This paper deals with the singular behavior of the diffraction of transverse magnetic (TM) waves by a perfectly conductive triangular periodic surface at a low grazing limit of incidence. The wave field above the highest excursion of the surface is represented as a sum of Floquet modes with modified diffraction amplitudes, whereas the wave field inside a triangular groove is written as a sum of guided modes with unknown mode amplitudes. Then, two sets of equations are derived for such amplitudes. From the equation sets, all the amplitudes are analytically shown to vanish at a low grazing limit of incidence. From this fact, it is concluded analytically that no diffraction takes place and only reflection occurs at a low grazing limit of incidence for any period length and any triangle height. This theoretical result is verified by a numerical example.

This paper deals with the diffraction of TM plane wave by a perfectly conductive periodic surface. Applying the Rayleigh hypothesis, a linear equation system determining the diffraction amplitudes is derived. The linear equation is formally solved by Cramer's formula. It is then found that, when the angle of incidence becomes a low grazing limit, the amplitude of the specular reflection becomes -1 and any other diffraction amplitudes vanish for any perfectly conductive periodic surfaces with small roughness and gentle slope.

This paper deals with the scattering of a TM plane wave from a periodic grating with single defect, of which position is known. The surface is perfectly conductive and made up with a periodic array of rectangular grooves and a defect where a groove is not formed. The scattered wave above grooves is written as a variation from the diffracted wave for the perfectly periodic case. Then, an integral equation for the scattering amplitude is obtained, which is solved numerically by use of truncation and the iteration method. The differential scattering cross section and the optical theorem are calculated in terms of the scattering amplitude and are illustrated in figures. It is found that incoherent Wood's anomaly appears at critical angles of scattering. The physical mechanisms of Wood's anomaly and incoherent Wood's anomaly are discussed in relation to the guided surface wave excited by the incident plane wave. It is concluded that incoherent Wood's anomaly is caused by the diffraction of the guided surface wave.

The diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive surface made up of a periodic array of rectangular grooves is studied by the modal expansion method. It is found theoretically that the reflection coefficient approaches -1 but no diffraction takes place when the angle of incidence reaches a low grazing limit. Such singular behavior is shown analytically to hold for any finite values of the period, groove depth and groove width and is then demonstrated by numerical examples.

This paper deals with the scattering of TE plane wave from a periodic grating with single defect, of which position is known. The surface is perfectly conductive and made up with a periodic array of rectangular grooves and a defect where a groove is not formed. By use of the modal expansion method, the field inside grooves is expressed as a sum of guided modes with unknown amplitudes. The mode amplitudes are regarded as a sum of the base component and the perturbed component due to the defect, where the base component is the solution in case of the perfectly periodic grating. An equation for the base component is obtained in the first step. By use of the base component, a new equation for the perturbed component is derived in the second step. A new representation of the optical theorem, relating the total scattering cross section with the reduction of the scattering amplitude is obtained. Also, a single scattering approximation is proposed to express the scattered field. By use of truncation, we numerically obtain the base component and the perturbed component, in terms of which the total scattering cross section and the differential scattering cross section are calculated and illustrated in figures.

This paper deals with the scattering of transverse magnetic (TM) plane wave by a perfectly conductive surface made up of a periodic array of finite number of rectangular grooves. By the modal expansion method, the total scattering cross section pc is numerically calculated for several different numbers of grooves. It is then found that, when the groove depth is less than wavelenght, the total scattering cross section pc increases linearly proportional to the corrugation width W. But an exception takes place at a low grazing angle of incidence, where pc is proportional to Wα and the exponent α is less than 1. From these facts, it is concluded that the total scattering cross section pc must diverge but pc/W the total scattering cross section per unit surface must vanish at a low grazing limit when the number of grooves goes to infinity.