Arbitrary Plane Wave Research Articles

Antenna Pattern Impact on MIMO OTA Testing

This paper investigates the impact of the DUT antenna pattern on the test area performance for multi-probe based MIMO OTA setup in terms of received voltage and spatial correlation. The plane wave synthesis (PWS) technique has been proposed for vertical polarization in the literature, where the goal is to approximate plane waves with arbitrary directions. The received voltage at the antenna terminal depends on the antenna radiation pattern and the impinging plane waves. A novel closed form technique to reproduce the received voltage with arbitrary incoming plane waves based on trigonometric interpolation is presented. The proposed technique provides a closed form solution for the PWS when the probe ring radius is infinite. The proposed technique shows that the impact of the antenna pattern on the induced received voltage accuracy is ruled by Nyquist sampling theory. Furthermore, the impact of the antenna pattern on spatial correlation accuracy for prefaded signal synthesis (PFS) technique is investigated as well. Simulation and measurement results show that the number of required probes depend directly on the DUT antenna pattern. To test realistic DUTs with higher variations in directivity, we need more probes to maintain the same received voltage and spatial correlation accuracy level.

HYBRID TECHNIQUE FOR THE ANALYSIS OF SCATTERING FROM PERIODIC STRUCTURES COMPOSED OF IRREGULAR OBJECTS

In the paper, the analysis of electromagnetic wave scattering from multilayered frequency selective surfaces is presented. The surface is composed of periodically arranged posts with irregular shapes. The multimodal scattering matrix of such structure is derived and the transmission and re∞ection characteristic for the structure with arbitrary plane wave illumination are calculated. The exact full- wave theory based on the hybrid approach employing mode-matching method and flnite-difierence frequency-domain (FDFD) technique is applied to develop an e-cient theory to analyze such structures. The validity and accuracy of the approach are verifled by comparing the results with those obtained from alternative methods and own measurements of manufactured periodic structures.

Localizing the angular momentum of linear gravity

In a previous article [Phys. Rev. D 82 104040 (2010)], we derived an energy-momentum tensor for linear gravity that exhibited positive energy density and causal energy flux. Here we extend this framework by localizing the angular momentum of the linearized gravitational field, deriving a gravitational spin tensor which possesses similarly desirable properties. By examining the local exchange of angular momentum (between matter and gravity) we find that gravitational intrinsic spin is localized, separately from orbital angular momentum, in terms of a gravitational spin tensor. This spin tensor is then uniquely determined by requiring that it obey two simple physically motivated algebraic conditions. Firstly, the spin of an arbitrary (harmonic-gauge) gravitational plane wave is required to flow in the direction of propagation of the wave. Secondly, the spin tensor of any transverse-traceless gravitational field is required to be traceless. (The second condition ensures that local field redefinitions suffice to cast our gravitational energy-momentum tensor and spin tensor as sources of gravity in a quadratic approximation to general relativity.) Additionally, the following properties arise in the spin tensor spontaneously: all transverse-traceless fields have purely spatial spin, and any field generated by a static distribution of matter will carry no spin at all. Following the structure of our previous paper, we then examine the (spatial) angular momentum exchanged between the gravitational field and an infinitesimal detector, and develop a microaveraging procedure that renders the process gauge-invariant. The exchange of nonspatial angular momentum (i.e., moment of energy) is also analyzed, leading us to conclude that a gravitational wave can displace the center of mass of the detector; this conclusion is also confirmed by a first principles treatment of the system. Finally, we discuss...

Quasiclassical approach to high-energy QED processes in strong laser and atomic fields

An approach, based on the use of the quasiclassical Greenʼs function, is developed for investigating high-energy quantum electrodynamical processes in combined strong laser and atomic fields. Employing an operator technique, we derive the Greenʼs function of the Dirac equation in an arbitrary plane wave and a localized potential. Then, we calculate the total cross section of high-energy electron–positron photoproduction in an atomic field of arbitrary charge number (Bethe–Heitler process) in the presence of a strong laser field. It is shown that the laser field substantially modifies the cross section at already available incoming photon energies and laser parameters. This makes it feasible in principle to observe with present technology the analogous effect in a laser field of the Landau–Pomeranchuk–Migdal effect for the Bethe–Heitler process.

Shielding Effectiveness of an Enclosure With Finite Wall Thickness and Perforated Opposing Walls at Oblique Incidence and Arbitrary Polarization by GMMoM

An efficient and accurate technique based on a modal method of moments (MoM) is introduced to evaluate shielding effectiveness (SE) of a rectangular enclosure with apertures at opposing walls. The perforated walls are obliquely illuminated by arbitrary polarized incident plane waves. This technique takes the effect of the perforated wall thickness into account as well. The method is validated by comparing the results with measurements and fully numerical methods for an enclosure with various apertures illuminated by an arbitrary incident plane wave. It is shown that wall thickness affects SE for different polarized incident waves.

