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Published June 2010 | Published
Journal Article Open

Higher-order moments and overlaps of Cartesian beams

Abstract

We introduce a closed-form expression for the overlap between two different Cartesian beams. In the course of obtaining this expression, we establish a linear relation between the overlap of circular beams with azimuthal symmetry and the overlap of Cartesian beams such that the knowledge of the former allows the latter to be calculated very easily. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M2 factors, the kurtosis parameters, the expansion coefficients of Cartesian beams, and therefore of all their relevant special cases, including the standard, elegant, and generalized Hermite–Gaussian beams, cosh-Gaussian beams, Lorentz beams, and Airy beams, among others.

Additional Information

© 2010 IOP Publishing Ltd. Received 4 February 2010, accepted for publication 19 April 2010. Published 28 May 2010. We acknowledge support from Consejo Nacional de Ciencia y Tecnología (grant 82407) and from the Tecnológico de Monterrey (grant CAT-141).

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August 22, 2023
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