Wave propagation through nonuniform gratings with slowly varying parameters

Light propagation through nonuniform gratings with slowly varying parameters is studied using a Schrodinger-like equation. This treatment is intuitively pleasing when applied to uniform gratings as the results are then expressed in terms of the dispersion of the grating. It is shown here that when applied to nonuniform gratings, this method leads to an additional and potentially significant contribution to the dispersion that is not included in naive treatments. It is found that the magnitude of this dispersion can be larger than the total dispersion of the structure. An approximate expression for the reflectivity is also given.