Electromagnetic model of a nanodipole array above a double‐layer graphene by periodic green's function

Presents a novel technique for the efficient computation of the periodic Green's function in layered dielectric media. This technique is based on approximating the spectral Green's function by a set of inverse-transformable complex exponential function. This enables the use of Poisson's summation formula to express the periodic Green's function as a combination of a spectral series and a spatial series each of which is rapidly convergent. The proposed technique can be applied to a wide class of problems where periodic structures are to be modeled.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new approach for the scattering of electromagnetic (EM) waves from periodic dielectric rough surfaces is addressed. The method is an extension of the buried object approach (BOA), which is developed for rough surfaces of infinite extend, to the present problem. The BOA allows to model the original problem as the scattering of EM waves from cylindrical objects located in a two-half-space medium with planar interface. Then, the problem is reduced to the solution of a Fredholm integral equation of second kind through the periodic Green's function of two-half-space medium. The periodic Green's function of two-half-space medium is calculated via the Floquet mode expansion, whose numerical evaluation can be accelerated by using effective methods. The method can also be used to solve the scattering problems of rough surfaces of infinite extend and having a localized roughness. Numerical simulations show that the method yields effective and accurate results for surfaces of arbitrary variation.

In many engineering applications, relatively difficult infinite summations with quite complex terms need to be computed numerically. These applications may include the calculation of free-space or planar-media periodic Green's functions in electromagnetics (EM), the determination of the electrostatic energy of ionic crystals in chemistry and the nucleic acid simulations in molecular dynamics. The difficulty of such computations usually arises from the fast oscillatory and slowly convergent nature of the summations. For instance, the EM analysis of cylindrical geometries may require the computation of slow convergent infinite summations of cylindrical Hankel and Bessel type functions; in numerical simulations of periodic structures, e.g. in the analysis of antenna arrays and photonic band gap materials, the periodic Green's functions need to be calculated for each impedance matrix elements in the method of moments, requiring the evaluation of many infinite summations of complex functions to fill in the entire matrix.

Alternate acceleration procedures are evaluated for the two-dimensional free-space periodic Green's function. Two of these techniques yield exponential convergence rates and are preferable if high accuracies are required. Numerical aspects of these procedures are described.

In this paper, a new method based on the complex images technique is presented for analysis of 2-D periodic devices such as waveguides, directional couplers, and coupled cavity waveguides (CCW). The main idea of this method lies in representing the infinite summation of the periodic Green's functions of such kind of structures in terms of finite terms of complex images. The electric field integral equation has been used to formulate the problem and the method of moments has been applied afterward for solving the equation. The method has been used successfully in the analysis of different waveguides, directional couplers, and CCWs in both rectangular and triangular lattices. Fast convergence, simple formulations, and flexibility of the method in analyzing different structures are the main advantages of the proposed method.

An efficient scheme is introduced for computing the two-dimensional periodic Green's function. By using Kummer's method to accelerate the Hankel function series, accurate results can be rapidly obtained when the source and field points coincide in the vertical direction. Unlike with the integral acceleration form, convergence of the series is maintained when the source and field points differ horizontally by a complete period.

This paper compares several methods to accelerate the convergence of the computation of infinite periodic Green's functions for potentials. Shanks' algorithm, the summation by parts method and Ewald's transform are investigated, for an acceleration of the summation both in the space and spectral domains. The algorithms are compared for several array examples.

This paper presents a unified method to predict the effective properties of the composite materials with periodic microstructure. First, based on the energy analysis, we use the multiple scale asymptotic analysis for a periodic unit cell to achieve a series of differential equations. Those equations include the first-order and the second-order strain gradient constitutive equations besides the conventional homogenized constitutive equations. Second, we further show that these equations can be converted into solving unified formal differential equations. Finally, we give the numerical method based upon Fast Fourier Transforms and taking the strain gradients into account and the solution is based on the explicit form of the periodic Green's function of the reference medium. This method is different from classically investigated by the Finite Element Method which need meshing.

In this paper, an efficient numerical technique is presented for analyzing the reflection and transmission characteristics of planar finite frequency selective surfaces (FSS) structures with multilayered dielectric substrate. For ideal infinite size FSS structures, only one single unit cell is of interest with the help of Floquet's theorem and periodic Green's functions. However, for FSS structures that are of finite size, full-wave numerical techniques must be employed to determine the electromagnetic characteristics. In this paper, the mixed potential integral equation (MPIE) for a general structure in multilayer media is first presented by using the spatial domain multilayered Green's functions. In order to simulate large-size FSS structures, the subentire- domain (SED) basis function method is then utilized to decrease memory requirement and computational complexity of method of moments (MoM). Different types of SED basis functions can be generated according to the locations of the cells in the entire structure, and then the original problem can be simplified into two smaller problems. In this way, a reduced system can be constructed and solved instead of the original large-size problem. This method enables a significant reduction to the matrix size and storage, and efficient analysis of finite FSS can be performed. To further decrease memory requirement and computational complexity, the presented numerical technique can be applied together with the fast fourier transform (FFT) algorithm for the matrix multiplication. The reflection and transmission coefficients of FSS are calculated using the far field of the FSS array and of the metallic plate with the same size. Several finite FSS structures are presented and analyzed to demonstrate the validate and efficiency of this method.

