Poincare sphere representation of the fixed-polarizer rotating-retarder optical system

The trajectory of the polarization state of a monochromatic light beam afte r it passes through a fixed linear polarizer and a rotating linear retarder of arbitrary retardance Delta is determined on the Poincare sphere. The th ree-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 (s(3)) axis, touches the sphere at the equator (at the point that re presents the linear polarization transmitted by the fixed polarizer), and h as a radius r = sin(2)(Delta /2). Projections of the trajectory in the coor dinate planes of the normalized Stokes parameter space (s(1), s(2), s(3)) a re also determined. 0 2000 Optical Society of America [S0740-3232(00)02411- X].