Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel–Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.
© 2012 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: May 3, 2012
Revised Manuscript: June 14, 2012
Manuscript Accepted: June 21, 2012
Published: July 31, 2012
Bin Tang, Chun Jiang, and Haibin Zhu, "Propagation of Bessel–Gaussian beams through a double-apertured fractional Fourier transform optical system," J. Opt. Soc. Am. A 29, 1728-1733 (2012)