Generalized Ince Gaussian beams

Miguel A. Bandres; Julio C. Gutiérrez-Vega

doi:10.1117/12.681505

9 September 2006 Generalized Ince Gaussian beams

Miguel A. Bandres, Julio C. Gutiérrez-Vega

Proceedings Volume 6290, Laser Beam Shaping VII; 62900S (2006) https://doi.org/10.1117/12.681505
Event: SPIE Optics + Photonics, 2006, San Diego, California, United States

Abstract

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Citation Download Citation

Miguel A. Bandres and Julio C. Gutiérrez-Vega "Generalized Ince Gaussian beams", Proc. SPIE 6290, Laser Beam Shaping VII, 62900S (9 September 2006); https://doi.org/10.1117/12.681505

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