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Four-wave mixing instabilities are theoretically studied for continuous wave propagation in ultrasmall core photonic-crystal and tapered fibers. The waveguide, or geometrical, contribution to the overall dispersion of these structures is much stronger than in conventional fibers. This leads to the appearance of unstable frequency bands that are qualitatively and quantitatively different from those seen in conventional fibers. The four-wave mixing theory developed here is based on the full wavedoi:10.1103/physreve.68.046603 pmid:14683061 fatcat:eocbtqicpjditnuedkd4ycfqay