Stopband position and width in resonant grating waveguide structures

We derived approximation formulae that allow to analytically estimate film thickness and grating period necessary for a required stopband position. The derived formulae allow a straightforward and simple estimation of the film thickness for a resonant grating waveguide structures, the results have been confirmed by accurate rigorous coupled wave approximation (RCWA) calculations. We discuss the merit of stopband position and stopband width estimation, as well as the effects caused by dispersion and absorption of the high refractive index film material.