The trajectory of the polarization state of a monochromatic beam passing through a fixed linear polarizer and a rotating elliptical retarder on the Poincaré sphere is found to be a three-dimensional 8-shaped contour, which is determined as the line of intersection of a right-circular cylinder with the Poincaré sphere. The cylinder is parallel to the S3 axis, and the projection of the contour on the S1S2 plane is a circle whose center and radius are determined. A method of projecting the three-dimensional geometric relationships to the two-dimensional S1S2 plane to locate the position of the polarization state of the emerging beam on the Poincaré sphere for a given azimuth of the elliptical retarder is presented, and applied to solve a problem of polarization optics. The proposed graphic method substantially simplifies the polarization state analysis involving elliptical retarders.
"A Simple Graphic Method for Analyzing the Polarization State of an Optical System with a Fixed Polarizer and a Rotating Elliptical Retarder," Progress In Electromagnetics Research,
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