Revisiting the Poincaré Sphere as a Representation of Polarization State

Graphical representations of the polarization state of an antenna or an electromagnetic wave propagating through space are useful tools to supplement rigorous mathematical analyses. One such example, the polarization ellipse, is frequently used in combination with the mathematical development of polarization theory. The Poincaré sphere is another graphical representation but is much less widely used. Since each possible polarization state appears as a point on the surface of the sphere, it has limited value in representing a single polarization state. However, it can be quite useful for visualizing the relationships between multiple polarization states. In this paper, we show a different way of presenting the Poincaré sphere using a Mercator projection and elliptical parameters. We also describe a tool that implements this technique and provides a real-time display of polarization state as a function of frequency.