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Hypergeometric-Gaussian Modes

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Hypergeometric-Gaussian modes are paraxial wave modes with cylindrical symmetry. The complex amplitude involves a confluent hypergeometric function and a gamma function. Such modes are of importance in laser beam optics.

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

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In cylindrical coordinates, the paraxial equation is

,

and its solutions are of the form

.

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