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Generalized Ince Gaussian beams

Bandres, Miguel A. and Gutiérrez-Vega, Julio C. (2006) Generalized Ince Gaussian beams. In: Laser Beam Shaping VII. Proceedings of SPIE. No.6290. Society of Photo-Optical Instrumentation Engineers (SPIE) , Bellingham, WA, Art. No. 62900S. ISBN 9780819463692. https://resolver.caltech.edu/CaltechAUTHORS:20191106-141757099

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Abstract

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1117/12.681505DOIArticle
ORCID:
AuthorORCID
Bandres, Miguel A.0000-0002-7145-8567
Additional Information:© 2006 Society of Photo-Optical Instrumentation Engineers (SPIE). This research was supported by Tecnológico de Monterrey (grant CAT-007) and by Consejo Nacional de Ciencia y Tecnología (grant 42808). M. A. Bandres acknowledge support from Secretaría de Educación Pública de México.
Funders:
Funding AgencyGrant Number
Tecnológico de MonterreyCAT-007
Consejo Nacional de Ciencia y Tecnología (CONACYT)42808
Secretaría de Educación Pública de MéxicoUNSPECIFIED
Subject Keywords:Gaussian beams, Ince—Gaussian, Laguerre—Gaussian, Hermite—Gaussian, Paraxial wave equation
Series Name:Proceedings of SPIE
Issue or Number:6290
Record Number:CaltechAUTHORS:20191106-141757099
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191106-141757099
Official Citation:Miguel A. Bandres and Julio C. Gutiérrez-Vega "Generalized Ince Gaussian beams", Proc. SPIE 6290, Laser Beam Shaping VII, 62900S (9 September 2006); https://doi.org/10.1117/12.681505
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99705
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2019 22:31
Last Modified:06 Nov 2019 22:31

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