Nonparaxial optical vortices and Kummer laser beams

Alexander Alexeevich Kovalev; Viktor V. Kotlyar; Anton G. Nalimov

doi:10.1117/1.OE.52.9.091716

10 April 2013 Nonparaxial optical vortices and Kummer laser beams

Alexander Alexeevich Kovalev, Viktor V. Kotlyar, Anton G. Nalimov

Author Affiliations +

Optical Engineering, Vol. 52, Issue 9, 091716 (April 2013). https://doi.org/10.1117/1.OE.52.9.091716

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.

Citation Download Citation

Alexander Alexeevich Kovalev, Viktor V. Kotlyar, and 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

Published: 10 April 2013

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available