Bandres, Miguel A. and Lopez-Mago, Dorilian and Gutiérrez-Vega, Julio C. (2010) Higher-order moments and overlaps of Cartesian beams. Journal of Optics, 12 (6). Art. No. 065702. ISSN 2040-8978. doi:10.1088/2040-8978/12/6/065702. https://resolver.caltech.edu/CaltechAUTHORS:20100802-151742564
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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.
| Item Type: | Article | |||||||||
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| 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). | |||||||||
| Group: | Caltech Theory | |||||||||
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| Subject Keywords: | Cartesian beams; intensity moments; M-2 factor; kurtosis; Appell; hypergeometric functions | |||||||||
| Issue or Number: | 6 | |||||||||
| Classification Code: | PACS: 42.60.Jf; 42.25.Bs | |||||||||
| DOI: | 10.1088/2040-8978/12/6/065702 | |||||||||
| Record Number: | CaltechAUTHORS:20100802-151742564 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100802-151742564 | |||||||||
| Official Citation: | Miguel A Bandres et al 2010 J. Opt. 12 065702 doi: 10.1088/2040-8978/12/6/065702 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 19249 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 03 Aug 2010 20:39 | |||||||||
| Last Modified: | 08 Nov 2021 23:50 |
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