scholarly journals Polarizability Extraction of Above-Half-Space Transversal Dipole Scatterers Using a Fast Waveguide-Based Approach

2019 ◽  
Vol 8 (4) ◽  
pp. 66-73
Author(s):  
Y. Bigdeli ◽  
M. Dehmollaian
Keyword(s):  
Half Space ◽  
Homogeneous Medium ◽  
Extraction Methods ◽  
Scattering Parameters ◽  
Electric Resonance ◽  
Dielectric Sphere ◽  
S Parameters ◽  
Resonance Particle ◽  
Waveguide Method ◽  
Sub Wavelength

We present a semi-analytical method to extract transverse polarizability parameters of an arbitrary bi-anisotropic sub-wavelength scatterer both in homogeneous medium and placed at the boundary of two simple (homogeneous, isotropic, and linear) media. Using this technique, polarizability parameters of various dielectric and/or metallic scatterers are obtained, effectively. In this method, a scatterer is placed at the middle of a rectangular waveguide which in general is filled by two different simple media in either sides of the scatterer. The waveguide is designed so that the two TE10 and TE01 fundamental modes are propagating in a given frequency band. All 16 transverse polarizabilities are fast obtained having 16 different generalized scattering parameters (S-parameters). The S-parameters are associated with excitations at two different ports of the waveguide and the two different modes (TE10 and TE01). Comparing to existing polarizability extraction methods, the presented waveguide method is easy to run, fast and almost accurate. In order to validate the method, we present three examples including omega particle and magneto-dielectric sphere in free-space and an electric resonance particle, placed on top of a dielectric half-space.

scholarly journals Imaging of a small dielectric sphere buried in a half space

2009 ◽  
Vol 26 ◽  
pp. 123-134 ◽  
Author(s):  
S. Gdoura ◽  
D. Lesselier ◽  
P. C. Chaumet ◽  
G. Perrusson
Keyword(s):  
Half Space ◽  
Dielectric Sphere

Accuracy Improvement for Scattering-Parameters Evaluating of Microwave Coplanar Probe Using One-Port Two-Tier Multi-TRL Calibration Method

2013 ◽  
Vol 333-335 ◽  
pp. 254-258 ◽  
Author(s):  
Hui Huang ◽  
Xin Meng Liu ◽  
Xin Lv
Keyword(s):  
Calibration Method ◽  
Vector Network Analyzer ◽  
Network Analyzer ◽  
Random Errors ◽  
Scattering Parameters ◽  
Accuracy Improvement ◽  
S Parameters ◽  
Improving Accuracy ◽  
System Errors ◽  
Residual Errors

This paper presents a method improving accuracy for evaluating S-parameters (Scattering-parameters) of MCP (Microwave Coplanar Probe). This method may be named one-port two-tier Multi-TRL (Thru-Reflect-Line) calibration method. It measures two-port devices only at one port of VNA (Vector Network Analyzer). It decreases the random errors caused of cable movements and connecting times. This method is implemented with coaxial OSL (Open-Short-Load) and on-wafer TRL calibration kit. It directly calculates and removes the residual errors caused of coaxial OSL calibration kit imperfection. It significantly reduced system errors by using on-wafer TRL calibration kit. To verify the effectiveness of the proposed method, the measured S-parameters up to 50GHz of MCP configured with GSG-100 are given and discussed.

The Interaction of a Cylindrical Elastic Inclusion with Semicircular Disconnected Curve and Linear Cracks in an Homogeneous Medium by SH-Waves

2007 ◽  
Vol 348-349 ◽  
pp. 357-360
Author(s):  
Qi Hui ◽  
Jia Xi Zhao
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Function Method ◽  
Dynamic Stress ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Homogeneous Medium ◽  
Sh Waves

The scattering of SH waves by a cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks in an homogeneous medium is investigated and the solution of dynamic stress intensity factor is given by Green’s function, complex function method. Firstly, we can divide the space into up-and-down parts along the X axis. In the lower half space, a new suitable Green’s function for the present problem is constructed.In the upper half space, the Green’s function has been given by reference [5]. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded along the interface and the linear cracks can be constructed using the method of crack-division and the integral equations can be obtained by the use of continuity conditions at the X axis. Finally, some examples and results of dynamic stress intensify factor are given and the influence of the parameters is discussed.

scholarly journals Fourier Expansion to Elastic Vector Wave Functions and Applications of Wave Bases to Scattering in Half-Space

2012 ◽  
Vol 28 (1) ◽  
pp. 19-39 ◽  
Author(s):  
P.-J. Shih ◽  
T.-J. Teng ◽  
C.-S. Yeh
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Fourier Expansion ◽  
Homogeneous Medium ◽  
Wave Functions ◽  
Basis Set ◽  
Plane Boundary ◽  
Surface Boundary ◽  
Infinite Plane ◽  
Vector Wave

ABSTRACTThis paper proposes a complete basis set for analyzing elastic wave scattering in half-space. The half-space is an isotropic, linear, and homogeneous medium except for a finite inhomogeneity. The wave bases are obtained by combining buried source functions and their reflected counter-waves generated from the infinite-plane boundary. The source functions are the vector wave functions of infinite-space. Based on the source functions expressed in the Fourier expansion form, the reflected counter-waves are easily obtained by solving the infinite-plane boundary conditions. Few representations adopt Wely's integration, but the Fourier expansion is developed from it and applied to decouple the angular-differential terms of the vector wave functions. In addition to the scattering of the finite inhomogeneity, the transition matrix method is extended to express the surface boundary conditions. For the numerical application in this paper, the P- and the SV- waves are assumed as the incoming fields. As an example, this paper computes stress concentrations around a cavity. The steepest-descent path method yielding the optimum integral paths is used to ensure the numerical convergence of the wave bases in the Fourier expansion. The resultant patterns from these approaches are compared with those obtained from numerical simulations.

