Volume integral equations combined with orthogonality of guided mode and non-guided field are proposed for the TE incidence of two-dimensional optical slab waveguide. The slab waveguide is assumed to satisfy the single mode condition. The formulation of the integral equations are described in detail. The matrix equation obtained by applying the method of moments to the integral equations is shown. Numerical results for step, gap, and grating waveguides are given. They are compared to published papers to validate the proposed method.

The higher-order characteristic basis function method (HO-CBFM) is clearly formulated. HO-CBFM provides results accurately even if a block division is arbitrary. The HO-CBFM combined with a volume integral equation (VIE) is used in the analysis of various antennas in the vicinity of a dielectric object. The results of the numerical analysis show that the HO-CBFM can reduce the CPU time while still achieving the desired accuracy.

An integral equation approach with a new solution procedure using moment method (MoM) is applied for the computation of coupled currents on the surface of a printed dipole antenna and inside its high-permittivity three-dimensional dielectric substrate. The main purpose of this study is to validate the accuracy and reliability of the previously proposed MoM procedure by authors for the solution of a coupled volume-surface integral equations system. In continuation of the recent works of authors, a mixed-domain MoM expansion using Legendre polynomial basis function and cubic geometric modeling are adopted to solve the tensor-volume integral equation. In mixed-domain MoM, a combination of entire-domain and sub-domain basis functions, including three-dimensional Legnedre polynomial basis functions with different degrees is utilized for field expansion inside dielectric substrate. In addition, the conventional Rao-Wilton-Glisson (RWG) basis function is employed for electric current expansion over the printed structure. The accuracy of the proposed approach is verified through a comparison with the MoM solutions based on the spectral domain Green's function for infinitely large substrate and the results of FDTD method.

An alternative polynomial expansion for electromagnetic field estimation inside three-dimensional dielectric scatterers is presented in this article. In a continuation with the previous work of authors, the Tensor-Volume Integral Equation (TVIE) is solved by using the Galerkin-based moment method (MoM) consisting of a combination of entire-domain and sub-domain basis functions including three-dimensional polynomials. Instead of using trivial power polynomials, Legendre polynomials are adopted for electromagnetic fields expansion in this study. They have the advantage of being a set of orthogonal functions, which allows the use of high-order basis functions without introducing an ill-condition MoM matrix. The accuracy of such approach in MoM is verified by comparing its numerical results with that of exact analytical method such as Mie theory and conventional procedures in MoM. Besides, it is also confirmed that the condition number of the MoM matrix obtained with the proposed approach is lower than that of the previous approaches.

This paper includes different approaches for analysis of a thin-wire antenna in the presence of de-ionized water box at different temperatures as a high-permittivity three-dimensional dielectric body. In continuation with the previous work of authors, first, the coupled tensor-volume/line integral equations is solved by using Galerkin-based moment method (MoM) consisting of a combination of entire-domain and sub-domain basis functions including three-dimensional polynomials with different degrees. Then, the accuracy of such MoM, specifically for a high-permittivity dielectric scatterer, is substantiated by comparing its numerical results with that of FDTD method and some experimental data.

A new approach for solution of the Tensor-Volume Integral Equation (TVIE) using Galerkin-based moment method (MoM) for three-dimensional dielectric bodies is proposed. Two problems of plane wave scattering by a dielectric sphere and a thin-wire antenna in close proximity to a dielectric body are investigated. In both cases, cubic modeling is applied and a combination of entire-domain and sub-domain basis functions, including three-dimensional polynomial functions with different degrees is utilized for field expansion inside dielectric bodies. Power polynomial is adopted for this purpose and its property is discussed over the proposed mixed-domain MoM formulation. Numerical examples show that based on the proposed method, a relative fast algorithm and suitable accuracy are achieved compared with conventional MoM. The accuracy of the proposed method is verified by comparing it with the Mie theory, conventional MoM and the FDTD method.

Optical near-field distributions of planar dielectric and metallic objects placed on a large dielectric substrate plate have been calculated by the volume integral equation using an iterative method called generalized minimal residual method with the fast Fourier transform technique. The basic characteristics of the near-field have been investigated in detail for large and small objects, dielectric and metallic objects and incident p-polarized and s-polarized evanescent fields.