Axial electromagnetic wave propagation in inhomogeneous dielectrics

We review the mathematical description of axial propagation in inhomogeneous dielectrics, focusing on two canonical examples: scalar Bragg gratings and thin film helicoidal bianisotropic media (TFHBM). Coupled wave analysis is reviewed for the former, and exact methods based on rotational transforms are discussed for the latter. There are many similarities between the physical descriptions that are emphasised in reviewing the modelling techniques, although the transform which allows the TFHBM case to be solved exactly is shown to be inapplicable in the scalar case.