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Most dielectric waveguides depend for guidance on total internal reflection within a region of elevated refractive index. A little‐explored alternative to this is Bragg reflection. Here we consider a ‘‘Bragg’’ optical fiber in which a cylindrical Bragg grating is used to inhibit radial power flow. We find that such Bragg fibers can be guaranteed to be effectively single‐moded, with no polarization degeneracy; the electric field in this fundamental mode is purely azimuthal (transverse electric polarized).