Existence criterion of surface waves in diffraction gratings

Summary form only given. It is known that the diffraction properties of gratings can remarkably change at certain (threshold) frequencies. Sometimes these changes (known as Wood´s anomalies) are so strong that lead to destruction of a grating. Such catastrophic consequences may be caused by an excitation of surface waves whose energy is concentrated inside the grating. That is why an opportunity to predict the appearance of surface waves is of great importance. A new general existence criterion of surface waves is proposed. It is based on the consideration of the so-called augmented scattering matrix. This matrix arises if one takes into account not only oscillating Rayleigh waves but also those which grow (attenuate) far from the grating. If such a matrix has an eigenvalue equal to 1 then surface waves exist. We apply this criterion to the analysis of a planar dielectric-layer grating and represent nontrivial examples of gratings which support surface waves. We also discuss gratings with rapidly oscillating properties