Analytical solutions for beams passing apertures with sharp boundaries. (14th June 2016)

• Record Type: Journal Article
• Authors: Luz, Eitam; Granot, Er'el; Malomed, Boris A
• Is Part Of: Journal of optics. Volume 18:Number 7(2016:Jul.)
• Publication Date: 2016-06-14
• Subjects: diffraction theory -- propagation methods -- optics in computing; Optics -- Periodicals; 535.05
• DOI: 10.1088/2040-8978/18/7/075607
• Languages: English
• ISSNs: 2040-8978

Abstract

Abstract: An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, in terms of the exact analytical solution.