Nonparaxial optical vortices and Kummer laser beams

作者：Kovalev Alexey A^*; Kotlyar Victor V; Nalimov Anton G

来源：Optical Engineering, 2013, 52(9): 091716.

DOI：10.1117/1.OE.52.9.091716

• refractive spiral phase plate
• optical vortex
• thin element
• microrelief
• Huygens-Fresnel's principle
• nonparaxial propagation
• Helmholtz equation
• Kummer's function

Two approaches to describe nonparaxial optical vortices were considered. One approach is to use a revised Kirchhoff integral, which does not neglect the relief of an optical element. Using this integral and the finite-difference time-domain method it is shown that an optical vortex generated by a refractive spiral plate with a relief step has an asymmetric profile. The annular diffraction pattern in the vortex beam cross-section is found to be disturbed not only for the near-field diffraction but also for the middle-field diffraction, at a distance of several Fresnel lengths. Another approach is to solve the Helmholtz equation without any approximations. An analytical solution to describe propagation of a light beam in the positive direction of the optical axis was found. The complex amplitude of such a beam is found to be in direct proportion to the product of two linearly independent solutions of Kummer's differential equation. Relationships for a particular case of such beams-namely, the Hankel-Bessel (HB) beams-are deduced. The auto-focusing of the HB beams is studied.

• 出版日期2013-9