Birefringent network forming a rotator

An optical system consisting of a large number N of identical retardation plates, where each of the plates is rotated by an angle θ with respect to the one preceding it, has been examined by Reusch and Sohncke. The product of N and θ must be equal to mπ, where m is an integer. This system behaves equivalent to a simple optical retarder under certain conditions. The system, which is quite difficult to examine by ordinary methods, has been treated using Jones calculus by Jones himself. But the treatment seems to be still quite complicated. We have treated the same system using Jones calculus, Pauli’s spin matrices and Chebyshev polynomial which gives the treatment quite elegant formalism.