Ciencias Exactas y Ciencias de la Salud

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Experimental characterization of vector Parabolic-Gauss beams
(Instituto Tecnológico y de Estudios Superiores de Monterrey, 2024-12) Ramírez Ríos, Diego Armando; Hernández Aranda. Raúl Ignacio; emipsanchez; Yepiz Escalante, Adad; Gutiérrez Vega, Julio César; School of Engineering and Sciences; Campus Monterrey; Pérez García Benjamín Jesús de
The theoretical and experimental study of optical beams that satisfy Helmholtz equation un der the paraxial regime is a relatively recent field in Optics and Photonics. Assuming quasi parallel propagation of a beam along a longitudinal axis, transversal planes of it can be mathe matically stated, which, embedded to a Gaussian apodization, are known as Helmholtz-Gauss (HzG) beams. Scalar orthogonal families of solutions of HzG beams such as Mathieu-Gauss, Bessel-Gauss, Parabolic-Gauss (PG), have been thoroughly studied trough numerical and ex perimental generation. Nonetheless, the Helmholtz equation admits vector solutions con structed from scalar HzG beams. Such vector HzG beams present electrical polarization dependent of the transversal locality, so that every point in the xy plane manifests its own polarization state. In this dissertation, motivated by the absence of report of experimental
Novel polarimetric techniques enabled by the geometric phase
(Instituto Tecnológico y de Estudios Superiores de Monterrey, 2020-12) Garza Soto, Luis Alejandro; López Mago, Dorilian; 262725; López Mago, Dorilián; puemcuervo; Gutiérrez Vega, Julio César; Hagen, Nathan; Engineering; Campus Monterrey
Polarimetry consists on being able to predict the state of polarization of a beam of light or the parameters that characterize the polarization properties of a material. In this thesis I propose two new polarimetric techniques that specifically aim at characterizing a material. The first one is based in a relationship between visibility and the geometric phase acquired by a polarized light beam after traversing the material. The second one uses structured light to perform multiple experiments simultaneously and determines through intensity measurements properties of the associated Jones matrix: eigenpolarizations and retardance. The document is divided in 5 chapters. Chapter 1 presents an introduction to my research and the motivation behind it. Chapter 2 is a review of the theoretical framework in which our research takes place. In this chapter we explain basic principles of polarization, interference, visibility, geometric phase, and structured light. We offer a brief explanation that is focused on helping the reader understand the foundations of the derivations and experiments that are presented as a novelty in this thesis. Chapter 3 is titled "Visibility and its relation to geometric phase". In this chapter I try to explain how I started getting hints of the relationship between these physical quantities. The chapter then leads us to the derivation of an expression that relates visibility of fringes and geometric phase. The proof-of-concept experiments to confirm this relationship are described and we present results that validate our claims. Chapter 4 explains all the details about a technique that finds the optical properties of a material through the interference of Full Poincare beams. For this chapter I offer an explanation on the equations that help us understand the technique and then I present a simulation to show how the technique would work. Experimental confirmation of this technique is challenging and this lead me to presenting results based on the simulation only. Regardless, if this technique is seem as interesting then we would expect to be able to work on it experimentally in the future. Chapter 5 is the final chapter of this thesis and I present my conclusions.

Ciencias Exactas y Ciencias de la Salud

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