Geometric analysis of the spiral intensity distribution to determine the order of the vortex phase component

Abstract

This work is dedicated to the geometric analysis of spiral intensity distributions generated by diffractive optical elements with transmission functions that depend nonlinearly on the angular coordinate, including generalized spiral phase plates and spiral-vortex axicons. According to the theoretical model, the intensity distribution forms a spiral with a linearly varying radius and a characteristic discontinuity between its beginning and end. A distinctive property of such fields is the presence of orbital angular momentum (OAM), whose magnitude is related to the difference between the radii of the spiral endpoints.
It is shown that introducing an additional vortex phase component modifies the geometric characteristics of the spiral by changing the endpoint radii and rotating the overall spiral structure. These variations are reflected in the discontinuity angle and depend on both the magnitude and the sign of the vortex topological charge. The revealed relationships make it possible to determine the vortex order directly from measurable geometric features of the spiral intensity distribution.
To automate the analysis, a software tool, was developed. The algorithm processes radial profiles extracted in 720 directions from the image center and determines the coordinates of the spiral endpoints, the radius difference, the discontinuity angle, and the slit-center angular direction. The extracted features are divided into orientation-invariant and orientation-sensitive groups. Pairwise comparison and similarity matrix construction provide the basis for automatic classification of spiral intensity distributions and reliable determination of the vortex phase order.

Speaker

Dmitry
Samara National Research University
Russia

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