It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior 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 a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.
© 2004 Optical Society of America
(000.3860) General : Mathematical methods in physics
(140.3410) Lasers and laser optics : Laser resonators
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation
Gustavo Rodríguez-Morales and Sabino Chávez-Cerda, "Exact nonparaxial beams of the scalar Helmholtz equation," Opt. Lett. 29, 430-432 (2004)