SUMMARY Planetary-scale mass redistributions occur on Earth for certain spatiotemporal periods, and these surface mass changes excite the global periodic loading deformations of a viscoelastic Earth. However, the characteristics of periodic viscoelastic deformations have not been well investigated even in a simple earth model. In this study, we derive the semi-analytical Green's functions (fully analytical Love numbers) for long-standing point sources with given periods using a modified asymptotic scheme in a homogeneous Maxwell spherical earth model. Here, the asymptotic scheme is needed in order to obtain accurate semi-analytical time-dependent Green's functions. The amplitudes and phases of the Green's functions may be biased if only the series summations of the Love numbers are used because the influence of viscoelasticity is degree-dependent. We compare the viscoelastic and elastic periodic Green's functions with different material viscosities and loading periods and investigate the amplitude increase percentage and phase delay of the periodic displacement and geoid change. For example, our analysis revealed that the viscosity increases the amplitude by 40–120 per cent and delays the phase approximately −100° to 60° for the displacement and geoid change when bearing a 10-yr loading period, assuming a viscosity of 1018 Pa s and a shear modulus 4 × 1010 Pa.

A fast interpolation method (FIM) is presented for rapidly evaluating electromagnetic fields in a periodic unit cell of general periodic problems. For a problem with N sources and N observers, the computational cost is of O(N) with O(1) evaluations of the periodic Green's functions (PGF). The method is kernel independent, i.e. it can be applied to many period problem types, and it allows using simple Floquet summations for the evaluation of the PGF.

We discuss effects on the propagation of surface acoustic waves (SAW) due to heavy mass loading on Y-cut lithium niobate and lithium tantalate substrates. An abrupt reduction in the leaky-SAW (LSAW) attenuation is observed in the measured admittance of a long resonator test structure on 64 degrees -YX-cut lithium niobate for aluminum electrodes of thickness h/lambda(0) beyond 9-10%. This experimental fact is explained theoretically as the slowing down of the leaky wave below the velocity of the slow shear surface-skimming bulk wave (SSBW), such that energy dissipation into bulk-wave emission becomes inhibited. An infinite transducer structure is modeled using the periodic Green's function and the boundary-element method (BEM); the computed theoretical properties well explain for the experimental findings. The model is further employed to quantify the leaky surface-wave attenuation characteristics as functions of the crystal-cut angle and the thickness of the electrodes. The resonance and antiresonance frequencies and the corresponding Q values are investigated to facilitate the selection of crystal cuts and electrode thicknesses. The transformation of the leaky SAW into a SAW-type nonleaky wave is also predicted to occur for gold electrodes, with considerably thinner finger structures.

We introduce a numerically efficient technique to analyze doubly infinite periodic structures by applying Floquet's theorem and the Characteristic Basis Function Method to the corresponding truncated array.We use reciprocity to compute the reflection coefficient of the array and avoid integration of induced currents for calculating scattered far fields by the periodic Green's function. We show that our method is able to analyze both planar and nonplanar frequency selective surfaces by comparing the reflection coefficient of frequency selective surface of standard elements with other codes. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:2332–2340, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26250

The authors present an efficient analysis and characterization of narrow resistive strip arrays residing on a dielectric substrate. Simple closed-form formulas for mode reflection and transmission coefficients of the resistive grating on a substrate are presented. This is accomplished by employing a single physical basis or edge mode to represent the strip current. The periodic Green's function is derived using the procedure employed by K. Sarabandi (1990), and the resulting series has a relatively fast convergence. A careful study is done to establish the accuracy bounds of the physical basis expansion and the resulting mode coefficients. From the derived closed-form formulas, equivalent sheet boundary conditions and equivalent circuit parameters are given for a complete characterization of the grating.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The paper presents an integral equation (IE) based scheme to analyze scattering from inhomogeneous bodies with anisotropic electromagnetic properties. Newly emerging metamaterials have both anisotropic /spl epsiv/ and /spl mu/ due to the structured orientation of inclusions. We develop the necessary mathematics to enable the modeling of 3D bodies of arbitrary shape using tetrahedral tessellation and apply Galerkin testing to solve the problem numerically. Evaluation of elements in the resulting matrix equation is considerably more involved with the introduction of generalized /spl epsiv/ and /spl mu/ tensors; computing these integrals is elucidated. Also, schemes for accurately compensating the artificial surface charges for tetrahedral basis functions is demonstrated. The proposed scheme can be easily retrofitted with acceleration techniques like the fast multipole method (FMM) to permit large scale computations. It is shown that incorporation of such techniques is a trivial task. Likewise, periodic Green's functions can be used for the analysis of periodic band-gap structures.