Browsing by Subject "Eigenfunctions"

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    A class of impulsive eigenfunctions of multidimensional Fourier transform
    (2024) Onural, Levent
    The coordinate axes of ${\mathbb {R}}^{N}$ are arbitrarily partitioned into two sets; each set defines a hyperplane passing through the origin and these two hyperplanes are orthogonal. After a review of impulse functions over such hyperplanes and their Fourier transforms, it is shown that an impulse function over the union of these two hyperplanes is an eigenfunction of the $N$-dimensional Fourier transform. Furthermore, based on the simple rotation property of the Fourier transform, it is also shown that impulse functions over unions of finite number of arbitrarily rotated versions of those two hyperplane sets are also eigenfunctions of the $N$-dimensional Fourier transform.
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    ItemOpen Access
    Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators
    (Optical Society of America, 1994) Özaktaş, Haldun M.; Mendlovic, D.
    The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting the fractional Fourier transform as a mathematical tool in analyzing such systems.