A geometrical construct used to describe polarization
. The Poincare Sphere is isomorphic
to the Bloch Sphere
for two level atoms
, because all two level systems are equivelent
Picture a sphere. Left and Right circularly polarized states (The X component leads or lags the Y component by 90 degrees) are the north and south poles, respectively.
Linearly polarized states are on the equator. Usually |H> is on the right, |V> on the left, |45> in front and |-45> in back. Notice that states Pi/2 apart are Pi degrees apart on the sphere. This is because there are 2*Pi radians around a great circle, but polariztion only ranges from 0 to Pi: |H> and -|H> are the same state.
Eliptically polarized stares are in either hemisphere, depending on whether they rotate clockwise or counterclockwise.
Most optical elements, such as rotators, wave plates, and mirrors can be represented as a simple geometric transform on the Poincare Sphere, making it very easy to check the expected behavior of an optical system.