Figure 5: Theoretical analysis of the pseudospin-mediated vortex generation.

(a,b) Pseudospin-mediated vortex generation calculated directly from the Dirac equation. When only one of the spinor components ψ_A (ψ_B) is given an initial Gaussian-modulated excitation, the output intensity at z=30 is identical (top panel of a) but the corresponding phase is different. The left (right) bottom panel of a shows the vortex phase of ψ_B (ψ_A), whereas the other component has uniform phase. Comparison between results from numerical solution (dark) and asymptotic calculation is shown in b. (c–h) Intensity and phase of the output optical field obtained from numerical simulation of the paraxial model with a graphene-type HCL potential based on decomposing the optical field into its spinor components. In the top (bottom) row, only sublattice A (B) is initially excited with a Gaussian modulation, which leads to similar intensity patterns (c, f) but opposite phase structures. The second column (d,g) shows the interferograms of the wavefunction Ψ_A and the third column (e,h) shows the corresponding interferograms of Ψ_B. These components Ψ_A and Ψ_B are derived by restricting the paraxial wavefuction Ψ to the discrete locations that are determined by the lattice elements A and B (see the relevant discussion in the text and Supplementary Information section). When the eigenstate of the lattice spin corresponding to A (B) is initially excited, a vortex is generated in the sublattice B (A) with a topological charge +1 (−1), respectively. For illustration purposes, we crop the area outside a disk that consists almost solely of the irrelevant plane-wave contribution.