We present the Ince–Gaussian modes that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and that are transverse eigenmodes of stable resonators. The transverse shape of these modes is described by the Ince polynomials and is structurally stable under propagation. Ince–Gaussian modes constitute the exact and continuous transition modes between Laguerre– and Hermite–Gaussian modes. The expansions between the three families are derived and discussed. As with Laguerre–Gaussian modes, it is possible to construct helical Ince–Gaussian modes that exhibit rotating phase features whose intensity pattern is formed by elliptic rings and whose phase rotates elliptically.
© 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 Julio C. Gutiérrez-Vega, "Ince–Gaussian modes of the paraxial wave equation and stable resonators," J. Opt. Soc. Am. A 21, 873-880 (2004)