Rigorous Full Wave Research Articles

Development of terahertz two-dimensional phase gratings for multiple beam generation based on a high-accuracy phase retrieval algorithm.

High efficiency and accuracy phase gratings are of crucial importance for large format heterodyne array receivers at terahertz frequencies. Here, by developing a design approach that can create gratings with arbitrary two-dimensional diffraction distributions, we have realized a reflective metallic phase grating that generates 2×2 diffraction beams at 0.85 THz. The measured total power efficiency of the diffraction beam pattern is 81.9%, which demonstrates at least 17% improvement in efficiency compared with the standard pseudo-2D Fourier phase grating. In addition, we report the realization of up to 10×10 diffraction beam two-dimensional phase grating designs at terahertz wavelengths, using an adaptation of the Gerchberg-Saxton (GS) scheme known as the Mixed-Region-Amplitude-Freedom algorithm. Rigorous full wave simulation proves the efficiency and accuracy of the design, which overcomes the inaccurate intensity of the beam distribution drawbacks originated from the standard GS algorithm. The results pave the way for the development of large-pixel terahertz multi-beam heterodyne receivers.

Vlasov Launcher Diagrammatic Design Using the RT Method

In this paper, a simple and fast method relied upon for designing a Vlasov launcher with a helical cut is proposed. The method is based on graphic interpretation of analytical relationships that link wave parameters (EM field mode) to the launcher’s geometrical dimensions. Using the ray tracing method, a simplified graphic analysis may be carried out. The results obtained are not significantly different from those of rigorous full-wave analyzes. The family of normalized curves that is created in the process greatly facilitates the stage of optimizing the geometrical parameters of the Vlasov launcher

Modeling of Waveguide Filter Using Wave Concept Iterative Procedure

A rigorous full wave technique based on the Transverse Wave Concept Iterative Procedure (WCIP) is used to design a complex Frequency Selective Surface (FSS). These surfaces include a periodically arrangement of identical circuit. There are used as filters and reflector antenna as well as deep-space exploration for multi-frequencies operations. A simple FSS structure is studied in the first stage to validate our approach. In the second stage two different complex structures are studied. The good agreement between simulated and published data justifies the design procedure.

Generalized Network Model for Energization of Grounding Electrodes

The main difference between the application of the method of moments (MoM) to grounding system and antenna analysis is the shunt energization by the injection of current. There is no consensus on the modeling of such energization, which is also crucial for the definition of quantities that characterize grounding system time and frequency behavior. The contributions of this paper are as follows: The presentation of a simple and unified approach to model all important cases of energization based on a generalized network representation of the grounding electrodes; the demonstration that the mesh current method, whose matrix equation is identical to that of the MoM, leads to straightforward procedures in the analysis of all cases of energization; and the approach enables the computation of uniquely defined impedances to ground and transfer impedances at arbitrary points at the grounding electrodes (required for N -port representation) by simple matrix manipulations. The proposed approach is general since it allows for a rigorous full-wave and an approximate quasi-static modeling, depending on the choice of Green's functions.

Electromagnetic modes and resonances of two-dimensional bodies

The electromagnetic modes and the resonances of homogeneous, finite size, two-dimensional bodies are examined in the frequency domain by a rigorous full wave approach based on an integro-differential formulation of the electromagnetic scattering problem. Using a modal expansion for the current density that disentangles the geometric and material properties of the body the integro-differential equation for the induced surface (free or polarization) current density field is solved. The current modes and the corresponding resonant values of the surface conductivity (eigen-conductivities) are evaluated by solving a linear eigenvalue problem with a non-Hermitian operator. They are inherent properties of the body geometry and do not depend on the body material. The material only determines the coefficients of the modal expansion and hence the frequencies at which their amplitudes are maximum (resonance frequencies). The eigen-conductivities and the current modes are studied in detail as the frequency, the shape and the size of the body vary. Open and closed surfaces are considered. The presence of vortex current modes, in addition to the source-sink current modes (no whirling modes), which characterize plasmonic oscillations, is shown. Important topological features of the current modes, such as the number of sources and sinks, the number of vortexes, the direction of the vortexes are preserved as the size of the body and the frequency vary. Unlike the source-sink current modes, in open surfaces the vortex current modes can be resonantly excited only in materials with positive imaginary part of the surface conductivity. Eventually, as examples, the scattering by two-dimensional bodies with either positive or negative imaginary part of the surface conductivity is analyzed and the contributions of the different modes are examined.

