Non-existence of separable spheroidal beams

作者:Boyack Rufus*; Lekner John
来源:Journal of Optics, 2011, 13(8): 085701.
DOI:10.1088/2040-8978/13/8/085701

摘要

We show that psi = R(xi) S(eta) e(im phi), 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 psi in the focal plane, where psi is not a solution of the Helmholtz equation on the disc xi = 0.

  • 出版日期2011-8