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Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping
L.L. Doskolovich 1,2, A.A. Mingazov 1,2, E.V. Byzov 1,2, D.A. Bykov 1,2, E.A. Bezus 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 3324 kB

DOI: 10.18287/2412-6179-CO-1029

Pages: 173-183.

Full text of article: Russian language.

Abstract:
We develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a problem of the maximization of a concave function. For finding the solution to the latter problem, a gradient method is used, with analytical expressions obtained for the gradient. Using the developed method, we calculate an eikonal function that provides the formation of a “discontinuous” hexagram-shaped irradiance distribution. We demonstrate that the use of the solution obtained in the framework of the geometrical optics as an initial approximation in iterative Fourier transform algorithms allows one to calculate diffractive optical elements having a quasi-regular microrelief.

Keywords:
geometrical optics, inverse problem, eikonal, diffractive optical element, Fresnel approximation, Gerchberg-Saxton algorithm.

Citation:
Doskolovich LL, Mingazov AA, Byzov EV, Bykov DA, Bezus EA. Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping. Computer Optics 2022; 46(2): 173-183. DOI: 10.18287/2412-6179-CO-1029.

Acknowledgements:
The development of the gradient method and the design of the geometrical-optics phase function was funded by Russian Science Foundation under project 18-19-00326, the design of DOEs in the framework of the scalar diffraction theory was funded by Russian Federation Ministry of Science and Higher Education (State contract with the “Crystallography and Photonics” Research Center of the RAS under agreement 007-GZ/Ch3363/26), and the development of the software implementing the iterative Fourier transform algorithms was funded by Russian Federation Ministry of Science and Higher Education in the framework of the research performed by the laboratory "Photonics for a smart home and smart city" (State contract with the Samara University) (project FSSS-2021-0016).

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