Rigorous Full-Wave Resistance and Inductance Computation of 3-D Interconnects

A full-wave technique to rigorously extract the resistance and the inductance of 3-D interconnects is proposed. A novel and full 3-D differential surface admittance operator and a boundary integral equation approach are combined in a circuit interpretation which provides a simple way to evaluate the characteristics of the interconnects. The method is accurate for various examples over a broad frequency range, thus conforming its appositeness for the modeling of 3-D interconnects.

Rigorous full-wave calculation of optical forces on dielectric and metallic microparticles immersed in a vector Airy beam.

Based on the generalized Lorenz-Mie theory and the Maxwell stress tensor approach we present the first rigorous full-wave solution of the optical forces acting on spherical microparticles immersed in a two-dimensional vector Airy beam beyond the paraxial approximation. The critical aspect lies in evaluating efficiently and accurately the partial wave expansion coefficients of the incident Airy beam, which are achieved by using the vector angular spectrum representation for a variety of polarizations. The optical field distributions are then simulated to show the self-accelerating and self-healing effects of the Airy beam. The dielectric and gold microparticles are shown to be trapped within the main lobe or the nearby side-lobes mostly by the transverse gradient optical force while driven forward along the parabolic trajectory of the Airy beam by the longitudinal scattering force. It is thus demonstrated theoretically that the vector Airy beam has the capability of precisely transporting both dielectric and metallic microparticles along the prespecified curved paths.

A Rigorous Approach for the Modeling of Through-Silicon-Via Pairs Using Multipole Expansions

This paper presents a novel multipole expansion method for the rigorous analysis of wave propagation along a through-silicon-via (TSV) pair. TSV models are often constructed using equivalent circuits under the assumption that the interfaces between different media are equipotential. In comparison with that, the proposed method is a rigorous full-wave solution of the propagation mode. It takes advantage of cylindrical wave expansion functions and matches the boundary conditions at both the metal-to-insulator and insulator-to-silicon interfaces exactly. The method is validated against a full-wave finite-element method solver, and analysis examples using the method are demonstrated in a frequency range up to 100 GHz.

Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem

Rapid development of computers allows for application of the direct numerical solution of the global electromagnetic resonance problem in the Earth-ionosphere cavity. Direct numerical solutions exploit the cavity models with the given conductivity profile of atmosphere such as exponential or the knee profiles. These profiles are usually derived from the knee model by Mushtak and Williams (2002) developed for obtaining the realistic ELF propagation constant. It is usually forgotten that profiles of the knee model are only a convenient approximate interpretation for the heuristic relations used in computations. We demonstrate that the rigorous full wave solution of the electromagnetic problem for such profiles deviates from that obtained in the knee model. Therefore the direct numerical solutions must also depart from the heuristic one. We evaluate deviations of the heuristic knee model data from those pertinent to equivalent profile of atmospheric conductivity.

Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere

In this work, the electromagnetic scattering in general rotationally symmetric inhomogeneous anisotropic spheres is investigated. A rigorous full-wave solution is presented based on the volume integral equation. The solution is achieved by expanding the unknown fields in fully orthogonal Dini-type spherical vector wave functions. This formulation allows the study of general rotationally symmetric gyrotropic spheres with varying permittivity and permeability tensors. We investigate the validity of the developed method, which is next applied on the computation of the scattering cross sections of inhomogeneous rotationally symmetric gyroelectric and gyromagnetic spheres.