Time Domain Diffraction by a Right-Angled Penetrable Wedge

The electromagnetic diffraction by a right-angled dielectric wedge normally illuminated by a plane wave is considered in the time domain. The proposed approach exploits the knowledge of uniform asymptotic diffraction coefficients in the frequency domain, and uses the inverse Laplace transform for obtaining the response to an impulse plane wave. Then, the response to an arbitrary function plane wave is determined in the dielectric material and the surrounding space via a convolution integral. Comparisons with FDTD data prove the validity of the approach. At best authors' knowledge, time domain solutions are not available to date for the considered diffraction problem.

ANALYSIS OF ELECTROMAGNETIC PLANE WAVE SCATTERING FROM 2-D PERIODIC ARRANGEMENTS OF POSTS

In the paper, the analysis of electromagnetic wave scattering from frequency selective surface is presented. The surface is composed of periodically arranged posts. The multimodal scattering matrix of such structure is derived and the transmission and re∞ection characteristic for the structure with arbitrary plane wave illumination are calculated. The exact full-wave theory based on the mode-matching method is applied to develop an e-cient theory to analyze such structures. The validity and accuracy of the approach are verifled by comparing the results with those obtained from alternative methods. The analysis of plane wave scattering form the frequency selective surface (FSS) composed of periodic arrangements of scatterers is conducted in this paper. The constructive elements of this structure are comparable in size to the operation wavelength and are composed of conducting and dielectric material. FSSs when multilayered can be utilized as an electromagnetic band structure (EBG) in microwave wavelength range or photonic band structure (PBG) in optical range. Recently, EBGs and PBGs are of great interest due to their extraordinary properties and potential applications, e.g., fllters, polarizers, substrates for radiating elements, or optical switches (1{14). Many numerical techniques have been utilized to investigate band gap structures. The most popular are the cylindrical-harmonic expansion method (15), the flnite element method (16), the flnite difierence method (17), and Fourier modal method (18). FSSs can also flnd application in polarizers

A fast 2‐D parallel multilevel fast multipole algorithm solver for oblique plane wave incidence

We present a multilevel fast multipole algorithm (MLFMA) implementation to numerically solve Maxwell's equations for large two‐dimensional geometries illuminated by an arbitrary plane wave in three‐dimensional space. The solver's capabilities are augmented by means of an asynchronous and hierarchical parallelization. Its accuracy is demonstrated by comparing the analytical and numerically obtained scattering width of several canonical examples with a size of 700,000 wavelengths.

A spice model for multiconductor microstrip lines excited by an incident plane wave

AbstractThis article presents a SPICE model to analyze the terminal response of multiconductor microstrip lines excited by an incident plane wave. The analysis is based on multiconductor transmission line equations with the quasi‐TEM propagation mode approximation on microstrip lines and an accurate calculation of electromagnetic fields in the air/dielectric medium. The proposed SPICE model can be directly used for both the time‐domain and frequency‐domain analyzes and allows incorporating nonlinear and time‐varying loads. Several cases with an arbitrary plane wave incidence are simulated by using the proposed SPICE model. The results are in good agreement with those obtained using the Baum‐Liu‐Tesche equations model and full‐wave analysis simulator (by CST Microwave Studio Software). © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:2754–2761, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26396

On Spatial Aliasing in Microphone Arrays

Microphone arrays sample the sound field in both space and time with the major objective being the extraction of the signal propagating from a desired direction-of-arrival (DOA). In order to reconstruct a spatial sinusoid from a set of discrete samples, the spatial sampling must occur at a rate greater than a half of the wavelength of the sinusoid. This principle has long been adapted to the microphone array context: in order to form an unambiguous beampattern, the spacing between elements in a microphone array needs to conform to this spatial Nyquist criterion. The implicit assumption behind the narrowband beampattern is that one may use linearity and Fourier analysis to describe the response of the array to an arbitrary wideband plane wave. In this paper, this assumption is analyzed. A formula for the broadband beampattern is derived. It is shown that in order to quantify the spatial filtering abilities of a broadband array, the incoming signal's bifrequency spectrum must be taken into account, particularly for nonstationary signals such as speech. Multi-dimensional Fourier analysis is then employed to derive the broadband spatial transform, which is shown to be the limiting case of the broadband beampattern as the number of sensors tends to infinity. The conditions for aliasing in broadband arrays are then determined by analyzing the effect of computing the broadband spatial transform with a discrete spatial aperture. It is revealed that the spatial Nyquist criterion has little importance for microphone arrays. Finally, simulation results show that the well-known steered response power (SRP) method is formulated with respect to stationary signals, and that modifications are necessary to properly form steered beams in nonstationary signal environments.

