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

Abstract

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.

Circuit and Multipolar Approaches to Investigate the Balance of Powers in 2d Scattering Problems

“…They also provide a means to investigate the associated balance of powers and the fundamental limits on each contribution. This work therefore completes previous studies based on 3D geometries [3,21,22]. Specifically, we have presented upper bounds of the absorbed, scattered and extracted power for 2D geometries, thus revealing the main similarities and differences between the 2D and 3D scenarios, as well as the difficulties of analyzing 3D objects with high aspect ratio by using a vector spherical harmonic decomposition.…”

“…Specifically, one finds from (37) that the upper bound of absorbed power for 2D objects increases as 2N + 1 along with the number of harmonics N , while it was found to increase as N 2 + 2N for 3D geometries [22]. Thus, it can be concluded that the growth rate per harmonic is much smaller in 2D geometries.…”

“…For example, circuit models to describe the scattering of spherical bodies of arbitrary size were presented in [22]. To illustrate this concept further, this section presents a circuit model to describe the scattering of electrically small 2D bodies.…”

“…For example, his cautionary note on the inaccuracy of the Thévenin/Norton circuit models has stimulated research on new analytical tools to address this problem. In particular, these efforts include using the optical theorem [20] and spherical harmonic decompositions [3,21,22], to investigate the intimate correlation between the associated absorption and scattering processes. In addition, his work has motivated the development of new circuit models that overcome the difficulties of the Thévenin/Norton models, and provide an accurate description of the scattered power [22].…”

“…In particular, these efforts include using the optical theorem [20] and spherical harmonic decompositions [3,21,22], to investigate the intimate correlation between the associated absorption and scattering processes. In addition, his work has motivated the development of new circuit models that overcome the difficulties of the Thévenin/Norton models, and provide an accurate description of the scattered power [22]. Complementary efforts include the completion of the analytical description of a receiving dipole antenna, including all components of the scattered field, while ensuring a proper energy balance [23].…”