Design and analysis of Brewster's angle polariser using inhomogeneous planar layers and Hill's method

This study presents a generalised and easy-to-use method based on Hill's equation to analyse the electromagnetic wave propagation in inhomogeneous planar layers with arbitrary permittivity profiles. We explore the effects of polarisation, incidence angle, layers thickness and permittivity profiles on reflection and transmission characteristics. Hill's method is as an efficient tool to obtain an analytical solution to the propagation equations and is applicable to all arbitrary profiles of permittivity and permeability. Using Hill's method and an arbitrary profile of permittivity, numerical simulations for both polarisations transverse electric (TE)- and transverse magnetic (TM)-polarised waves are performed to compute the reflection and transmission of Brewster's angle polarisers having optimised thicknesses. The proposed polariser is analysed and optimally designed in microwave domain systems. The results obtained agree well with other published data.