Polarization orthogonalization properties of optical systems

We investigate the conditions under which an optical system (or device) may transform polarization states at its input into orthogonal states at its output. We find that such polarization orthogonalization is possible if the Jones matrix of the optical system satisfies a specific inequality. One, two, or an infinite number of input polarization states may be orthogonalized. In the latter case, the locus of input states is a circle in the complex plane (and on the Poincaré sphere) of polarization. Several examples are given for illustration.