This paper gives an overview on the design process of modulated metasurface (MTS) antennas and focus on their performance in terms of efficiency and bandwidth. The basic concept behind MTS antennas is that the MTS imposes the impedance boundary conditions (IBCs) seen by a surface wave (SW) propagating on it. The MTS having a spatially modulated equivalent impedance transforms the SW into a leaky wave with controlled amplitude, phase and polarization. MTS antennas are hence highly customizable in terms of performances by simply changing the IBCs imposed by the MTS, without affecting the overall structure. The MTS can be configured for high gain (high aperture efficiency) with moderate bandwidth, for wide bandwidth with moderate aperture efficiency, or for a trade-off performance for bandwidth and aperture efficiency. The design process herein described relies on a generalized form of the Floquet wave theorem adiabatically applied to curvilinear locally periodic IBCs. Several technological solutions can be adopted to implement the IBCs defined by the synthesis process, from sub-wavelength patches printed on a grounded slab at microwave frequencies, to a bed of nails structure for millimeter waves: in any case, the resulting device has light weight and a low profile.

The problem of E-polarized plane wave diffraction by a thin material strip is analyzed using the Wiener-Hopf technique together with approximate boundary conditions. Exact and high-frequency asymptotic solutions are obtained. Our final solution is valid for the case where the strip thickness is small and the strip width is large in comparison to the wavelength. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Numerical examples on the radar cross section (RCS) are presented for various physical parameters and the scattering characteristics of the strip are discussed in detail.

The diffraction by a thin material strip is analyzed for the H-polarized plane wave incidence using the Wiener-Hopf technique together with approximate boundary conditions. An asymptotic solution is obtained for the case where the thickness and the width of the strip are small and large compared with the wavelength, respectively. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Scattering characteristics are discussed in detail via numerical results of the radar cross section.

Recently, we proposed a weak-form discretization scheme to derive second-order difference equations from the governing equation of the scattering problem. In this paper, under the scope of the proposed scheme, numerical expressions for the waveguide boundary conditions are derived as perfectly absorbing conditions for input and output ports. The waveguide boundary conditions play an important role in extracting the quasi-localized wave as an eigenstate with a complex eigenvalue. The wave-number dependence of the resonance curve in Fano resonance is reproduced by using a semi-analytic model that is developed on the basis of the phase change relevant to the S-matrix. The reproduction confirms that the eigenstate with a complex eigenvalue does cause the observed Fano resonance.

This paper deals with a characteristic of the so-called effective boundary condition for a plane wave scattering from periodic surfaces with perfect conductivity. The perturbation solution with all orders is explicitly given under the effective boundary condition. It is newly found that such a perturbation solution satisfies the optical theorem under the exact boundary condition. A comparison between such a perturbation solution and a reference solution for the exact boundary condition by other methods is performed. Then, the validity of such a perturbation solution is concretely discussed.

In this paper, we propose and discuss efficient GPU implementation techniques of absorbing boundary conditions (ABCs) for a 3D finite-difference time-domain (FDTD) electromagnetic field simulation for antenna design. In view of architectural nature of GPUs, the idea of a periodic boundary condition is introduced to implementation of perfect matched layers (PMLs) as well as a transformation technique of PML equations for partial boundaries. We also present efficient implementation method of a non-uniform grid. The evaluation results with a typical simulation model reveal that our proposed technique almost double the simulation performance and eventually achieve the 55.8% of the peak memory bandwidth of a target GPU.

A Mur type analytical absorbing boundary condition (A-ABC), which is based on the one-dimensional one-way wave equation, is proposed for multidimensional wave analysis by introducing the directional splitting technique. This new absorbing boundary condition is expansion of the first-order Mur. The absorbing ability, required memory, and calculation speed of the Mur type A-ABC are evaluated by comparison with those of conventional ABCs. The result indicated that absorbing ability of the proposed ABC is higher than the first-order Mur and lower than the second-order Mur at large incident angle. While, our proposed ABC has advantage in both required memory and calculation speed by comparison with the second-order Mur. Thus, effectivity of the proposed Mur type A-ABC is shown.

This paper presents a formulation of two-dimensional photonic crystal waveguide devices formed by circular cylinders. The device structures are considered as cascade connections of straight waveguides. Decomposing the structure into layers of the cylinder arrays, the input/output properties of the devices are obtained using an analysis method of multilayer structure. We introduce periodic boundary conditions in the direction perpendicular to the wave propagation, and the Floquet-modes of each layer are calculated by the Fourier series expansion method with the help of the recursive transition-matrix algorithm. Then, the input/output properties of the devices are obtained by recursive calculation of scattering matrix with each layer. The presented formulation is validated by numerical experiments by comparing with the previous works.

