Generalized reflection coefficient for non uniform transmission lines

this paper we present the formula for the generalized reflection coefficient that relates the upgoing wave to the downgoing wave at the interface between an isotropic homogeneous half-space and an isotropic inhomogeneous dielectric slab. Various forms of ε(z) that admit closed-form solutions for the generalized reflection coefficient when the inhomogeneous planar profile is analytic and continuos are also derived