Exact nonparaxial beams of the scalar Helmholtz equation

Details Exact nonparaxial beams of the scalar Helmholtz equation Exact nonparaxial beams of the scalar Helmholtz equation

2003-12-06

arxiv.org/abs/physics/0312040v1

Physics

Optics

8 pages, 3 figures, accepted by Optics Letters

Scientific paper

10.1364/OL.29.000430

It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For the first time, their beam behaviour is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by an hyperbola, the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams is formally stablished. These results are also helpful to investigate the exact vector nonparaxial beams.

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