Light: The Poincare sphere.
What is the Poincare Sphere? How does the Poincare Sphere relate to the polarization of light?
Henri Poincare in about 1892 formulated a concept that resulted in a virtual sphere that can used to
graphically represent any polarization state of light. This virtual sphere now is called the Poincare Sphere.
Light can have a variety of polarizations states which include Linear, Right or Left Elliptical, and Right or
Left Circular polarization. These polarizations graphically correspond to various points on the surface
of the Poincare Sphere illustrated in the simulation below. Notice how the state of light polarization
correspond to various points on the surface of the Poincare Sphere.
Poincare used the circular polarization basis, with the latitude representing the relative magnitudes for
the left and right circularly polarized components and the longitude represnting the relative phase difference between
left and right circularly polarized components.
The Poincare Sphere can be used interactively to understand how different polarizations states of light are possible. There are several regions on the sphere where the polarization state can be visualized more clearly. This table summarizes the polarization states:
| Poincare Sphere Region | Polarization State |
| North Pole | Left Circular (pure left) |
| North Lattitudes | Left Elliptical |
| Equator | Linear (equal left and right) |
| South Lattitudes | Right Elliptical |
| South Pole | Right Circular (pure right) |
| Zero Longitude on Equator | Vertical |
| 180 Longitude on Equator | Horizontal |
In the simulations below the horizontal hlider changes the phase of the left and right circularly polarized components that produce the resulting polarization. The vertical slider changes the amplitudes of the left and right circularly polarized components that produce the resulting polarization. As the sliders are moved the position of the cross-hair on the Poincare Sphere shows the resulting polarization. In the lower right corner of the simulation is a graphic showing the Left Polarization (Blue), Right Polarization (Green), and Resulting Polarization (Red).
Experiment with this simulation to develop a more thorough understanding of the use of the Poincare Sphere. You may find it helpful to reproduce these polarizations using the circular basis in the first CLAW polarization page .
Use the above simulation to answer the following questions?