Electromagnetics of Helical Medial

This chapter addresses chiral media, from the perspective of both macroscopic electromagnetics and geometric optics. The main liquid crystal focus is on cholesteric liquid crystals, which can be seen as twisted nematics. We begin with a brief background on helical media and introduce the helical pitch. To address some of the mathematics of chiral media, we introduce four material parameters which classify media, ranging from isotropic to nonreciprocal chiral. In the macroscopic electromagnetic regime, we show well-posedness of a chiral Maxwell system on a Lipschitz domain in 3D. In particular, we show higher order Sobolev regularity of classical solutions. Then we move to the optics of chiral media and consider various special phenomena which occur for such materials, such as Bragg reflection. We obtain variants of the classical Snell Law and a version of the Bragg–Snell Law for cholesteric liquid crystals.