Complete mode spectrum of a grounded dielectric slab with double negative metamaterials

The properties of a grounded dielectric slab with double negative (DNG) metamaterials are investigated in this paper. Dramatically different dispersion curves of evanescent surface modes (electromagnetic fields exponentially decay both in air and inside the slab) are observed. They are highly dependent on the medium parameters. As the counterpart of the improper complex leaky modes in a double positive (DPS) medium, the complex modes in a DNG medium are proved to be exclusively proper. They have exponentially decaying fields in the air region and are termed complex surface modes. It is found that there are an infinite number of complex surface modes and they cannot be suppressed. The Poynting vectors of complex surface modes are studied and it is proved that their integrals along the transverse direction are simply zero. The complete mode spectrum of the dielectric slab for both DPS and DNG media are tabled and compared. Surface wave suppression is discussed and its necessary and sufficient conditions are presented

Efficient and accurate approximation of infinite series summation using asymptotic approximation and fast convergent series

We present an approach for very quick and accurate approximation of infinite series summation arising in electromagnetic problems. This approach is based on using asymptotic expansions of the arguments and the use of fast convergent series to accelerate the convergence of each term. It has been validated by obtaining very accurate solution for propagation constant for shielded microstrip lines using spectral domain approach (SDA). In the spectral domain analysis of shielded microstrip lines, the elements of the Galerkin matrix are summations of infinite series of product of Bessel functions and Green\u27s function. The infinite summation is accelerated by leading term extraction using asymptotic expansions for the Bessel function and the Green\u27s function, and the summation of the leading terms is carried out using the fast convergent series

A novel boundary integral equation for surface crack model

A novel boundary integral equation (BIE) is developed for eddy‐current nondestructive evaluation problems with surface crack under a uniform applied magnetic field. Once the field and its normal derivative are obtained for the structure in the absence of cracks, normal derivative of scattered field on the conductor surface can be calculated by solving this equation with the aid of method of moments (MoM). This equation is more efficient than conventional BIEs because of a smaller computational domain needed

Full Wave Modeling of Ultrasonic Scattering Using Nystrom Method for NDE Applications

Approximate methods for ultrasonic scattering like the Kirchhoff approximation and the geometrical theory of diffraction (GTD) can deliver fast solutions with relatively small computational resources compared to accurate numerical methods. However, these models are prone to inaccuracies in predicting scattered fields from defects that are not very large compared to wavelength. Furthermore, they do not take into account physical phenomena like multiple scattering and surface wave generation on defects. Numerical methods like the finite element method (FEM) and the boundary element method (BEM) can overcome these limitations of approximate models. Commercial softwares such as Abaqus FEA and PZFlex use FEM, while CIVA has a 2D FEM solver [1-3]. In this work, we study the performance of the Nyström method (NM) [4,5], an alternative boundary integral equation solver to the BEM, in modeling ultrasonic scattering from defects. To handle larger problems, the Nyström method is accelerated by the multilevel fast multipole algorithm (MLFMA). We apply the NM to benchmark problems and compare its predictions with those of exact and approximate analytical models as well as with experimental results from the World Federation of NDE Centers (WFNDEC). Several examples will be presented to demonstrate the prediction of creeping waves by the NM while also illustrating its improved accuracy over the Kirchhoff approximation. We will conclude with a discussion on the validity and limitations of the NM in modelling practical NDE problems

Efficient Triangular Interpolation Method: Error Analysis and Applications

The interpolation errors of bivariate Lagrange polynomial and triangular interpolations are studied for the plane waves. The maximum and root-mean-square (RMS) errors on the right triangular, equilateral triangular and rectangular (bivariate Lagrange polynomial) interpolations are analyzed. It is found that the maximum and RMS errors are directly proportional to the (p+1)’th power of kh for both one-dimensional (1D) and two-dimensional (2D, bivariate) interpolations, where k is the wavenumber and h is the mesh size. The interpolation regions for the right triangular, equilateral triangular and rectangular interpolations are selected based on the regions with smallest errors. The triangular and rectangular interpolations are applied to evaluate the 2D singly periodic Green’s function (PGF). The numerical results show that the equilateral triangular interpolation is the most accurate interpolation method, while the right triangular interpolation is the most efficient interpolation method

