On the response of an antenna to polarized electromagnetic plane waves using a tensorial and spinorial approach

Abstract

Geometric Polarimetry [1] has recently been introduced as a new analytical framework to express fundamental relationships in polarimetry, characterizing these in geometric terms which guarantees their invariance with respect to spatial reference frame and choice of basis. It was shown via a rigorous derivation from Maxwell's equations that there is a formal argument for representing elementary coherent states algebraically as spinors, and geometrically as generators of the Poincaré sphere. While [1] only considered the characterization of field states, there is in remote sensing contexts a corresponding need also to characterize the polarization states of antennas. This needs to be completely generic and not dependent on the detailed structure of the antenna. This paper presents a derivation based on Schelkunov's reaction theorem [2] which fulfils these requirements. The statement of the theorem is translated from its usual form to a tensor representation, and this is finally reduced to obtain the new spinor representation of the antenna in terms of its polarization spinor and its phase flag.