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Reverse canonical energy flux near the initial plane of a non-paraxial 2D sinc-beam
V.V. Kotlyar1,2, A.A. Kovalev1,2, A.G. Nalimov1,2, A.M. Telegin1,2

1Image Processing Systems Institute, NRC "Kurchatov Institute", Molodogvardeyskaya 151, Samara, 443001, Russia;
2Samara National Research University, Moskovskoye Shosse 34, Samara, 443086, Russia

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DOI: 10.18287/COJ1752

Article ID: 1752

Language: Russian

Abstract:
In this paper, several 2D non-paraxial light fields near the initial plane (including a sinc beam, Gaussian beam and Hankel beam) are considered. These TE-polarized beams are shown theoretically and numerically to have a reverse canonical energy flux in the initial plane. The negative value of the longitudinal projection of the canonical flux vector means that the longitudinal derivative of the phase is negative, and hence the local wave vector is directed against the positive direction of the optical axis. The reverse flux occurs in the presence of evanescent waves. Although the evanescent waves themselves traveling along the initial plane do not transfer energy along the optical axis perpendicular to the initial plane, they nonetheless participate in the formation of the reverse flux. Near the initial plane, the amplitude of the light field consists of a linear combination of amplitudes of the propagating and evanescent waves. Therefore, the evanescent waves participate in the formation of the phase function of the amplitude of the entire field and affect the sign of the longitudinal phase derivative. For a sinc-beam, the backflow occurs in the first intensity side lobes, where the standing evanescent wave has odd-numbered antinodes.

Keywords:
linear polarization, sinc-beam, Hankel beam, reverse energy flux.

Acknowledgements:
The work was partly funded by the Russian Science Foundation under grant #26-12-00117 (theoretical part) and NRC "Kurchatov Institute" under a government project (numerical simulation).

Citation:
Kotlyar VV, Kovalev AA, Nalimov AG, Telegin AM. Reverse canonical energy flux near the initial plane of a non-paraxial 2D sinc-beam. Computer Optics 2026; 50(4): 1752. doi: 10.18287/COJ1752.

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