## Fractional Fourier transform for an anomalous hollow beam

JOSA A, Vol. 26, Issue 12, pp. 2571-2576 (2009)

http://dx.doi.org/10.1364/JOSAA.26.002571

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### Abstract

Based on the definition of fractional Fourier transform (FRT), the propagation properties of an anomalous hollow beam (AHB) through the FRT have been investigated in detail. An analytical formula is derived for the FRT of an AHB. By using the derived formula, the properties of an AHB in the FRT plane are illustrated numerically. The results show that the properties of an AHB in the FRT plane are closely related to the parameters of the beam and the fractional order *p*. The derived formula provides an effective and convenient way for analyzing and calculating the FRT of an AHB.

© 2009 Optical Society of America

**OCIS Codes**

(140.3300) Lasers and laser optics : Laser beam shaping

(350.5500) Other areas of optics : Propagation

(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: August 4, 2009

Manuscript Accepted: September 25, 2009

Published: November 16, 2009

**Citation**

Kuilong Wang and Chengliang Zhao, "Fractional Fourier transform for an anomalous hollow beam," J. Opt. Soc. Am. A **26**, 2571-2576 (2009)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-12-2571

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