Coupled-mode theory for resonant gratings with a varying period

We propose a coupled-mode theory for resonant diffraction gratings with a varying period. We consider diffractive structures, in which the reciprocal lattice vector, a quantity inversely proportional to the period, varies linearly in the direction of periodicity. It is shown that optical properties of such a structure essentially depend on the period change rate. On the basis of a comparison with the results of rigorous numerical simulations using the rigorous coupled-wave analysis, high accuracy of the proposed theoretical model is demonstrated. In particular, the developed coupled-mode theory describes the broadening of the resonant peak and the appearance of secondary maxima caused by a non-zero period change rate. The obtained results can be used for the development of linear variable filters based on resonant diffraction gratings with varying parameters.