We demonstrate the existence of the Ince–Gaussian beams that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation. Their transverse structure is described by the Ince polynomials and has an inherent elliptical symmetry. Ince–Gaussian beams constitute the exact and continuous transition modes between Laguerre and Hermite–Gaussian beams. The propagating characteristics are discussed as well.
© 2004 Optical Society of America
(050.1960) Diffraction and gratings : Diffraction theory
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3410) Lasers and laser optics : Laser resonators
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation
Miguel A. Bandres and JulioC. Gutiérrez-Vega, "Ince Gaussian beams," Opt. Lett. 29, 144-146 (2004)