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Calculation of the intensity at the sharp focus of a cylindrical vector beam by three methods
A.G. Nalimov 1,2, V.V. Kotlyar 1,2, Yu.V. Khanenko 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,

2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1160 kB

DOI: 10.18287/2412-6179-CO-1346

Pages: 734-741.

Full text of article: Russian language.

Abstract:
We conduct a comparative analysis of diffraction fields upon sharply focusing vortex and non-vortex incident beams, calculated using three non-paraxial methods. The methods employed are a finite difference time domain (FDTD) method, a Rayleigh–Sommerfeld integral, and a Richards–Wolf transformation. The Richards–Wolf transformation is used with two apodization functions of the exit pupil, for a spherical lens and a thin diffractive lens. The numerical simulation shows that the Rayleigh–Sommerfeld integral and the Richards–Wolf transformation can produce almost the same result and save time significantly. Meanwhile, the root-mean-square deviation of the results of both methods from the FDTD method can be as low as 2%. If an ultra-short focal length is used, the Richards–Wolf transformation is found to be more accurate, whereas with increasing distance from the initial plane and outside the focal plane, the Rayleigh-Sommerfeld integral is more accurate.

Keywords:
vector beam, sharp focusing, Rayleigh-Sommerfeld integral, Richards-Wolf transformation.

Citation:
Nalimov AG, Kotlyar VV, Khanenko Y.V. Calculation of the intensity at the sharp focus of a cylindrical vector beam by three methods. Computer Optics 2023; 47(5): 734-741. DOI: 10.18287/2412-6179-CO-1346.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant #23-12-00236 (Sections "Numerical simulation", "Discussion") and the RF Ministry of Science and Higher Education within a state contract with the FSRC "Crystallography and Photonics" RAS (Sections "Introduction", "Conclusion").

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