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Laguerre-Gaussian Modes of Paraxial Wave Equation

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Laguerre–Gaussian modes are solutions of the paraxial wave equation. They have circular symmetry and can be written in terms of the Laguerre polynomials , where is the radial index and is the azimuthal index.

Contributed by: Enrique Zeleny (May 2014)
Open content licensed under CC BY-NC-SA

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The paraxial equation in cylindrical coordinates is given by

.

A simple separable solution can be written in the form

.

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