The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves)

The theory of Wood's anomalous diffraction gratings, which was developed some years ago, has been reexamined in order to visualize its physical meaning. Each wave diffracted by a grating is identified through the component of its "wave vector" tangential to the grating. Surface waves similar to those found in total internal reflection are included (§2). The amplitudes of these waves can be calculated by successive approximations (§3). One feature of the anomalies is connected with the infinite dispersion of spectra at grazing emergence (§4). Emphasis is put on the existence of polarized quasi-stationary waves which represent an energy current rolling along the surface of a metal (§5). These waves can be strongly excited on the surface of metallic gratings under critical conditions depending also on the profile of the grooves; secondary interference phenomena arise then in the observed spectra (§6). The connection of the quasi-stationary surface waves with the wireless ground waves is discussed (§7). A general formulation is introduced to discuss the significance of the approximation used (Appendix).