Exact paraxial diffraction theory for polygonal apertures under Gaussian illumination

Abstract

Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the recently proposed paraxial boundary diffraction wave theory framework [J. Opt. Soc. Am. A 36, 1048 (2019)10.1364/JOSAA.36.001048)]. Surprisingly enough, exact closed-form expressions of the diffracted wavefield can be obtained by using only elementary calculus and Euclidean geometry. An interesting connection between paraxial optics and probability theory is also outlined.