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Cartesian beams

Bandres, Miguel A. and Gutiérrez-Vega, Julio C. (2007) Cartesian beams. Optics Letters, 32 (25). pp. 3459-3461. ISSN 0146-9592.

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A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three 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. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite-Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams.

Item Type:Article
Additional Information:© 2007 Optical Society of America. Received September 12, 2007; revised October 8, 2007; accepted October 17, 2007; posted October 23, 2007 (Doc. ID 87481); published November 29, 2007. We acknowledge support from Consejo Nacional de Ciencia y Tecnología (grant 42808), from the Tecnológico de Monterrey (grant CAT-007), and from the Secretaría de Educación Pública de México.
Subject Keywords:Paraxial wave optics; ABCD transforms; Diffraction theory
Issue or Number:25
Record Number:CaltechAUTHORS:BANol07
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Official Citation:M. A. Bandres and J. C. Gutiérrez-Vega, "Cartesian beams," Opt. Lett. 32, 3459-3461 (2007)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9588
Deposited By: Archive Administrator
Deposited On:11 Feb 2008
Last Modified:03 Oct 2019 00:01

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