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 has odd . This condition makes odd in η, which ensures the convergence of integrals of physical quantities over a cross section of the beam. The odd condition also makes zero in the focal plane outside the circle , and thus allows for the physically necessary discontinuity in phase at 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
Equations on this page are rendered with MathJax. Learn more.