Non-existence of separable spheroidal beams
Boyack, Rufus; Lekner, John; Boyack, Rufus; School of Chemical and Physical Sciences and The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, PO Box 600, Wellington, New Zealand; Lekner, John; School of Chemical and Physical Sciences and The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
Журнал:
Journal of Optics
Дата:
2011-08-01
Аннотация:
We show that ψ = R(ξ)S(η) e<sup>imφ</sup>, a product of radial and angular oblate spheroidal functions and an azimuthal factor, cannot represent physical free-space scalar beams. The reason lies in the discontinuity in the longitudinal derivative of ψ in the focal plane, where ψ is not a solution of the Helmholtz equation on the disc ξ = 0.
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