Propagation of four-petal Gaussian beams in apertured fractional Fourier transforming systems

Abstract

Based on the Collins diffraction integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation of a four-petal Gaussian beam passing through an apertured fractional Fourier transform (FRFT) optical system has been studied in detail. Some typical numerical examples are given to illustrate the properties of the four-petal Gaussian beam in the FRFT plane. The results indicate that the intensity distributions of the beam in the FRFT plane are closely related to not only the fractional order but also the beam parameters and the aperture parameters.

Keywords:

• four-petal Gaussian beam
• fractional Fourier transform
• aperture
• propagation

Acknowledgements

This work was supported by Scientific Fund of Jiangsu Polytechnic University (Grant No. ZMF08020014) and Scientific Research Fund of Jiangsu Provincial Education Department (Grant No. 08KJD140007).