Effect of the number of sublayers on axial optics of anisotropic helical structures

The transition from the continuously rotating dielectric ellipsoid approach to the discrete periodic collection of wave plates is investigated by comparing an exact analytic solution found using a Bloch-Lyaponov transformation on the 4 × 4 matrix form of Maxwell's equations and the numerical solution. The validity of the analytic solution depends only on the number of sublayers within the unit cell and not on the number of periods in the sample. The circularly polarized Bragg-type selective reflection peak is shown to exist with helices containing as few as N_l = 3 sublayers in a single period, but due to the appearance of higher Fourier harmonics in the dielectric tensor, additional selective reflection peaks appear. The case of N_l = 4 corresponds to the folded Sole-type filter case with a twist angle of π/4, but it acts as a reflection filter for unpolarized light. Hence using this fact with liquid crystalline structures, polarization insensitive tunable filters can be built.