A simple inverter for polarization transformations

It is shown that a transparent birefringent element whose eigenstates are a pair of elliptical polarizations with principalaxes along the x and y axes, sandwiched between a pair of orthogonal halfwave plates with principal axes along directions at 45 deg to the x and y axes, is equivalent to an element with the same eigenstates and eigenvalues but with the fast and the slow eigenstates interchanged. The device thus produces the inverse of the original unitary transformation. A similar result holds for a puredichroic element. With electrically switchable halfwave plates such a device can be used to switch the sign of optical activity or to rotate through 90 deg, without any moving parts, a linear retarder or a linear polarizer.