The propagation of polarized light within the cholesteric structure along its helical axis is conveniently expressed in terms of four 2-by-2 matrix operators. This description is useful in studying the change in the state of polarization of a beam propagating along the helical axis. The well-known properties of the liquid crystals come out as natural consequences of the properties of these operators. In particular, for a certain region of wavelengths as the beam propagates along the helical axis, a vector representing the state of polarization in Stokes space precesses about the S3 axis. The S3 axis stands for circular polarization. Furthermore, owing to the properties of the matrix operators, if the propagation of polarized light within the liquid crystal is described in diagonal form for propagation in one direction along the helical axis, then it cannot have a diagonal form for propagation in the opposite direction.
A. S. MARATHAY, "Matrix-Operator Description of the Propagation of Polarized Light through Cholesteric Liquid Crystals," J. Opt. Soc. Am. 61, 1363-1372 (1971)