New boundary integral equations are proposed for two-port slab waveguides which satisfy single mode condition. The boundary integral equations are combined with the orthogonality of guided mode and non-guided field. They are solved by the standard boundary element method with no use of mode expansion technique. Reflection and transmission coefficients of guided mode are directly determined by the boundary element method. To validate the proposed method, step waveguides for TE wave incidence and triangular rib waveguides for TM wave incidence are investigated by numerical calculations.

“How to get the original ideas” is the fundamental and critical issue for the researchers in science and technology. In this paper, the author writes his experiences concerning how he could encounter the interesting and original ideas of three research subjects, i.e., the accelerating medium effect, the guided-mode extracted integral equation and the surface plasmon gap waveguide.

We describe elements of a fast integral equation solver for large periodic and partly periodic finite array systems. A key element of the algorithm is utilization (in a rigorous way) of a block-Toeplitz structure of the impedance matrix in conjunction with either conventional Method of Moments (MoM), Fast Multipole Method (FMM), or Fast Fourier Transform (FFT)-based Adaptive Integral Method (AIM) compression techniques. We refer to the resulting algorithms as the (block-)Toeplitz-MoM, (block-)Toeplitz-AIM, or (block-)Toeplitz-FMM algorithms. While the computational complexity of the Toeplitz-AIM and Toeplitz-FMM algorithms is comparable to that of their non-Toeplitz counterparts, they offer a very significant (about two orders of magnitude for problems of the order of five million unknowns) storage reduction. In particular, our comparisons demonstrate, that the Toeplitz-AIM algorithm offers significant advantages in problems of practical interest involving arrays with complex antenna elements. This result follows from the more favorable scaling of the Toeplitz-AIM algorithm for arrays characterized by large number of unknowns in a single array element and applicability of the AIM algorithm to problems requiring strongly sub-wavelength resolution.

We show examples of accurate computer-aided design of power coupling between two dielectric slab waveguides of finite length by using the boundary-element method (BEM) based on guided-mode extracted integral equations (GMEIE's). The integral equations derived in this paper can be solved by the conventional BEM. Various properties in numerical calculations of GMEIE's are examined. The reflection and coupling coefficients of the guided wave as well as the scattering power are calculated numerically for the case of incidence TM guided-mode. The presented results are checked by the energy conservation law and reciprocity theorem. The results show that it is possible to design an optimum coupling between two dielectric slab waveguides by using the BEM based on GMEIE's.

The H-polarized diffraction by a wedge consisting of perfect conductor and lossless dielectric is investigated by employing the dual integral equations. Its physical optics diffraction coefficients are expressed in a finite series of cotangent functions weighted by the Fresnel reflection coefficients. A correction rule is extracted from the difference between the diffraction coefficients of the physical optics field and those of the exact solution to a perfectly conducting wedge. The angular period of the cotangent functions is changed to satisfy the edge condition at the tip of the wedge, and the poles of the cotangent functions are relocated to cancel out the incident field in the artificially complementary region. Numerical results assure that the presented correction is highly effective for reducing the error posed in the physical optics solution.

In the paper a problem of wave scattering from a local penetrable inhomogeneity inside a planar dielectric waveguide is studied. The surface potentials method is applied for the problem and the set of systems of BIE is obtained and analyzed from the view-point of their numerical solution. The effective numerical algorithm based on the Nyström method is proposed. The equations for a scattering diagram and mode conversion coefficients are derived.

An accurate numerical solution is presented for the electromagnetic scattering from a double strip grating, where the strip planes are each supported by a dielectric slab. This structure is a model of polarization diplexers. The direction of propagation and the polarization of the incident plane wave are arbitrary. We derive a set of singular integral equations and solve it by the moment method, where the Chebyshev polynomials are successfully used as the basis and the testing functions. By numerical computations we examine the dependence of the diplexing properties on grating parameters in detail. The cross-polarization characteristics at skew incidence are also referred. From these results we construct an algorithm for the design of polarization diplexers.

An accurate numerical solution is presented for the electromagnetic scattering from infinite strip gratings attached to both sides of a dielectric slab. This structure is a model of polarization discriminating devices. The period of the strips is common to both planes, but the widths and the axes may be different. The direction of propagation and the polarization of an incident plane wave are arbitray. We derive a set of singular integral equations and solve it by the moment method, where the Chebyshev polynomials are successfully used as the basis and the testing functions. This method is accurate and effective owing to the incorporation of the edge condition and the decomposition of the kernel functions into the singular and the regular parts. Numerical calculations are carried out for the purpose of designing polarization discriminators, and it is shown that the band width is widened by decreasing the permittivity of the slab. The cross-polarization characteristics at skew incidence are also discussed.