Free-space diffraction and the fractional Fourier transform

Author: Sheppard C. J. R.  

Publisher: Taylor & Francis Ltd

ISSN: 1362-3044

Source: Journal of Modern Optics, Vol.45, Iss.10, 1998-01, pp. : 2097-2103

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Abstract

An explicit expression is derived for free-space propagation in terms of the fractional Fourier transform. The expression contains two arbitrary parameters, which can be, for example, an original phase curvature together with a scaling parameter or, alternatively, the order of fractional transformation. Appropriate choice of these parameters is discussed. This approach is then applied to the free-space propagation of Gaussian beams.