General theory of asymmetrical polarization-dependent optics in functional material-doped 90° twisted nematic liquid crystals

General theory, which can completely describe the asymmetrical optics in a functional material (FM)-doped 90° twisted nematic liquid crystals (TNLCs), is proposed using Cayley–Hamilton theorem and Jones calculus. The FMs, whose shape and size are similar to those of the adopted NLCs, can be aligned along the long axes of the NLCs. The FMs discussed herein are dichroic dye (DD) and polymer. The experimental results of asymmetrical transmission in DD-doped 90° TNLCs are consistent with the theoretical calculation. Such asymmetrical characterization can be further used in the current applications based on 90° TNLCs in all fields to obtain new potential functions.