Distinguishing plane, circular, elliptical light

Plane, circularly and elliptically polarized light can be told apart using a Nicol prism (as analyzer) and a quarter-wave plate (QWP). The same tests also separate them from unpolarized and partially polarized light.

 beam --> [QWP] --> [Nicol analyzer, rotated] --> eye

Step 1: Nicol alone

Rotate the Nicol through 360° and watch the transmitted intensity.

Step 2: Quarter-wave plate in front of the Nicol

1. Plane polarized: with the QWP's axis parallel or perpendicular to the vibration, the light stays plane polarized, so extinction by the Nicol remains. At other angles the QWP makes it elliptical and extinction is lost.
2. Circular: the QWP introduces a further π/2 phase difference, giving δ = π or 0, and so converts it to plane polarized light. On rotating the Nicol, complete extinction occurs twice per turn. Unpolarized light stays unpolarized, so there is no extinction.
3. Elliptical: with the QWP's axis along a principal axis of the ellipse, the light becomes plane polarized, and rotating the Nicol now gives complete extinction at some angle. For partially polarized light the minimum never becomes zero.

Summary

• Extinction with the Nicol alone: plane.
• Constant with the Nicol, extinction after the QWP: circular.
• Minimum not zero with the Nicol, extinction after the QWP (axis set along the ellipse axis): elliptical.
• No extinction in any case: unpolarized or partially polarized.