Abstract
Polarization singularities are superpositions of orbital angular momentum (OAM) states in orthogonal circular polarization basis. The intrinsic OAM of light beams arises due to the helical wavefronts of phase singularities. In phase singularities, circulating phase gradients and, in polarization singularities, circulatingϕ12Stokes phase gradients are present. At the phase and polarization singularities, undefined quantities are the phase andϕ12Stokes phase, respectively. Conversion of circulating phase gradient into circulating Stokes phase gradient reveals the connection between phase (scalar) and polarization (vector) singularities. We demonstrate this by theoretically and experimentally generating polarization singularities using phase singularities. Furthermore, the relation between scalar fields and Stokes fields and the singularities in each of them is discussed. This paper is written as a tutorial-cum-review-type article keeping in mind the beginners and researchers in other areas, yet many of the concepts are given novel explanations by adopting different approaches from the available literature on this subject.
Highlights
A singular point is characterized by an undefined physical parameter surrounded by a region of high gradient [1,2,3]
In the neighbourhood of a polarization singularity, the Stokes phase φ12 has values ranging from 0 to 2πσ12 [8, 9], where σ12 is the Stokes polarization singularity index. e phase gradient in a phase singularity and azimuth gradient in a polarization singularity circulate around the respective singularities. e phase and azimuth contours emanate from a phase and a polarization singularity, respectively
Collimated He-Ne laser light illuminates a polarizer at 45°. e light coming from the polarizer is split into two arms by a polarizing beam splitter (PBS)
Summary
A singular point is characterized by an undefined physical parameter surrounded by a region of high gradient [1,2,3]. At a phase singularity, the phase and, at a polarization singularity, the polarization parameter azimuth is undefined. At the immediate neighborhood of a phase singularity, all phase values ranging from 0 to 2πm are present [11, 12], where m is the topological charge. E phase and azimuth contours emanate from a phase and a polarization singularity, respectively. 2. Phase Singularity e complex field of a phase singular beam is of the form given as follows: U (x, y) f(r)expiφ f(r)exp{imθ},. E phase distribution φ is given by azimuthally varying function mθ, where θ is the polar angle. Among the various detection methods of phase singular beams, interferometric [78, 79] and diffractive [80, 81] methods are commonly used due to their simplicity
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