With the ability to directly write phase gratings whose peak refractive index modulation exceeds 10−3 in the cores of optical fibers, interesting effects are observed. These refractive index modulations begin to approach the core-cladding index difference of the fiber. We present data taken on the wavelength dependent transmission, as well as reflection, of such strong fiber gratings. A comparison is made with calculations based on solving the coupled wave equations, which take into account possible coupling to radiation modes. It is found that the slowly varying (in space) contribution to the refractive index is essential in order to account for the detailed structure that is observed.