Sharp-edge diffraction under Bessel beam illumination: a catastrophe optics perspective

Boundary diffraction wave theory and catastrophe optics have already proved to be a formidable combination in computational optics. In the present paper, a general paraxial theory aimed at dealing paraxial diffraction of Bessel beams by arbitrarily shaped sharp-edge apertures is developed. A key ingredient of our analysis is the δ-like nature of the angular spectrum of nondiffracting beams. This allows the diffracted wavefield to be effectively represented through two-dimensional integrals defined onto rectangular domains, whose numerical evaluation is easily achievable via standard Monte Carlo techniques. As a byproduct of the present analysis, a simple explanation of a recently observed property of some "heart-like" apertures to flatten the axial intensity of apodized Bessel beams is also provided.