Light propagation and light scattering in cholesteric liquid crystals

The exact solution to Maxwell's equations in a cholesteric planar texture is described and an algorithm for computing it is given. This algorithm makes use of a matrix continued fraction which converges so rapidly that the solution is, for practical purposes, in closed form. The solutions thus found can be used to describe scattering from dielectric inhomogeneities in a cholesteric in Born approximation, taking exact account of the cholesteric medium in which the scattering takes place. The general expression for the $S$ matrix in the Born approximation is given. The consequences for scattering from slowly varying order-parameter fluctuations are worked out in detail and several features are noted which depend in an essential way on the form of the exact cholesteric modes. These features include: (1) the scattered amplitude goes to zero in the forward direction, (2) there is a kind of anomalous diffraction for wavelengths near the pitch length, and (3) the scattered light may show complex spatial structure, even if the scatterer is essentially structureless, due to a kind of spatial beating of the cholesteric modes.