Rigorous Full-Wave Analysis of Rectangular Microstrip Patch Antenna on Suspended and Composite Substrates

In this paper, Galerkin's method in the Fourier transform domain is applied to the determination of the resonant frequencies and half-power bandwidth of rectangular microstrip patch on composite and suspended substrates. Using Galerkin's method in solving the integral equation numerically, the complex resonant frequency of the microstrip antenna on suspended and composite substrates is studied with sinusoidal functions as basis functions, which show fast numerical convergence. The validity of the solution is tested by comparison of the computed results with experimental data. Finally, numerical results for the effects of suspended and composite substrates on the resonant frequency and half-power bandwidth are also presented.

A New Agile Radiating System Called Electromagnetic Band Gap Matrix Antenna

Civil and military applications are increasingly in need for agile antenna devices which respond to wireless telecommunications, radars, and electronic warfare requirements. The objective of this paper is to design a new agile antenna system called electromagnetic band gap (EBG) matrix. The working principle of this antenna is based on the radiating aperture theory and constitutes the subject of an accepted CNRS patent. In order to highlight the interest and the originality of this antenna, we present a comparison between it and a classical patch array only for the (one-dimensional) 1D configuration by using a rigorous full wave simulation (CST Microwave software). In addition, EBG matrix antenna can be controlled by specific synthesis algorithms. These algorithms use inside their; optimization loop an analysis procedure to evaluate the radiation pattern. The analysis procedure is described and validated at the end of this paper.

Strong coupling between plasmonic Fabry–Pérot cavity mode and magnetic plasmon

We demonstrate strong coupling between the Fabry-Pérot cavity plasmons and magnetic nanowire plasmons. The strong coupling leads to drastic enhancement of magnetic field intensity beneath a silver nanowire inside a metallic cavity. A Rabi splitting of 280 meV and a magnetic field intensity enhancement of 845 times the incident is achieved using the proposed geometry. The theoretical prediction agrees well with rigorous full wave simulations. The effect provides efficient tools for applications such as magnetic nonlinearity and magnetic sensors.

Electromagnetic Wave Propagation in Body Area Networks Using the Finite-Difference-Time-Domain Method

A rigorous full-wave solution, via the Finite-Difference-Time-Domain (FDTD) method, is performed in an attempt to obtain realistic communication channel models for on-body wireless transmission in Body-Area-Networks (BANs), which are local data networks using the human body as a propagation medium. The problem of modeling the coupling between body mounted antennas is often not amenable to attack by hybrid techniques owing to the complex nature of the human body. For instance, the time-domain Green's function approach becomes more involved when the antennas are not conformal. Furthermore, the human body is irregular in shape and has dispersion properties that are unique. One consequence of this is that we must resort to modeling the antenna network mounted on the body in its entirety, and the number of degrees of freedom (DoFs) can be on the order of billions. Even so, this type of problem can still be modeled by employing a parallel version of the FDTD algorithm running on a cluster. Lastly, we note that the results of rigorous simulation of BANs can serve as benchmarks for comparison with the abundance of measurement data.

Fast Full-Wave Solution That Eliminates the Low-Frequency Breakdown Problem in a Reduced System of Order One

Full-wave solutions of Maxwell's equations break down at low frequencies. Existing methods for solving this problem either are inaccurate or incur additional computational cost. In this paper, a fast full-wave finite-element-based solution is developed to eliminate the low-frequency breakdown problem in a reduced system of order one. It is applicable to general 3-D problems involving ideal conductors as well as nonideal conductors immersed in inhomogeneous, lossless, lossy, and dispersive materials. The proposed method retains the rigor of a theoretically rigorous full-wave solution recently developed for solving the low-frequency breakdown problem, while eliminating the need for an eigenvalue solution. Instead of introducing additional computational cost to fix the low-frequency breakdown problem, the proposed method significantly speeds up the low-frequency computation.

DRIVING A DIELECTRIC CYLINDRICAL PARTICLE WITH A ONE DIMENSIONAL AIRY BEAM: A RIGOROUS FULL WAVE SOLUTION

We present a rigorous full wave calculation of the optical force on a dielectric cylindrical particle of an arbitrary size under the illumination of one dimensional (1D) Airy beam. The radiation force is written in terms of the cylindrical partial wave expansion coe-cients of the non-paraxial 1D Airy beams. Our simulation results demonstrate that an Airy beam can accelerate the microparticles along its parabolic trajectory, while transverse to which the particles are trapped at the center of its main lobe, corroborating the possibility of the long distance particle transport by means of an Airy beam.

