The existence of elegant Ince–Gaussian beams that constitute a third complete family of exact and biorthogonal elegant solutions of the paraxial wave equation is demonstrated. Their transverse structure is described by Ince polynomials with a complex argument. Elegant Ince–Gaussian beams constitute exact and continuous transition modes between elegant Laguerre–Gaussian and elegant Hermite–Gaussian beams. The expansion formulas among the three elegant families are derived.
© 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, "Elegant Ince-Gaussian beams," Opt. Lett. 29, 1724-1726 (2004)