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We demonstrate the existence of a stable black self-guided beam of circular symmetry in a bulk self-defocusing Kerr medium. There are no gray or higher-order self-guided beams of circular symmetry. The stability of black beams of circular symmetry is in sharp contrast to analogous bright beams in a self-focusing medium, which are unstable. Black self-guided beams are ideal for all-optical devices in bulk material as they can induce a single-mode optical fiber to guide a (weak) signal beam.
Snyder et al. (Mon,) studied this question.