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
Lasers and Laser Optics
Original Manuscript: August 4, 2009
Manuscript Accepted: September 25, 2009
Published: November 16, 2009
Kuilong Wang and Chengliang Zhao, "Fractional Fourier transform for an anomalous hollow beam," J. Opt. Soc. Am. A 26, 2571-2576 (2009)