Differential theory of diffraction by finite cylindrical objects

We present a differential theory for solving Maxwell equations in cylindrical coordinates, projecting them onto a Fourier-Bessel basis. Numerical calculations require the truncation of that basis, so that correct rules of factorization have to be used. The convergence of the method is studied for different cases of dielectric and metallic cylinders of finite length. Applications of such a method are presented, with a special emphasis on the near-field map inside a hole pierced in a plane metallic film.