Vortex, the winding of a vector field in two dimensions, has its core the
field singularity and its topological charge defined by the quantized winding
angle of the vector field. Vortices are one of the most fundamental topological
excitations in nature, widely known in hair whorls as the winding of hair
strings, in fluid dynamics as the winding of velocities, in angular-momentum
beams as the winding of phase angle and in superconductors and superfluids as
the winding of order parameters. Nevertheless, vortices have hardly been
observed other than those in the real space. Although band degeneracies, such
as Dirac cones, can be viewed as momentum-space vortices in their mathematical
structures, there lacks a well-defined physical observable whose winding number
is an arbitrary signed integer. Here, we experimentally observed momentum-space
vortices as the winding of far-field polarization vectors in the Brillouin zone
(BZ) of periodic plasmonic structures. Using a home-made polarization-resolved
momentum-space imaging spectroscopy, we completely map out the dispersion,
lifetime and polarization of all radiative states at the visible wavelengths.
The momentum space vortices were experimentally identified by their winding
patterns in the polarization-resolved iso-frequency contours and their
diverging radiative quality factors. Such polarization vortices can exist
robustly on any periodic systems of vectorial fields, while they are not
captured by the existing topological band theory developed for scaler fields.
This work opens up a promising avenue for exploring topological photonics in
the momentum space, studying bound states in continuum (BICs), as well as for
rendering and steering vector beams and designing high-Q plasmonic resonances.Comment: 7 pages, 4 figure
