Separation of polarization singularities of optical fields generated by multiple point-like sources of light

In this presentation, we will present our study of morphology of polarization singularities of electromagnetic fields generated from interference of point-like optical sources. We identify C-lines, C-planes, L-lines and L-planes for circular (C) and linear (L) polarization of electric and magnetic vector fields. In the far field, electromagnetic gauge invariance requires inclusion of the longitudinal field components near the phase singularity, leading to formation of the singularity doublets.

We investigate spatial separation of electric- and magnetic-type singularities and demonstrate that splitting between them is at the wavelength scale, is propagation-invariant, {\it i.e.} it is protected against diffraction and depends on the topological charge of the singularity. Higher-order effects beyond the paraxial approximation are included in the theory analysis. Theory predictions are illustrated with a numerical analysis.