This function calculates the Ince Gaussian beams 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 laser 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.
For more information about Ince–Gaussian beams:

"Ince-Gaussian beams," Miguel A. Bandres and J. C. Gutierrez-Vega
Optics Letters, 29(2), 144-146 (2004) ( http://goo.gl/U18mol )

"Ince-Gaussian modes of the paraxial wave equation and stable resonators,"
Miguel A. Bandres and Julio C. Gutierez-Vega
Journal of the Optical Society of America A, 21(5), 873-880 (2004) ( http://goo.gl/rqq7nQ )

"Observation of Ince-Gaussian modes in stable resonators,"
Ulrich T. Schwarz, Miguel A. Bandres and Julio C. Gutierrez-Vega
Optics Letters, 29(16), 1870-1872 (2004) ( http://goo.gl/7lkSb4 )

AUTHOR: Miguel A. Bandres ( www.mabandres.com )