Exact paraxial diffraction theory for polygonal apertures under Gaussian illumination

Borghi, Riccardo

doi:10.1364/osac.3.000214

OSA Continuum

2020

DOI: 10.1364/osac.3.000214

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Exact paraxial diffraction theory for polygonal apertures under Gaussian illumination

Riccardo Borghi

Abstract: Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are obtained, as well as an interesting connection between classical optics and probability theory.

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2022

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Cited by 2 publications

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

Borghi

Carosella

2022

J. Opt. Soc. Am. A

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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.

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

Borghi

Carosella

2022

J. Opt. Soc. Am. A

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Paraxial sharp-edge diffraction: a general approach

Borghi¹

2022

Opt. Express

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A general reformulation of classical sharp-edge diffraction theory is proposed within paraxial approximation. The, not so much known, Poincaré vector potential construction is employed directly inside Fresnel’s 2D integral in order for it to be converted into a single 1D contour integral over the aperture boundary. Differently from the recently developed paraxial revisitation of BDW’s theory, such approach should be applicable, in principle, to arbitrary wavefield distributions impinging onto arbitrarily shaped sharp-edge planar apertures. However, in those cases where such a conversion were not analytically achievable, our approach allows Fresnel’s integral to be easily converted, irrespective of the shape and the regularity features of the aperture geometry, into a double integral defined onto a square domain. A couple of interesting examples of application of the proposed method is presented.

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Exact paraxial diffraction theory for polygonal apertures under Gaussian illumination

Cited by 2 publications

References 20 publications

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

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

Paraxial sharp-edge diffraction: a general approach

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