The loci of polarization states for which either the ellipticity alone or the azimuth alone remains invariant upon passing through an optical system are introduced. The cartesian equations of these two loci are derived in the complex plane in which the polarization states are represented. The equations are quartic and are conveniently expressed in terms of the elements of the Jones. matrix of the optical system. As an exple the loci are determined for a system composed of a π/4 rotator followed by a quarter-wave retarder.
R. M. A. Azzam and N. M. Bashara, "Loci of Invariant-Azimuth and Invariant-Ellipticity Polarization States of an Optical System," Appl. Opt. 12, 62-67 (1973)