In this paper the Laguerre-Gaussian (LG) series representation of the two-dimensional fractional Fourier transform is derived from conventional ordinary Fourier transform in polar coordinates. The kernel of this series representation is constituted by Laguerre-Gaussian functions, from which the series representation of a fractional Hankel transform can be easily derived. The connection between the gradient-index medium and the LG series representation is illustrated as an example of its applications.
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Yu et al. (1998) studied this question.
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