Geometric Visualization of the 3D Polarimetric Information of an Arbitrary Electromagnetic Field

Abstract

The geometric visualization in this study concerns the three−dimensional (3D) polarimetric information of an arbitrary electromagnetic field. Based on previous research, a 3 × 3 coherency matrix Φ can be decomposed into an incoherent superposition of a totally 3D−polarized component Φ3D_p, a specific partially 3D−polarized component Φ3D_pp with a 3D degree of polarization (DoP) of 1/2, and a totally 3D−unpolarized component Φ3D_up. Combining the physical meaning of this decomposition, we mathematically construct three polarization purities, namely, P3D_p, P3D_pp, and P3D_up, for an arbitrary electromagnetic field to quantify the weight of the three 3D−polarized components. In order to show the proportion of the three polarized components of an electromagnetic field intuitively, we propose a geometric representation of a spatially quadric surface. Finally, two examples are cited to demonstrate the applicability of intuitively displaying the 3D polarimetric information of an arbitrary electromagnetic field.