Phase Singularities to Polarization Singularities

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, circulating <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msub><a:mrow><a:mi>ϕ</a:mi></a:mrow><a:mrow><a:mn>12</a:mn></a:mrow></a:msub></a:math> Stokes phase gradients are present. At the phase and polarization singularities, undefined quantities are the phase and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:msub><c:mrow><c:mi>ϕ</c:mi></c:mrow><c:mrow><c:mn>12</c:mn></c:mrow></c:msub></c:math> Stokes 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.