Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses

Quantized x-ray phase vortices, namely, screw-type topological defects in the wave fronts of a coherent monochromatic scalar x-ray wave field, may be spontaneously nucleated by x-ray lenses. Phase retrieval is used to reconstruct the phase and amplitude of the complex disturbance created by aberrated gold nanolenses illuminated with hard x rays. A nanoscale quantized x-ray vortex-antivortex dipole is observed, manifest both as a pair of opposite-helicity branch points in the Riemann sheets of the multivalued x-ray phase map of the complex x-ray field and in the vorticity of the associated Poynting vector field