Near-field propagation of vortex beams: Models and computation algorithms

• Published in: Optical memory & neural networks Vol. 23; no. 2; pp. 50 - 73
• Main Authors: Khonina, S. N., Ustinov, A. V., Kovalyov, A. A., Volotovsky, S. G.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2014
• Subjects: Complexity; Computer Science; Information Storage and Retrieval; vortex beam; plane wave expansion; finite-difference time-domain method; Mansuripur modification; Reyleigh-Sommerfeld integral; diffraction on a round aperture
• ISSN: 1060-992X; 1934-7898
• DOI: 10.3103/S1060992X14020027

We have analyzed the diffraction of a plane wave and a vortex beam on a circular micro-aperture in the near field (a few wavelengths away from the source) using different models and computation algorithms: the Reyleigh-Sommerfeld integral, plane wave expansion method, and finite-difference time-domain (FDTD) method. Comparison of the models showed that the plane wave expansion method modified by the Mansuripur matrix allows us to avoid the singularity in the region of high spectral frequencies and take into account all components of the vector field when the incident beam is bounded with an aperture. Comparison of the computation algorithms in respect to accuracy and computation time showed that it is possible to use integral methods even if the distance from the optical element is less than a wavelength. The simulation of the near-field diffraction of a vortex beam on a circular micro-aperture allowed us to discover oscillations of the vortex beam in the central shade area: the size of the light vortex oscillates as the beam propagates and can be much smaller than it is predicted by the paraxial theory. In addition, the expressions obtained for vortex beams show that near the axis the total intensity will not be zero when the order of the vortex is | m | ≤ 2.