Analytical boundary-based method for diffraction calculations

  Eitam Luz  ,  Er'el Granot  ,  Boris Malomed  
Bar Ilan University
Tel -Aviv University
Ariel University

We present a 1D contour integral based method for diffraction calculations of 2D optical beams passing 2D apertures. It follows Miyamoto and Wolf's well-known approach but is more straightforward and does not lead to singularities. First, we present an exact (in the paraxial approximation) 1D contour-integral-based solution for the diffraction of a uniform, i.e., plane-wave incident beam, through any 2D apertured shape. Then, we use that solution to derive a simple short-distance (near field) approximation for the propagation of any 2D beam profile (when the beam's field is distributed non-uniformly across the aperture). It is thus shown that at short propagation distances, most results depend on values of the beam's field at the aperture's boundaries rather than the entire beam profile. These findings may replace heavy calculations with a simpler one and are relevant to other fields that obey the Schrodinger-like equation. Comparisons of the analytical method and full numerical solutions demonstrate highly accurate agreement between them.