Angular momentum switching and orthogonal field construction of C-points.

In this Letter, we take on the non-trivial problem of transforming a C-point singularity into its orthogonal state by switching its angular momentum components. For homogeneous distribution, orthogonal transformation is a trivial operation using a single half-wave plate. For C-point singularity, this entails a change in the handedness without disturbing the index, followed by rotation of the state of polarizations in the distribution. Swapping the spin angular momentum (SAM) components of C-point singularities leads to index and handedness inversion, whereas, switching of orbital angular momentum (OAM) components results only in handedness inversion. By changing the SAM and OAM components in sequence, a C-point can be transformed into its orthogonal state. While experimentally demonstrating this, a spiral phase plate, which is a phase element, is shown to perform polarization transformation operation.

Edge enhancement by negative Poincare-Hopf index filters.

Phase and polarization are interrelated quantities, and hence polarization elements that perform like phase elements can be designed. In this Letter, we show that a polarizing element producing a negative Poincare-Hopf (PH) index beam can be used as a spatial filter to perform edge enhancement. Either isotropic or anisotropic edge enhancement can be achieved by polarization selection of the light that illuminates the sample. A conventional microscope imaging system is modified into a polarization-selective optical Fourier processor. Experimental results are presented to show that negative PH index filters, producing a set of orthogonal polarization distribution and their superpositions, can also be used for edge enhancement in optical signal processing.

Probing the degenerate states of V-point singularities.

V-points are polarization singularities in spatially varying linearly polarized optical fields and are characterized by the Poincare-Hopf index η. Each V-point singularity is a superposition of two oppositely signed orbital angular momentum states in two orthogonal spin angular momentum states. Hence, a V-point singularity has zero net angular momentum. V-points with given |η| have the same (amplitude) intensity distribution but have four degenerate polarization distributions. Each of these four degenerate states also produce identical diffraction patterns. Hence to distinguish these degenerate states experimentally, we present in this Letter a method involving a combination of polarization transformation and diffraction. This method also shows the possibility of using polarization singularities in place of phase singularities in optical communication and quantum information processing.

Diffraction of V-point singularities through triangular apertures.

In this paper we present experimental studies on diffraction of V-point singularities through equilateral and isosceles right triangular apertures. When V-point index, also called Poincare-Hopf index (η), of the optical field is +1, the diffraction disintegrates it into two monstars/lemons. When V-point index η is -1, diffraction produces two stars. The diffraction pattern, unlike phase singularity, is insensitive to polarity of the polarization singularity and the intensity pattern remains invariant. Higher order V-point singularities are generated using Sagnac interferometer and it is observed that the diffraction disintegrates them into lower order C-points.