This Demonstration plots constant phase retardation contours in the complex plane. The experimental setup consists of two liquid crystal (LC) retarders and a polarizer. The set of circles centered on the real and imaginary axes represent the polarization states generated with constant phase retardation from LC1 and LC2. The circles span the entire complex plane, showing that any state of polarization can be generated.

J. Liu and R. Azzam, "Polarization properties of corner-cube retroreflectors: theory and experiment," Applied Optics,36(7), 1997 pp. 1553-1559.

This is a method to generate and detect any state of polarization using two liquid crystal (LC) retarders with retardances and and a polarizer. The two LC retarders have their fast axes at azimuths of and with respect to an external reference direction. The complex variable is calculated using the Jones calculus. The equation for indicates that different states can be obtained by controlling the retardances.