[math-fun] A polarization puzzle

Here is a puzzle concerning the optics of polarized light. Every state of polarization has its opposite.  For linear polarization, it's linear but rotated 90 degrees.  For circular polarization, it's circular with opposite helicity.  For general elliptic polarization, it's elliptic with the ellipse rotated 90 degrees, and the helicity reversed.  On the Poincaré sphere, opposite states of polarization are represented by diametrically opposite points. The puzzle is to construct an optical device that reverses the polarization state.  For any input, the output is the opposite polarization.  Or, prove that it can't be done.   --  Gene