Question

Explain the working of a Poincare Sphere.

Answer 1

For any polarization state, ? represents the angle from the x-axis and ? ? (0,pi) ,so 2? ? (0,2pi). Similarly, ? represents the ellipticity of the state. ? ? (-pi/4,pi/4) so 2? ? (-pi/2,pi/2). All the points in the upper hemisphere will be representations of clockwise(right) motion. All points in the lower hemisphere will represent anti-clockwise(left) motion.(Taken from Arun Kumar and Ajoy Ghatak- Polarization of light)

Any point on the sphere represents a state of polarization. Apart from the equator, the north and south poles, every point is elliptic. A QWP having an angle of 90degrees between its fast and slow axis is represented as a diagonal of the sphere. If the fast axis is the x-axis, and the slow axis is the y-axis, then in the figure below, HV represents the QWP.

An analyser is also represented as a point(A). The fractional output intensity of any polarization state P is given as

, where PA is the arc length along the great circle connecting PA.

Now, passing of any polarization state through a QWP is done as:

Making an imaginary axis going in from the fast axis to the slow axis and rotating the sphere 90degrees

about the axis in clockwise direction. The new point that appears after this rotation is the output state

of polarization. In this way we could get the final state of polarization after passing any polarization

state light through a QWP.