Analytical and Equivalent Circuit Models to Elucidate Power Balance in Scattering Problems

Analytical and equivalent circuit models are presented to elucidate the balance of powers in scattering processes. Specifically, closed-form expressions of the associated maximal extracted, scattered, absorbed and reactive powers are formulated. The circuit model then helps to characterize in a straightforward manner these powers, to provide physical insights into the inter-relationships among this set, and thus guides the resolution of their fundamental limits. The analysis demonstrates that the absorbed power can not exceed 25% of the power extracted from the incident field (extracted power) for the lossless case and helps extricate the conditions for which the scattered and absorbed powers are equal or significantly different. A coated sphere illuminated by a plane wave under both resonant and cloaked states is selected as an illustrative example. Although the analysis and circuit models are rigorously derived for spheroidal particles, their extrapolation to arbitrary scatterers is also discussed.