Arbitrary polarization retarders and polarization controllers, constructed from sequences of half-wave and quarter-wave plates

We theoretically introduce several types of arbitrary polarization retarders constructed from sequences of half-wave and quarter-wave plates, each rotated at specific angles. By integrating these arbitrary polarization retarders with arbitrary polarization rotators, we develop a versatile device capable of performing arbitrary-to-arbitrary polarization transformations. While some of the proposed devices are documented in the literature, others are novel and, to the best of our knowledge, have not been previously presented. The continuous adjustment of retardance and rotation in these devices is achieved by altering the relative orientation of the wave plates in the sequence.