Bandres, Miguel A. and Gutiérrez-Vega, Julio C. (2008) Elliptical beams. Optics Express, 16 (25). pp. 21087-21092. ISSN 1094-4087. doi:10.1364/OE.16.021087. https://resolver.caltech.edu/CaltechAUTHORS:BANoe08
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Abstract
A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others.
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| Additional Information: | © 2008 Optical Society of America. Received 29 Oct 2008; revised 27 Nov 2008; accepted 2 Dec 2008; published 4 Dec 2008. We acknowledge support from Tecnológico de Monterrey (grant CAT141), from Consejo Nacional de Ciencia y Tecnología (grant 82407), and from the Secretaría de Educación Pública de México. | |||||||||
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| Subject Keywords: | INCE-GAUSSIAN MODES; STABLE RESONATORS; GENERATION; LASERS; EQUATION. | |||||||||
| Issue or Number: | 25 | |||||||||
| Classification Code: | OCIS Codes: (050.1940) Diffraction and gratings: Diffraction; (260.1960) Physical optics : Diffraction theory ; (350.5500) Other areas of optics : Propagation | |||||||||
| DOI: | 10.1364/OE.16.021087 | |||||||||
| Record Number: | CaltechAUTHORS:BANoe08 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:BANoe08 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 13806 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 15 Jul 2009 22:36 | |||||||||
| Last Modified: | 08 Nov 2021 22:40 |
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