10 April 2013 Nonparaxial optical vortices and Kummer laser beams
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Abstract
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 autofocusing of the HB beams is studied.
© 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)
Alexander Alexeevich Kovalev, Alexander Alexeevich Kovalev, Viktor V. Kotlyar, Viktor V. Kotlyar, Anton G. Nalimov, Anton G. Nalimov, } "Nonparaxial optical vortices and Kummer laser beams," Optical Engineering 52(9), 091716 (10 April 2013). https://doi.org/10.1117/1.OE.52.9.091716 . Submission:
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