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The effective indices of the cladding modes of optical fibers depend on the refractive index of the medium surrounding the fiber. We show experimentally and theoretically that while cladding modes with similar effective indices normally have similar refractometric sensitivities, the addition of a 50 nm thick gold sheath enhances the sensitivity of some EH modes by more than one order of magnitude while nearly completely suppressing the sensitivity of neighbouring HE modes (by three orders of magnitude, down to insignificant levels). A differential sensitivity of ∼1000 nm/(refractive index unit) is experimentally reported between adjacent EH and HE grating resonances.