An optical fiber with a low-index core and a core grating has a solid and generally cylindrical annular cladding having a refractive index ncl, a central axis, an inner surface with a radius r wherein r≧2 μm, an outer surface with a radius R, and an annular thickness ΔR≧10 μm. The fiber core has the radius r and a refractive index nc, wherein ncl>nc. The grating is defined by grating elements that extend from the cladding inner surface into the core and that run generally parallel to the central axis. The grating elements define a period Λ, a width t, a spacing a and a height h, wherein 0.5