Dispersion relation of guided-mode resonances and Bragg peaks in dielectric diffraction gratings

We present the dispersion relation of guided-mode resonances in non-dissipative dielectric diffraction gratings, both for s-polarized (TE mode) and p-polarized (TM mode) incident waves. We present a simple approximate theory as well as a rigorous calculation within the so-called coupled-wave theory. We discuss the dependence of the positions and the lifetimes of the resonances on the thickness of the gratings and on the strength of its modulation. We find that the diffraction efficiency of the different orders show peaks at different Bragg orders.