An Efficient Multilevel Fast Multipole Algorithm to Solve Volume Integral Equation for Arbitrary Inhomogeneous Bi-Anisotropic Objects

A volume integral equation (VIE) based on the mixed-potential representation is presented to analyze the electromagnetic scattering from objects involving inhomogeneous bi-anisotropic materials. By discretizing the objects using tetrahedrons on which the commonly used Schaubert-Wilton-Glisson (SWG) basis functions are defined, the matrix equation is derived using the method of moments (MoM) combined with the Galerkin’s testing. Further, adopting an integral strategy of tetrahedron-to-tetrahedron scheme, the multilevel fast multipole algorithm (MLFMA) is proposed to accelerate the iterative solution, which is further improved by using the spherical harmonics expansion with a faster implementation and low memory requirement. The memory requirement of the radiation patterns of basis functions in the proposed MLFMA is several times less than that in the conventional MLFMA

Miniaturized-Element Frequency-Selective Rasorber Design Using Characteristic Modes Analysis

A dual-polarization frequency-selective rasorber with two absorptive bands at both sides of a passband is presented. Based on the characteristic mode analysis, a circuit analog absorber is designed using a lossy FSS that consists of miniaturized meander lines and lumped resistors. The positions and values of resistors are determined according to the analysis of modal significances and modal current. After that, the presented rasorber is designed by cascading of the lossy FSS and a lossless bandpass FSS. Equivalent circuits of the frequency-selective rasorber are modelled, and surface current distributions of both FSSs are illustrated to explain the operation mechanism. Measurement results show that, under the normal incidence, a minimum insertion loss of 0.27 dB is achieved at a passband around 6 GHz, and the absorption bands with an absorption rate higher than 80% are 2.5 to 4.6 GHz in the lower band and 7.7 to 12 GHz in the higher band, respectively. Our results exhibit good agreements between measurements and simulations

Analysis of a concentric coplanar capacitive sensor using a spectral domain approach

Previously, concentric coplanar capacitive sensors have been developed to quantitatively characterize the permittivity or thickness of one layer in multi‐layered dielectrics. Electrostatic Green’s functions due to a point source at the surface of one‐ to three‐layered test‐pieces were first derived in the spectral domain, under the Hankel transform. Green’s functions in the spatial domain were then obtained by using the appropriate inverse transform. Utilizing the spatial domain Green’s functions, the sensor surface charge density was calculated using the method of moments and the sensor capacitance was calculated from its surface charge. In the current work, the spectral domain Green’s functions are used to derive directly the integral equation for the sensor surface charge density in the spectral domain, using Parseval’s theorem. Then the integral equation is discretized to form matrix equations using the method of moments. It is shown that the spatial domain approach is more computationally efficient, whereas the Green’s function derivation and numerical implementation are easier for the spectral domain approach

Array-Based Guided Wave Source Location Using Dispersion Compensation

An important advantage of guided waves is their ability to propagate large distances and yield more information about flaws than bulk waves. Unfortunately, the multi-modal, dispersive nature of guided waves makes them difficult to use for locating flaws. In this work, we present a method and experimental data for removing the deleterious effects of multi-mode dispersion allowing for source localization at frequencies comparable to those of bulk waves. Time domain signals are obtained using a novel 64-element phased array and processed to extract wave number and frequency spectra. By an application of Auld’s electro-mechanical reciprocity relation, mode contributions are extracted approximately using a variational method. Once mode contributions have been obtained, the dispersion for each mode is removed via back-propagation techniques. Excepting the presence of a small artifact at high frequency-thicknesses, experimental data successfully demonstrate the robustness and viability of this approach to guided wave source location