Application of Hill´s functions to problems of propagation in stratified media

A novel method of solving Maxwell´s equations in a plane-stratified dielectric layer is presented, The governing differential equations for each polarization are solved in terms of Hill´s functions. The formulation yields solutions which are formally exact and applicable to an extremely wide range of dielectric variations within the layer, without restriction to any particular frequency regime. The method is used to study the reflection of a plane wave polarized parallel to the plane of incidence by an inhomogeneous layer separating two homogeneous regions of infinite extent. The effect of the graded boundary on the Brewster-angle phenomenon is discussed for the case where the two homogeneous regions have different dielectric properties. Reflections from a dielectric duct are also considered as an illustration of the utility of the method.