Abstract

Lorentz–Gauss beams are introduced to describe certain laser sources that produce highly divergent beams. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz–Gauss beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz–Gauss beam passing through an FRFT system has been derived. By using the derived expression, the properties of a Lorentz–Gauss beam in the FRFT plane are graphically illustrated with numerical examples.

© 2009 Optical Society of America

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