This paper newly proposes a fast computation technique on the method of image Green's function for p-characteristic calculations, when a plane wave with the transverse wavenumber p is incident on a periodic rough surface having perfect conductivity. In the computation of p-characteristics, based on a spectral domain periodicity of the periodic image Green's function, the image integral equation for a given incidence p maintains the same form for other particular incidences except for the excitation term. By means of a quadrature method, such image integral equations lead to matrix equations. Once the first given matrix equation is performed by a solution procedure as calculations of its matrix elements and its inverse matrix, the other matrix equations for other particular incidences no longer need such a solution procedure. Thus, the total CPU time for the computation of p-characteristics is largely reduced in complex shaped surface cases, huge roughness cases or large period cases.

This paper proposes a novel image integral equation of the first type (IIE-1) for a TE plane wave scattering from periodic rough surfaces with perfect conductivity by means of the method of image Green's function. Since such an IIE-1 is valid for any incident wavenumbers including the critical wavenumbers, the analytical properties of the scattered wavefield can be generally and rigorously discussed. This paper firstly points out that the branch point singularity of the bare propagator inevitably appears on the incident wavenumber characteristics of the scattered wavefield and its related quantities just at the critical wavenumbers. By applying a quadrature method, the IIE-1 becomes a matrix equation to be numerically solved. For a periodic rough surface, several properties of the scattering are shown in figures as functions of the incident wavenumbers. It is then confirmed that the branch point singularity clearly appears in the numerical solution. Moreover, it is shown that the proposed IIE-1 gives a numerical solution satisfying sufficiently the optical theorem even for the critical wavenumbers.

This paper deals with an integral equation method for analyzing the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface. In the region below the periodic surface, the extinction theorem holds, and the total field vanishes if the field solution is determined exactly. For an approximate solution, the extinction theorem does not hold but an extinction error field appears. By use of an image Green's function, new formulae are given for the extinction error field and the mean square extinction error (MSEE), which may be useful as a validity criterion. Numerical examples are given to demonstrate that the formulae work practically even at a critical angle of incidence.

This paper deals with an integral method analyzing the diffraction of a transverse electric (TE) wave by a perfectly conductive periodic surface. The conventional integral method fails to work for a critical angle of incidence. To overcome such a drawback, this paper applies the method of image Green's function. We newly obtain an image integral equation for the basic surface current in the TE case. The integral equation is solved numerically for a very rough sinusoidal surface. Then, it is found that a reliable solution can be obtained for any real angle of incidence including a critical angle.

This paper deals with the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface by an integral method. However, it is known that a conventional integral method does not work for a critical angle of incidence, because of divergence of a periodic Green's function (integral kernel). To overcome such a divergence difficulty, we introduce an image Green's function which is physically defined as a field radiated from an infinite phased array of dipoles. By use of the image Green's function, it is newly shown that the diffracted field is represented as a sum of radiation from the periodic surface and its image surface. Then, this paper obtains a new image integral equation for the basic surface current, which is solved numerically. A numerical result is illustrated for a very rough sinusoidal surface. Then, it is concluded that the method of image Green's function works practically even at a critical angle of incidence.

A novel double-image Green's function approach is proposed to compute the frequency- dependent capacitance and conductance for the general CMOS oriented transmission lines with one protective layer. The ε-algorithm of Pade approximation is adopted to reduce the time for establishing coefficient matrix in this letter. The parameters gained from this new approach are shown to be in good agreement with the data obtained by the full-wave method and the total charge Green's function method.