Generalized reciprocity relations for resonant diffraction at metal gratings

Diffraction theory of electromagnetic waves is of significant value in modern optics and engineering [1,2]. One of its classical chapters constitute problems of light scattering from periodic structures, among which reflecting metal gratings are of particular interest. Diffraction at such gratings can lead to resonant excitation of surface electromagnetic waves (SEWs), which in optics are commonly called surface plasmon-polaritons [2,3]. Investigation of corresponding problems is very intensive in last decades, that is related to interesting characteristics of SEW field (high intensity and localization) useful for various applications [3]. For instance, excitation of SEWs can be used for polarization control of specularly reflected wave, significant enhancement of light absorption by a highly reflective media, suppression of specular reflection and realization of predicted energy flux distribution between different nonspecular outgoing diffracted waves.