Document Type


Publication Date



The trajectory of the polarization state of a monochromatic light beam after it passes through a fixed linear polarizer and a rotating linear retarder of arbitrary retardance Δ is determined on the Poincaré sphere. The three-dimensional figure-8 contour is shown to be the line of intersection of a right-circular cylinder with the sphere. The cylinder is parallel to the polar (s3) axis, touches the sphere at the equator (at the point that represents the linear polarization transmitted by the fixed polarizer), and has a radius r=sin2(Δ/2). Projections of the trajectory in the coordinate planes of the normalized Stokes parameter space (s1, s2, s3) are also determined.

Journal Name

Journal of the Optical Society of America A


This paper was published in Journal of the Optical Society of America A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.