Measurement of the local intrinsic curvature of a l =1 radio-vortex at 30 GHz

We exploit the properties of differential geometry of minimal surfaces to introduce a novel approach for characterizing wavefronts. Since Gaussian and mean curvatures describe global and local properties of any differentiable surface, a method for characterizing wavefronts endowed with non-trivial topological features has been introduced. We provide experimental evidence that the wavefront of an l = 1 radio-vortex at 30 GHz can be fully characterized by exploiting the wavefront phase in the far field of the source, accessing a small portion of the beam only. A particular care is dedicated to distinguish diffraction effects from the intrinsic curvature of the helicoidal wavefront. Results are applicable to the local measurement of the topological charge and to the local detection of orbital angular momentum radiation at the millimetric wavelengths.