Orthogonality derivation of polarization state based on Poincaré sphere

Abstract

To make full use of the polarization information of electromagnetic waves for the polarimetric sensor array, we derive the orthogonality expression of the polarization state based on the Poincaré sphere (PS) representation. The ellipticity angle and the orientation angle of the ellipse are used to describe the polarization ellipse and the point on the surface of the Poincaré sphere. The derivation shows that two points that characterize a pair of orthogonal polarization states are distributed in the opposite positions. Compared with the conventional linear and circular polarization state, the flexible elliptical polarization state would result in the maximum separation of co-polarization and cross-polarization components, thereby enhancing the accuracy of polarization information measurement. The simulation result displays the correctness of the theoretical derivation, which could provide a basis for the further polarization state configuration.