Vector Beams for Fundamental Physics and Applications

Lights salient degrees of freedom are the independent parameters that completely de- scribe an electromagnetic wave (in the paraxial approximation) and include polarization, wavelength, and time. Most recently, lights space degree of freedom has received sig- nificant attention via the sub-discipline of optics that can be referred to as complex light or structured light. The study of complex light is a veritable renaissance of optics; us- ing lights space degree of freedom many classical optics phenomena have been revisited with novel results. In this thesis, a novel form of structured light referred to as vector beams will be investigated. It will be shown that vector beams have properties very much connected to fundamental physical phenomena. In Chapters 1 and 2, it will be shown that Laguerre-Gaussian modes and cylindrical vector beams are inherently connected. The con- nection can be illustrated by their representation on what is referred to as a higher-order Poincare sphere. In analogy to the representation of linear and circular polarizations on the well-known Poincare sphere, on the higher-order Poincare sphere, radially and azimuthally polarized cylindrical vector beams are represented by points on the equator, and orthogonal circularly polarized Laguerre-Gaussian modes whose azimuthally varying phases have op- posite handedness are represented by North and South poles. In Chapter 3, it will be shown that vector beam can be generated using an optical element referred to as a q-plate inside. Using the q-plate, any state of polarization on the well-known Poincare sphere could be converted into any Laguerre-Gaussian mode or cylindrical vector beam on the higher-order Poincare sphere, effectively breaking the spatial modes degeneracy. In chapters 4 and 5, it will be shown that vector beams can be used for optical communication, i.e., they can be used to encode or carry that information. The transmitted vector beams’ spatial patterns must not change as they propagate so that the information they encode or carry can be re- ceived with minimal error. Equally important, solutions to the paraxial Helmholtz wave equation make up a complete and orthogonal set. As solutions to the paraxial Helmholtz wave equation, with regard to optical communication, the complete and orthogonal set of vector beams can be used as an ”N” dimensional state space with which to encode data, or as N channels to carry information. In chapter 6, it will be shown that vector Bessel beams can be generated by combining liquid crystal q-plates with ”Durnin’s” ring method. Similar to scalar Bessel beams, it will be shown that the spatially inhomogeneous states of polarization of vector Bessel beams can self-heal after they are obstructed. The polarization of vector Bessel beams was measured using Stokes polarimetry before and after they were obstructed. It will be experimentally verified that their spatially inhomogeneous states of polarization can self-heal