Scattering of a TE plane wave by the end-face of an ordered waveguide system

In the plane wave scattering by the periodic surfaces the diffracted waves disappear at a low grazing angle limit of incidence, the incident wave is perfectly canceled by the reflected wave and a dark shadow takes place (J. Nakayama, K. Hattori and Y. Tamura, IEICE Trans. Electron., E90-C, 2007, pp.536–538). On the basis of a shadow hypothesis a diffraction theory has been proposed (J. Nakayama, IEICE Trans. Electron., E92-C, 2009, pp.17–24). In there the scattering factor has been introduced as an essential quantity and an integral representation of Green´s function in terms of the scattering factor has been presented. So far, however, the execution of the integration is not reported.