Efficient Analysis of Complex FSS Structure Using the WCIP Method

A rigorous full wave technique based on the Transverse Wave Concept Iterative Procedure (WCIP) is used to design a complex Frequency Selective Surface (FSS). These surfaces include a periodically arrangement of identical circuit. There are used as filters and reflector antenna as well as deep-space exploration for multi-frequencies operations. A simple FSS structure is studied in first stage to validate our approach. In second stage two different complex structures are studied. The good agreement between simulated and published data justify the design procedure.

Graded index photonic hole: Analytical and rigorous full wave solution

We present a rigorous full wave approach to the omnidirectional photonic hole (PH), an optical system inspired by celestial phenomena and characterized by a radially graded refractive index $n(r)\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}/2}$. It is analytically demonstrated that light capture is effective for $\ensuremath{\alpha}\ensuremath{\ge}{\ensuremath{\alpha}}_{c}=2$. Our analyses are corroborated by precise numerical simulations of steady-state and time-evolution behaviors. The simulations indicate that the optical energy entering the PH system can be kept in captivity for a time duration ${t}_{d}$ scaling as ${t}_{d}\ensuremath{\sim}1/({\ensuremath{\alpha}}_{c}\ensuremath{-}\ensuremath{\alpha})$ when $\ensuremath{\alpha}$ approaches ${\ensuremath{\alpha}}_{c}$. A crucial difference in the time evolution of fields is shown between the cases with $\ensuremath{\alpha}$ close to and equal to ${\ensuremath{\alpha}}_{c}$.

A Theoretically Rigorous Full-Wave Finite-Element-Based Solution of Maxwell's Equations From dc to High Frequencies

It has been observed that finite element based solutions of full-wave Maxwell's equations break down at low frequencies. In this paper, we present a theoretically rigorous method to fundamentally eliminate the low-frequency breakdown problem. The key idea of this method is that the original frequency-dependent deterministic problem can be rigorously solved from a generalized eigenvalue problem that is frequency independent. In addition, we found that the zero eigenvalues of the generalized eigenvalue problem cannot be obtained as zeros because of finite machine precision. We hence correct the inexact zero eigenvalues to be exact zeros. The validity and accuracy of the proposed method have been demonstrated by the analysis of both lossless and lossy problems having on-chip circuit dimensions from dc to high frequencies. The proposed method is applicable to any frequency. Hence it constitutes a universal solution of Maxwell's equations in a full electromagnetic spectrum. The proposed method can be used to not only fundamentally eliminate the low-frequency breakdown problem, but also benchmark the accuracy of existing electromagnetic solvers at low frequencies including static solvers. Such a benchmark does not exist yet because full-wave solvers break down while static solvers involve theoretical approximations.

ERROR ANALYSIS OF A TWO-LAYER METHOD FOR THE ELECTROMAGNETIC CHARACTERIZATION OF CONDUCTOR-BACKED ABSORBING MATERIAL USING AN OPEN-ENDED WAVEGUIDE PROBE

A two-layer nondestructive method for characterizing the electric and magnetic properties of lossy conductor-backed magnetic materials using a ∞anged rectangular-waveguide probe is examined. The two re∞ection measurements necessary to determine both permittivity and permeability are made by flrst applying the probe to the material under test and then applying the probe to a known-material layer placed on top of the material under test. The theoretical re∞ection coe-cient is obtained using a rigorous full-wave solution, and an extrapolation scheme is used to minimize the error due to truncating the modal expansion of the waveguide flelds. An error analysis is performed to compare the performance of the technique to the two-thickness method, which utilizes two difierent thicknesses of the material under test. The properties of the known material layer that result in the least error due to network analyzer uncertainty are determined. The sensitivity of the two-layer method is also explored and discussed.