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Topological singularities (TSs) in momentum space give rise to intriguingfundamental phenomena as well as unusual material properties, attracting agreat deal of interest in the past decade. Recently, we have demonstrateduniversal momentum-to-real-space mapping of TSs and pseudospin angular momentumconversion using photonic honeycomb (graphene-like) and Lieb lattices. Suchmapping arises from the Berry phase encircling the Dirac or Dirac-like cones,and is thus of topological origin. In this paper, we briefly present previousobservations of topological charge conversion, and then we present our firsttheoretical analysis and experimental demonstration of TS mapping in a newT-graphene lattice. Unlike other lattices, there are two coexisting butdistinct TSs located at different high-symmetry points in the first Brillouinzone of T-graphene, which enables controlled topological charge conversion inthe same lattice. We show active manipulation of the TS mapping, turning thetwo TSs into vortices of different helicities, or one into a high-order vortexbut the other into a quadrupole. Such TS manipulation and pseudospin-to-orbitalconversion may find applications in optical communications and quantuminformation, and may bring insight into the study of other Dirac-likestructures with multiple TSs beyond the 2D photonic platform.

Mapping and manipulation of topological singularities: from photonic graphene to T-graphene