This paper considers numerical methods for stability analyses of periodic solutions of ordinary differential equations. Stability of a periodic solution can be determined by the corresponding monodromy matrix and its eigenvalues. Some commonly used numerical methods can produce inaccurate results of them in some cases, for example, near bifurcation points or when one of the eigenvalues is very large or very small. This work proposes a numerical method using a periodic boundary condition for vector fields, which preserves a critical property of the monodromy matrix. Numerical examples demonstrate effectiveness and a drawback of this method.

Generalized impedance boundary conditions are employed to simulate the effects of the parallel-stratified media on electromagnetic fields. Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series expansion of spherical Hankel functions.

The radar cross section (RCS) of a dielectric-coated cylindrical cavity was measured and the measurements were compared with those calculated according to the iterative physical optics (IPO). The IPO analysis used the equivalent-impedance boundary condition (EIBC) based on transmission-line theory which takes into account the thickness of the coating. It was consequently found that this condition is much more effective than the ordinary-impedance boundary condition based on the intrinsic impedance of the material.

The boundary integral equation (BIE) on interior walls with surface impedance conditions is implemented to the iterative physical optics method and how to treat the singularities involved in the BIE of an impedance cavity is described. Singular integrals over a rectangular region can be represented by simple elementary functions.

An electromagnetic wave scattering by a material loaded rectangular trough on a ground plane is approximately analyzed by using standard impedance boundary condition (SIBC). The validity of the derived approximate solution is examined by comparing with the rigorous one not only for the oblique incidence but also for the variation of both the filled material's parameters and the trough dimension. An applicability condition has been derived here for this trough structure.

The features of the method of moment (MoM) and the finite difference time domain (FDTD) method for numerical analysis of the electromagnetic scattering problem are presented. First, the integral equations for the conducting wire, conducting plane and the dielectric materials are described. Importance to ensure the condition of the continuity of the current of the scatterers is emphasized and numerical examples for a conducting structure involving a junction of wire segment and planar segment is presented. Finally, the advantages and the disadvantages of the FDTD method are discussed.

The recently proposed modified PML (MPML) absorbing boundary condition is extended to three dimensions. The performance of the MPML is investigated by FDTD simulation of a typical microstrip line and a rectangular waveguide. The dominant and higher order modes of the microstrip line and the waveguide are excited separately in the computation. In all of the cases of excitation, the reflection properties of the MPML boundaries are examined for the side walls and the end walls, respectively. Various values of the permittivity and permeability of the MPML medium are tested in the computation, and the variation behavior of reflection from the MPML boundaries is examined. The numerical results reveal that by choosing appropriate values of the permittivity and permeability of the MPML, we can realize efficient absorption of both evanescent waves and propagating waves over a wide frequency band.

One-dimensional Cellular Automata (CA's) are considered as potential pseudorandom pattern generators to generate highly random parallel patterns with simple hardware configurations. A class of linear, binary, and of nearest neighbor (radius = 1) CA's is referred to here as elementary ones. This paper investigates operations of such CA's with fixed boundary conditions when non-null boundary values are applied to them. By modifying transition matrices of elementary CA's to include the influence of boundary values, structures of state transition diagrams are determined.

This paper is concerned with the perfectly matched layer (PML) for a lossy medium in terms of a finite volume time domain (FVTD) method based only on the Cartesian coordinate system. In this point-oriented FVTD method, there are no spatial differences between electric and magnetic fields. We can take account of the inhomogenity of the lossy medium by considering averaged material constants in each rectangular cell. Numerical examples are given for the electromagnetic wave propagation in two-dimensional tunnels with bends and branches.

A new simple formulation of absorbing boundary conditions with higher order approximation is proposed for the solution of Maxwell's equations with the finite-difference time-domain (FD-TD) method. Although this higher order approximation is based on the third order approximation of the one-way wave equations, we have succeeded in reducing it to an equation in a form quite similar to the second order appoximation. Numerical tests exhibit smaller reflection errors than the prevalent second order approximation.

This paper shows that a convolution property holds for sixteen members of a sinusoidal unitary transform family (DCTs and DSTs), on condition that an impulse response is an even function. Instead of the periodicity of an input signal assumed in the DFT case, DCTs require the input signal to be even symmetric outside boundaries and DSTs require it to be odd symmetric. The property is obtained by solving the eigenvalue problem of the matrices representing the convolution. The content of the property is that the DCT (or the DST) element of the output signal is the product of the DCT (or the DST) element of the input signal and the DFT element of the impulse response. The result for the well-known DCT is useful for a strongly-correlated signal and two examples demonstrate it.

When we use the finite-difference time-domain (FD-TD) method to study time-domain electromagnetic fields in the unbounded surroundings, we frequently use a radiation boundary condition (RBC) by means of one-way wave equations. The reflection coefficient by the RBC is independent of frequency, but the reflection coefficient of the finite difference approximation for the RBC depends on a frequency also; this study examines how the reflection characteristics are affected by the frequency, and the study presents the coefficients used in the RBC which gives expected reflection characteristics for a frequency, and presents the application to simulation of the matched termination of a rectangular waveguide.