Study of caustics in the diffraction of a plane laser beam by a slit in form of a prescribed curve

Abstract

A study of Fresnel diffraction of a plane laser beam by slit apertures in the form of curves described using the Gillis transformation was carried out. Circular, elliptical and others geometries are considered to analyze the influence of curve shape and curvature distribution on the resulting diffraction pattern. For the investigated curves, analytical expressions for the evolutes were obtained by calculating derivatives of the parametric equations. The Gillis transformation was used as a universal method for defining smooth curves with controllable geometric characteristics, allowing variation of the size of individual lobes, and the order of rotational symmetry of the aperture. Numerical simulation of diffracted optical field propagation was performed using the Fresnel transform, which is based on the Fourier transform and enables the investigation of diffraction pattern formation in the near field, as well as the analysis of intensity and amplitude distributions at different propagation distances. It is shown that the intensity distribution of the generated field, bright regions (optical caustics), and their envelopes is related both to the geometry of the prescribed curve and to its evolute. It was established that curvature distribution features influence the localization of intensity maxima and the spatial structure of the diffraction field in both the near and far diffraction zones. Although the global symmetry of the field is preserved for each geometry, noticeable differences arise in peripheral regions and in the spatial modulation of intensity. The obtained results may be useful for controlled beam shaping applied in optical capture and manipulation of microparticles.

Speaker

Lyubov Dubman
Samara University, Samara
Russia

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