Arbitrary Polarization Retarders and Polarization Controllers, Constructed from Sequences of Half-Wave and Quarter-Wave Plates

We present a theoretical study of various designs for arbitrary polarization retarders, created using sequences of half-wave and quarter-wave plates arranged at specific rotation angles. When combined with arbitrary polarization rotators, these retarders form a flexible device capable of implementing transformations between any pair of polarization states. Some configurations discussed are known from existing literature, while others appear to be new and, to the best of our knowledge, have not been reported before. The devices allow for continuous tuning of both retardance and rotation by adjusting the relative angles between the wave plates in the sequence.