Figure 4. Transition from a trivial to a topologically non-trivial polarization pattern.

In panels a,b we report the experimental and theoretical intensity and polarization distribution of the near field (ζ = 0.01) for both radial and azimuthal VVB, respectively. We observe no polarization singularities (actually, C-points exist in a region where the beam intensity is too low, as shown in Fig. 5) when δ < π/2. At δ = π/2 an undefined number of C-point dipoles appears, in proximity of intersections between the Gaussian and the oscillating HyGG_−1,1 envelopes. When δ is increased, a pair of C-points with η = 1/2 appears in the polarization pattern, with the distance between these points getting smaller as δ → π. The topological charge associated with a path enclosing both singularities is η = 1. Here, red and blue colored ellipses are associated with left (s₃ > 1) and right handed (s₃ < 1) polarization states, respectively.