Analytical boundary-based method for diffraction calculations

We present a simple method for calculation of diffraction effects in a beam passing an aperture. It follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities. It is thus shown that in the near-field region, i.e. at short propagation distances, most results depend on values of the beam's field at the aperture's boundaries, making it possible to derive diffraction effects in the form of a simple contour integral over the boundaries. For a uniform, i.e. plane-wave incident beam, the contour integral predicts the diffraction effects exactly. Comparisons of the analytical method and full numerical solutions demonstrate highly accurate agreement between them.