Propagation of Electromagnetic Helmholtz-Gauss Beams Through Paraxial Optical Systems and Spatial Correlation Vortices

Hdl Handle:
http://hdl.handle.net/11285/572465
Title:
Propagation of Electromagnetic Helmholtz-Gauss Beams Through Paraxial Optical Systems and Spatial Correlation Vortices
Issue Date:
01/05/2008
Abstract:
The propagation of electromagnetic beams through a large variety of optical systems has received much attention during the last two decades. Similar attention has been paid to singular points arising on fields that represent optical beams, also known as optical vortices. This thesis studies the propagation of electromagnetic Helmholtz-Gauss beams through optical systems that can be represented by an ABCD matrix. Closed form expressions for the field distributions are derived, showing that the propagation of these beams can be described by the paraxial transformation of two parameters. Three special cases of ABCD systems are considered, namely a free-space segment, a quadratic index medium, and an unapertured thin lens. A complete characterization of these beams is made by studying their polarization properties and angular spectrum distribution. An important phenomenon known as the focal-shift is studied for the case of vector Mathieu-Gauss beams, and the existence of this shift is confirmed theoretically by means of two methods. All studies previously mentioned are performed assuming highly coherent sources. Partially coherent optical systems are considered as well, but we now look at singularities of the wave function describing the optical beam, which are commonly known as optical vortices. It is shown that partial coherence requires a beam to exhibit Rankine vortex characteristics, in analogy to vortices in fluids. We suggest a method to study the coherence properties of a beam by looking at its cross correlation function. Potential applications of this method are proposed, for instance we introduce a "vortex stellar interferometer" to determine the angular extent of distant objects such as stars, and the measurement of orbital angular momentum content in an optical beam is briefly discussed.
Keywords:
Elecromagnetismo; Generalizadores; Polarizaciones
Degree Program:
Programa de Graduados en Mecatrónica e Información Tecnológicas
Advisors:
Dr. Julio C. Gutiérrez Vega
Committee Member / Sinodal:
Dr. Grover A. Swatzlander; Jr.; Dr. Rodolfo Rodríguez y Masegosa; Dr. Hugo Alarcón Opazo; Dr. Carlos M. Hinojosa Espinosa
Degree Level:
Doctor in Information Technologies and Communications
School:
Escuela de Graduados en Informática y Computación
Campus Program:
Campus Monterrey
Discipline:
Ingeniería y Ciencias Aplicadas / Engineering & Applied Sciences
Appears in Collections:
Ciencias Exactas

Full metadata record

DC FieldValue Language
dc.contributor.advisorDr. Julio C. Gutiérrez Vegaes
dc.creatorHernández Aranda, Raúl I.en
dc.date.accessioned2015-08-17T11:32:54Zen
dc.date.available2015-08-17T11:32:54Zen
dc.date.issued01/05/2008-
dc.identifier.urihttp://hdl.handle.net/11285/572465en
dc.description.abstractThe propagation of electromagnetic beams through a large variety of optical systems has received much attention during the last two decades. Similar attention has been paid to singular points arising on fields that represent optical beams, also known as optical vortices. This thesis studies the propagation of electromagnetic Helmholtz-Gauss beams through optical systems that can be represented by an ABCD matrix. Closed form expressions for the field distributions are derived, showing that the propagation of these beams can be described by the paraxial transformation of two parameters. Three special cases of ABCD systems are considered, namely a free-space segment, a quadratic index medium, and an unapertured thin lens. A complete characterization of these beams is made by studying their polarization properties and angular spectrum distribution. An important phenomenon known as the focal-shift is studied for the case of vector Mathieu-Gauss beams, and the existence of this shift is confirmed theoretically by means of two methods. All studies previously mentioned are performed assuming highly coherent sources. Partially coherent optical systems are considered as well, but we now look at singularities of the wave function describing the optical beam, which are commonly known as optical vortices. It is shown that partial coherence requires a beam to exhibit Rankine vortex characteristics, in analogy to vortices in fluids. We suggest a method to study the coherence properties of a beam by looking at its cross correlation function. Potential applications of this method are proposed, for instance we introduce a "vortex stellar interferometer" to determine the angular extent of distant objects such as stars, and the measurement of orbital angular momentum content in an optical beam is briefly discussed.en
dc.language.isoenen
dc.rightsOpen Accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.titlePropagation of Electromagnetic Helmholtz-Gauss Beams Through Paraxial Optical Systems and Spatial Correlation Vorticesen
dc.typeTesis de Doctoradoes
thesis.degree.grantorInstituto Tecnológico y de Estudios Superiores de Monterreyes
thesis.degree.levelDoctor in Information Technologies and Communicationsen
dc.contributor.committeememberDr. Grover A. Swatzlanderes
dc.contributor.committeememberJr.es
dc.contributor.committeememberDr. Rodolfo Rodríguez y Masegosaes
dc.contributor.committeememberDr. Hugo Alarcón Opazoes
dc.contributor.committeememberDr. Carlos M. Hinojosa Espinosaes
thesis.degree.disciplineEscuela de Graduados en Informática y Computaciónes
thesis.degree.namePrograma de Graduados en Mecatrónica e Información Tecnológicases
dc.subject.keywordElecromagnetismoes
dc.subject.keywordGeneralizadoreses
dc.subject.keywordPolarizacioneses
thesis.degree.programCampus Monterreyes
dc.subject.disciplineIngeniería y Ciencias Aplicadas / Engineering & Applied Scienceses
All Items in REPOSITORIO DEL TECNOLOGICO DE MONTERREY are protected by copyright, with all rights reserved, unless otherwise indicated.