Scattering by a Dielectric Sphere Buried in a Half-Space With a Slightly Rough Interface

2018 ◽  
Vol 66 (1) ◽  
pp. 347-359 ◽  
Author(s):  
Hasan Zamani ◽  
Ahad Tavakoli ◽  
Mojtaba Dehmollaian
Keyword(s):  
Half Space ◽  
Rough Interface ◽  
Dielectric Sphere

Electric field of a horizontal antenna above a homogeneous half‐space: Implications for GPR

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 823-835 ◽  
Author(s):  
Christoph E. Baumann ◽  
Edson E. S. Sampaio
Keyword(s):  
Electric Field ◽  
Half Space ◽  
Homogeneous Medium ◽  
First Integral ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Branch Points ◽  
Order Zero ◽  
Homogeneous Half Space ◽  
Special Cases

Inverse modeling and interpretation of subsurface structures depend on accurate knowledge of the undisturbed field. This is especially true in the analysis of radargrams, in which it is difficult to resolve the upper homogeneous medium from the less shallow scatterers. The available forward models based on plane‐wave and ray approximation are not accurate enough for this task. To improve resolution capabilities, we determine the undisturbed field using exact expressions for the electric field of a sine‐shaped ground‐penetrating radar (GPR) signal antenna above a homogeneous half‐space. In the frequency domain it consists of the sum of two improper integrals with complex integrands. Each integrand contains a kernel multiplied by a Bessel function of the first kind and of order zero or one. In the general case these integrals do not have a solution in closed form, and their integrands are poorly convergent. Therefore, to solve the integrals we must use a special formalism involving integrals around branch points. When we assume that both the transmitter and the receiver are on the boundary of the half‐space, there exist analytic solutions for the first integral without further restrictions and for the second integral for two special cases: free space and half‐space, neglecting displacement currents. We check our corresponding numerical results against these analytic solutions. In the time domain we represent the electric field as a function of transmitter‐receiver offset and time. For a purely dielectric half‐space the backtransformation of the first integral is analytical under the assumed simplification, allowing us to check the numerical results obtained with a fast Fourier transform (FFT) algorithm. These results allowed us to design radargrams for five different models of a homogeneous earth, and they are fundamental for interpretation and further research of GPR modeling.

Acoustical Green’s Function and Boundary Element Techniques for 3D Half-Space Problems

2017 ◽  
Vol 25 (04) ◽  
pp. 1730001 ◽  
Author(s):  
Rafael Piscoya ◽  
Martin Ochmann
Keyword(s):  
Green’S Function ◽  
Frequency Domain ◽  
Boundary Element ◽  
Half Space ◽  
Green's Function ◽  
Homogeneous Medium ◽  
Practical Implementation ◽  
Infinite Plane ◽  
Exterior Problems ◽  
Basic Concepts

This paper presents a review of basic concepts of the boundary element method (BEM) for solving 3D half-space problems in a homogeneous medium and in frequency domain. The usual BEM for exterior problems can be extended easily for half-space problems only if the infinite plane is either rigid or soft, since the necessary tailored Green’s function is available. The difficulties arise when the infinite plane has finite impedance. Numerous expressions for the Green’s function have been found which need to be computed numerically. The practical implementation of some of these formulas shows that their application depends on the type of impedance of the plane. In this work, several formulas in frequency domain are discussed. Some of them have been implemented in a BEM formulation and results of their application in specific numerical examples are summarized. As a complement, two formulas of the Green’s function in time domain are presented. These formulas have been computed numerically and after the application of the Fourier Transformation compared with the frequency domain formulas and with a FEM calculation.

Self-similar problems in elastodynmics

1973 ◽  
Vol 274 (1240) ◽  
pp. 435-491 ◽  
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Natural Extension ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Dissimilar Materials ◽  
Step Function ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Self Similar

This paper presents a formulation of self-similar mixed boundary-value problems of elastodynamics that is a natural extension of one already developed by the writer for elastostatic problems. By thus exposing the analytical structure that is common to both the dynamic and static problems, the existence of properties common to certain static and dynamic problems is explained, and further such properties are derived. Common features of both two-dimensional and three-dimensional problems are brought out by reducing them to Hilbert problems, directly in two dimensions and by introducing the Radon transform in three dimensions. Several applications of the theory are presented, typical problems involving the indentation of a half-space by a conical or wedge-shaped indentor, and cracks expanding under the influence of a non-uniform applied stress. More difficult problems, that have not before been formulated, include dynamic indentation problems with adhesion, and problems of cracks expanding on interfaces between dissimilar materials. A method of solution of such problems is presented and an example of each type is worked out in detail. The method of analysis hinges upon representations of the solutions of ' unmixed ’ self-similar problems for half-spaces, which are obtained by use of an alternative to Cagniard’s technique whose application is routine, even for an anisotropic half-space. The representations provide more general solutions of the unmixed problems than were available previously. The main singularities, or ' arrivals ’, of the stress fields are extracted from the representations; these expressions are new and should be useful for certain problems in seismology. It is predicted, for instance, that a crack expanding on an interface can generate a ‘conical wave’, that is, a region in which the singularity has a logarithmic component as well as a step function, even in its P -wave arrival, which could not occur for a crack in a homogeneous medium. The properties of the equations of elastodynamics that are employed are that they are linear, homogeneous and self-adjoint and the methods that are developed are equally applicable to any other system with these properties.

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