Electromagnetic boundary and its realization with anisotropic metamaterial

A set of boundary conditions requiring vanishing of the normal components of the D and B vectors at the boundary surface is introduced and labeled as that of DB boundary. Basic properties of the DB boundary are studied in this paper. Reflection of an arbitrary plane wave, incident with a complex propagation vector, is analyzed for the planar DB boundary. It is shown that waves polarized transverse electric (TE) and transverse magnetic (TM) with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes. The basic problem of current source above the planar DB boundary is solved by applying TE and TM decomposition for the source. Realization of the DB boundary in terms of an interface of uniaxially anisotropic metamaterial half-space with zero axial medium parameters is considered. It is also shown that such a medium with small axial parameters acts as a spatial filter for waves incident at the interface which could be used for narrowing the beam of a directive antenna. Application of DB boundary as an isotropic soft surface with low interaction between antenna apertures also appears possible.

Classical dynamics of a charged particle in a laser field beyond the dipole approximation

The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the nonrelativistic Hamilton-Jacobi theory. The exact parametric representation for a particle's orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle's trajectory, as an explicit function of the laboratory frame's time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser's intensity and depends on the polarization of radiation. It is shown that the system exposes the intensity duality, correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative ``fundamental solution'' and applying a certain modular transformation one can obtain the particle's orbit in the monochromatic plane wave background with arbitrarily prescribed characteristics.

Scattering of an arbitrary plane wave by a dielectric wedge: Integral equations and fields near the edge

The behavior of the field components near the edge has been shown to be that of the static fields, which is derived here without rigor for an infinite wedge. Fields scattered by a finite dielectric wedge illuminated by an arbitrary plane monochromatic wave are computed using either singular or hypersingular integral equations (SIEs or HIEs), derived by the single integral equation method. Field components are then computed near the edge of a finite wedge. Longitudinal components of the fields behave like constants, other components of the electric field behave like those in the transverse magnetic mode, and other components of the magnetic field behave like those in the transverse electric mode. Exceptions occur when approaching the wedge along the bisector. Boundary functions and transverse field components computed with SIEs rise more sharply than predicted approaching the edge after a range in which the agreement with those computed with HIEs is good.

Hybrid $S$-Parameters for Transmission Line Networks With Linear/Nonlinear Load Terminations Subject to Arbitrary Excitations

We propose a generalized S-parameter analysis for transmission lines (TLs) with linear/nonlinear load terminations subject to arbitrary plane-wave and port excitations. S-parameters are prevalently used to model TLs such as cable bundles and interconnects on printed circuit boards (PCBs) subject to port excitations. The conventional S-parameter approach is well suited to characterize interactions among ports. However, nontraditional port excitations associated with plane-wave coupling to physical ports at TL terminals lead to forced, as well as propagating, modal waves, necessitating a modification of the standard S-parameter characterization. In this paper, we consider external plane-wave excitations, as well as port (internal) sources, and propose a hybrid S-parameter matrix for characterization of the associated microwave network and systems. A key aspect of the approach is to treat the forced waves at the ports as constant voltage sources and induced propagating modal waves as additional entries (hybrid S-parameters) in the S-parameter matrix. The resulting hybrid S-matrix and voltage sources can be subsequently exported to any circuit solver such as HSPICE and Agilent's Advanced Design System for the analysis of combined linear and nonlinear circuit terminations at ports. The proposed method is particularly suited for susceptibility analysis of cable bundles and PCBs for electromagnetic interference evaluations. It also exploits numerical techniques for structural and circuit domain characterization and allows for circuit design optimization without a need to perform any further computational electromagnetic analysis

