  We consider the solvability of the direct scattering problem of an obliquely
incident time-harmonic electromagnetic wave by a piecewise constant
inhomogeneous, penetrable and infinitely long cylinder. We prove the existence
and uniqueness of the solution using properties of the boundary value operators
and the integral equation method. For the numerical solution, we apply a
collocation method and we approximate the singular integral operators using
quadrature rules. We show convergence of the numerical scheme for the interior
and the scattered fields both in the near- and far-field regime.
