  Stable vortex lattices are basic dynamical patterns which have been
demonstrated in physical systems including superconductor physics,
Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV)
ensembles can be produced, self-organizing into the respective polar lattices.
However, these structures are in general highly unstable due to the strong VAV
attraction. Here, we demonstrate that multiple optical VAV clusters nested in
the propagating coherent field can crystallize into patterns which preserve
their lattice structures over distance up to several Rayleigh lengths. To
explain this phenomenon, we present a model for effective interactions between
the vortices and antivortices at different lattice sites. The observed VAV
crystallization is a consequence of the globally balanced VAV couplings. As the
crystallization does not require the presence of nonlinearities and appears in
free space, it may find applications to high-capacity optical communications
and multiparticle manipulations. Our findings suggest possibilities for
constructing VAV complexes through the orbit-orbit couplings, which differs
from the extensively studied spin-orbit couplings.
