  We theoretically demonstrate the existence of frozen light in near-zero-index
media with cubic nonlinearity. Light is stopped to a standstill owing to the
divergent wavelength and the vanishing group velocity, effectively rendering,
through nonlinearity, a positive-epsilon trapping cavity carved in an otherwise
slightly-negative-epsilon medium. By numerically solving Maxwell's equations,
we find a soliton-like family of still azimuthal doughnuts, which we further
study through an adiabatic perturbative theory that describes soliton
evaporation in lossy media or condensation in actively pumped materials. Our
results suggest applications in optical data processing and storage, quantum
optical memories, and soliton-based lasers without cavities. Additionally,
near-zero-index conditions can also be found in the interplanetary medium and
in the atmosphere, where we provide an alternative explanation to the rare
phenomenon of ball-lightning.
