## Propagation of a general-type beam through a truncated fractional Fourier transform optical system

JOSA A, Vol. 27, Issue 3, pp. 637-647 (2010)

http://dx.doi.org/10.1364/JOSAA.27.000637

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### Abstract

Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams—such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams—through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

© 2010 Optical Society of America

**OCIS Codes**

(350.5500) Other areas of optics : Propagation

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

(140.3295) Lasers and laser optics : Laser beam characterization

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: November 24, 2009

Revised Manuscript: January 6, 2010

Manuscript Accepted: January 6, 2010

Published: February 26, 2010

**Citation**

Chengliang Zhao and Yangjian Cai, "Propagation of a general-type beam through a truncated fractional Fourier transform optical system," J. Opt. Soc. Am. A **27**, 637-647 (2010)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-3-637

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