Energy flux in viscoelastic anisotropic media

SUMMARY We study properties of the energy-flux vector and other related energy quantities of homogeneous and inhomogeneous time-harmonic P and S plane waves, propagating in unbounded viscoelastic anisotropic media, both analytically and numerically. We propose an algorithm for the computation of the energy-flux vector, which can be used for media of unrestricted anisotropy and viscoelasticity, and for arbitrary homogeneous or inhomogeneous plane waves. Basic part of the algorithm is determination of the slowness vector of a homogeneous or inhomogeneous wave, which satisfies certain constraints following from the equation of motion. Approaches for determination of a slowness vector commonly used in viscoelastic isotropic media are usually difficult to use in viscoelastic anisotropic media. Sometimes they may even lead to non-physical solutions. To avoid these problems, we use the so-called mixed specification of the slowness vector, which requires, in a general case, solution of a complex-valued algebraic equation of the sixth degree. For simpler cases, as for SH waves propagating in symmetry planes, the algorithm yields simple analytic solutions. Once the slowness vector is known, determination of energy flux and of other energy quantities is easy. We present numerical examples illustrating the behaviour of the energy-flux vector and other energy quantities, for homogeneous and inhomogeneous plane P, SV and SH waves. 1 I NTR O DUCTION In this paper, we study the properties of the energy flux of homogeneous and inhomogeneous time-harmonic plane waves propagating in an unbounded viscoelastic anisotropic medium. The complexvalued energy-flux vector F (also called the Poynting or Umov‐ Poynting vector) is used as the quantity which fully characterizes the energy flux and the dissipation of energy of the wave. The real part of the vector F represents the time-averaged energy flux S. Both real, Re F = S, and imaginary, Im F, parts are closely related to the density of the time-averaged dissipated energy W d : W d equals twice the scalar product of −Im F and propagation vector P (real part of the slowness vector, perpendicular to the wave front) or twice the scalar product of Re F and attenuation vector A (imaginary part of the slowness vector, perpendicular to the plane of constant amplitude). The aim of this paper is to present a concise derivation of the expression for the complex-valued energy-flux vector F of homogeneous and inhomogeneous plane waves propagating in unbounded media of unrestricted anisotropy and viscoelasticity, to propose an algorithm for its calculation, and to perform analytical and numerical studies necessary for correct understanding of energy propagation and dissipation of the relevant plane waves. Considerable attention in seismology has been devoted to the energy flux of plane waves propagating in elastic anisotropic and in viscoelastic isotropic media. For elastic anisotropic media, see, for

Diffraction theory of an anisotropic circular cylinder

A fully analytical theory is developed to derive the field diffracted by an infinitely long circular cylinder made of an arbitrary anisotropic homogeneous material, illuminated by an arbitrary plane wave.

VECTOR CIRCUIT THEORY FOR SPATIALLY DISPERSIVE UNIAXIAL MAGNETO-DIELECTRIC SLABS

We present a general dyadic vector circuit formalism, applicable for uniaxial magneto-dielectric slabs, with strong spatial dispersion explicitly taken into account. This formalism extends the vector circuit theory, previously introduced only for isotropic and chiral slabs. Here we assume that the problem geometry imposes strong spatial dispersion only in the plane, parallel to the slab interfaces. The difference arising from taking into account spatial dispersion along the normal to the interface is briefly discussed. We derive general dyadic impedance and admittance matrices, and calculate corresponding transmission and reflection coefficients for arbitrary plane wave incidence. As a practical example, we consider a metamaterial slab built of conducting wires and split-ring resonators, and show that neglecting spatial dispersion and uniaxial nature in this structure leads to dramatic errors in calculation of transmission characteristics.

Realization of the PEMC boundary

Perfect electromagnetic conductor (PEMC) is a nonreciprocal generalization of both the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC). Because PEMC does not allow electromagnetic energy to enter, it can serve as boundary material. Possibilities for the realization of a PEMC boundary are studied in terms of a layer of certain nonreciprocal materials resting on a PEC plane. It is shown that the parameters of a bi-isotropic or a gyrotropically anisotropic medium can be chosen so that the interface of the layer acts as a PEMC boundary to normally incident waves. After a modification of medium parameters, the same is shown to be asymptotically valid for arbitrary plane waves. A structure for the realization of such a boundary is suggested.

Polarizing properties of crossed-beam volume holographic gratings

Abstract The polarizing properties of crossed-beam volume holographic gratings recorded by arbitrary polarization plane waves are considered, using the three-dimensional coupled wave theory. Simple analysis expressions for the amplitude profiles of the transmitted and diffracted waves are obtained. Detailed diffraction characteristics for the case of a finite plane wave of uniform amplitude distribution are presented. We discuss the influence of the polarized azimuths of the incident wave both at recording and at reconstruction on the amplitude profiles of the transmitted and diffracted waves.

General purpose software package for electromagnetics engineering education

AbstractThis article presents a general‐purpose educational software applied to electromagnetics engineering education. The program presented allows the students to obtain the RCS, current density, and near field distributions of perfectly electric conducting (PEC) canonical geometries being illuminated by arbitrary incident plane waves. © 2002 Wiley Periodicals, Inc. Comput Appl Eng Educ 10: 33–44, 2002; Published online in Wiley InterScience (www.interscience.wiley.com.); DOI 10.1002/cae.10015