  Polarization singularities of vectorial electromagnetic fields locate at the
positions (such as points, lines, or surfaces) where properties of polarization
ellipses are not defined. They are manifested as circular and linear
polarization, for which respectively the semi-major axes and normal vectors of
polarization ellipses become indefinite. First observed in conical diffraction
in the 1830s, the field of polarization singularities has been systematically
reshaped and deepened by many pioneers of wave optics. Together with other
exotic phenomena such as non-Hermiticity and topology, polarization
singularities have been introduced into the vibrant field of nanophotonics,
rendering unprecedented flexibilities for manipulations of light-matter
interactions at the nanoscale. Here we review the recent results on the
generation and observation of polarization singularities in metaphotonics. We
start with the discussion of polarization singularities in the Mie theory,
where both electric and magnetic multipoles are explored from perspectives of
local and global polarization properties. We then proceed with the discussion
of various photonic-crystal structures, for which both near- and far-field
patterns manifest diverse polarization singularities characterized by the
integer Poincare or more general half-integer Hopf indices (topological
charges). Next, we review the most recent studies of conversions from
polarization to phase singularities in scalar wave optics, demonstrating how
bound states in the continuum can be exploited to generate directly optical
vortices of various charges. Throughout our paper, we discuss and highlight
several fundamental concepts and demonstrate their close connections and
special links to metaphotonics. We believe polarization singularities can
provide novel perspectives for light-matter manipulation for both fundamental
studies and their practical applications.
