The angular momentum of light originates from two sources: one is the spin angular momentum (SAM) of individual photons, which is related to the polarization of light and the other is the orbital angular momentum (OAM) associated with helical wavefront of the light if it is helically phased (complex phase front). A beam of light that is composed of photons possessing both OAM and SAM states can be used in different areas of study such as rotating microscopic particles, interacting with nonlinear materials, investigating atom-light interactions, communication and medical imaging technologies, quantum information and quantum entanglement. In this dissertation we study coherent beams that convey photons in superposition states of polarization and complex phase front. Our study includes two fields: (I)~classical wave-like behavior with visible light in the field of singular optics. (II)~quantum particle-like behavior of photons of light in the field of quantum-entangled optics. The approach is to investigate the state of such photons both mathematically and experimentally in classical-singular and quantum-entangled fields.

We discuss seven projects based on this research. In one project we present a new method to encode OAM modes into perpendicular polarization components and making superpositions of polarization and spatial modes mapped to the Poincare sphere. In another project using spatial light modulators (SLM) we realized high-order disclination patterns in the polarization map of the cross section of the beam. We also realize new forms of polarization disclination patterns (line patterns where rotational invariance is violated) known as monstars that were not previously seen. We proposed a new definition for characterizing these patterns since they can have zero or negative singularity index. In another project, instead of SLM we used q-plates to generate new forms of monstars. We proposed a robust and easy method for determining the topological charge of a complex phase front beam by inspecting the interference pattern of the beam reflected from a wedged optical flat. In another project we encoded OAM modes onto orthogonal polarization components of a photon from an entangled pair and investigated the quantum entanglement. We also prepared a polarization entangled state and calculated some measures of entanglement. We summarize the projects and discuss the future prospects.