropic materials for the two nanospheres used to determine the coupling. As such, the expressions for currents induced comprise dyadic terms. These models are acceptable if quantum effects are not significant.