Abstract
We study the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptic coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded index media. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence between the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation between the three definitions.
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