Abstract

The oblate spheroidal wavefunctions proposed by Rodríguez-Morales and Chávez-Cerda are shown to be possible representations of physical beams only when the angular function Smn(β,η) has odd nm. This condition makes Smn odd in η, which ensures the convergence of integrals of physical quantities over a cross section of the beam. The odd nm condition also makes Smn(β,η) zero in the focal plane z=0 outside the circle ρ=b, and thus allows for the physically necessary discontinuity in phase at z=0 on the ellipsoidal surfaces of otherwise constant phase. Only a subset of the oblate spheroidal functions can be exact representations of nonparaxial scalar beams.

© 2010 Optical Society of America

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