  We describe the mechanism by which a metamaterial surface can act as an ideal
phase-controlled rotatable linear polarizer. With equal-power linearly
polarized beams incident on each side of the surface, varying the relative
phase rotates the polarization angles of the output beams, while keeping the
polarization exactly linear. The explanation is based on coupled-mode theory
and the idea of coherent perfect absorption into auxiliary polarization
channels. The polarization-rotating behavior occurs at a critical point of the
coupled-mode theory, which can be associated with the exceptional point of a
parity-time (PT) symmetric effective Hamiltonian.
