This report investigates how plane waves are diffracted by a screen with a small aperture.

Classically a screen with infinite extend, infinitesimal width, infinite conductivity and a circular aperture is considered. Using Kirchhoff's approximation, an expression of the diffracted electric field is derived. This field is computed and plotted by approximating the aperture field as a constant field and as a free plane wave.

Quantum mechanically a screen with infinite extend, finite width, finite conductivity and a cylindrical aperture is considered. We expand Babinet's principle to a screen with finite width and conductivity. The single electron wave functions and energy levels are found using the particle in a box approach. The conductivity tensor is found analytically for $0K$ and is used to calculate the current density numerically. The dyadic Green function is derived in cylindrical coordinates and used to calculate the scattered electric field of the cylinder numerically.