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