A new method for scattering from radially inhomogeneous cylinders of large radius is presented herein. It is based on the Coupled Azimuthal Potentials (CAP) Formulation [1], i.e., a description of the fields in terms of magnetic and electric azimuthal potentials. Since the cylinders considered are in 2D geometry of revolution, they are split in concentric layers where the Gaussian profile of the permittivity is approached by a piecewise constant function. The novelty of the method is to solve directly Maxwell's equations for a permittivity varying continuously radially, in terms of modal tangential electromagnetic fields, by making the steplength of the layers tend to zero. This allows us to minimize the size of linear systems. Properties of the potentials are used only on the cylinder axis and at infinity. The potential coefficients are developed by using cylindrical functions to express the boundary conditions. Then, asymptotic approximations are used to determine the diffracted fields at infinity. Numerical results of near-field map are compared with others obtained via the Finite Element Method codes. But these codes require quite small meshes and are thus limited in size of geometry. Moreover, polarized and depolarized scattering widths are presented which show the depolarization of the diffracted field for both TE and TM polarizations of the incident field. It is revealed that the fields are noticeably modified by the medium and that the angle of incidence has a great influence on the levels of scattering width.