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Geometrical representations of structured light: from paraxial to electromagnetic

URL to cite or link to: http://hdl.handle.net/1802/35243

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Thesis (Ph. D.)--University of Rochester. The Institute of Optics, 2019.
The term “structured light” is used to refer to light having nontrivial and interesting intensity, phase and/or polarization distributions. This concept has been at the center of research efforts ranging from quantum optics to biophysics. It is therefore important to propose theoretical models that highlight the main properties of such fields, e. g. their angular spread, polarization structure and orbital angular momentum content, to facilitate their understanding as well as their design. Throughout this thesis, several geometrical models are used to study structured light, from the paraxial scalar to the nonparaxial electromagnetic regimes. These models provide us with abstract spaces in which optical fields can be represented in an intuitive way. We start by studying self-similar structured-Gaussian (SG) beams through operator and ray-based formalisms. These two complementary approaches lead to distinct geometrical representations on the modal Poincaré sphere (MPS): the operator formalism leads to the Majorana constellation, which represents an SG beam by a collection of points on the surface of the MPS; while ray theory uses the Poincaré path, a curve on the surface of the MPS, to determine the rays that conform the same SG beam. Both representations provide information about the angular momentum content and invariances to specific astigmatic transformations through their rotational symmetries, which can lead to continuous or discrete geometric phases. Nonparaxial fields are then described in terms of their plane-wave amplitude representation providing us with an intuitive space, the sphere of directions, in which the polarization and directional spread of the field can be easily visualized. This space is ideal for introducing the concept of complex-focus fields and several complete bases that can be constructed from them. These exact solutions to the wave equation are well suited to describe highly focused fields, due to their controllable degree of focusing and similarity with fields used in experimental settings. Moreover, their Lorenz-Mie scattering by a spherical particle can be calculated analytically. This, in turn, provides us with a simple framework to compute the forces and torques exerted on the scattering particle. This work contributes towards deepening our understanding of structured light and its many interesting properties. What is more, the geometrical representations presented here allow us highlight analogies of these optical fields with other physical systems, clearly showing the reach of the results presented.
Contributor(s):
Rodrigo Gutierrez-Cuevas - Author

Miguel A. Alonso - Thesis Advisor

Primary Item Type:
Thesis
Identifiers:
LC Call No. AS38.6635
Language:
English
Sponsor - Description:
National Science Foundation (NSF) - PHY-1203931; PHY-1505189; PHY-1507278
CONACYT -
First presented to the public:
8/27/2019
Originally created:
2019
Original Publication Date:
2019
Previously Published By:
University of Rochester
Place Of Publication:
Rochester, N.Y.
Citation:
Extents:
Illustrations - illustrations (some color)
Number of Pages - xxix, 251 pages
License Grantor / Date Granted:
Angela Grunzweig / 2019-08-27 15:11:32.707 ( View License )
Date Deposited
2019-08-27 15:11:32.707
Submitter:
Angela Grunzweig

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