Total-field/scattered-field Research Articles

Wide-Angle Elimination of TF/SF-Generated Spurious Waves in the Nonstandard FDTD Technique

In the radar-cross section (RCS) analysis of electrically large objects via the nonstandard finite-difference time-domain method, spurious reflection or scattering waves arise from the total-field/scattered-field (TF/SF) separation surface. To suppress such waves, a novel TF/SF separation scheme with a multilayered structure for the suitable assumed-known incident-field calculations, is proposed. The scheme, which uses two adjustable parameters, is numerically verified and found to attain a drastic reduction of the spurious scattered field over a wide-angle regime, unlike previous TF/SF approaches, which is necessary for accurate RCS studies.

Dispersion optimised plane wave sources for scattering analysis with integral based high order finite difference time domain methods

The implementation of plane wave incidence using the total-field/scattered-field (TFSF) formulation for a three-dimensional finite volumes-based, extended-stencil finite-difference time-domain (FV24) algorithm is presented. This achievement required designing an auxiliary one-dimensional grid with the characteristics of (i) co-located electric field components uniformly spaced from co-located magnetic field components, (ii) grid spacing that dynamically changes with desired angles of propagation to eliminate the need for field interpolations when mapping the plane wave to the main grid, (iii) update equations that precisely match the numerical dispersion characteristics of the main FV24 algorithm, and (iv) auxiliary to main grid field mapping that encompasses six parallel surfaces along the TFSF boundary to satisfy the extended cell nature of the main FV24 algorithm. The resulting non-physical field leakage into the scattered-field region is observed to be independent of angle of incidence and has a −300 dB noise floor. This technique extends the high-order FV24 capabilities to include accurate and efficient simulations of electrically large scatterers using relatively low grid densities, bringing this capability to today's desk-side workstations.

Implementation of TF/SF boundary for unconditionally stable five-step LOD-FDTD method

The implementation of total-field/scattered-field (TF/SF) boundary for the unconditionally stable five-step locally one-dimensional finite-difference time-domain (LOD5-FDTD) method is proposed in this paper. There are 12 cases to be considered for each sub step, among them 8 cases for electric field grid points, based on the computational formulations and the particular location of grid points at the TF/SF face. Numerical results show that the plane wave can be successfully introduced into the TF region and maintains unconditional stabilization. Finally, the radar cross section (RCS) of a metal plate is computed, which further verifies the effectiveness of the proposed TF/SF connecting boundary.

An Enhanced Total-Field/Scattered-Field Scheme for the 3-D Nonstandard Finite-Difference Time-Domain Method

The nonstandard finite-difference time-domain (NS-FDTD) method exhibits high accuracy at fixed frequencies, and, thus, proves to be a powerful means of the radar cross section analysis of scattering objects with complex shapes and materials. To this aim, significant enhancement can be pursued in its combination with the FDTD total-field/scattered-field (TF/SF) concept. However, the principal implementation characteristics of the latter in the NS-FDTD technique have yet to be elaborately studied, especially for electrically large domains or structures. Hence, in this paper, a new advanced TF/SF scheme for the 3-D NS-FDTD algorithm is developed and fully validated. Numerical results reveal that the proposed method, considering the features of the NS-FDTD operators, is far more efficient and versatile than the original FDTD one.

Electromagnetic metamaterial simulations using a GPU-accelerated FDTD method

Metamaterials composed of artificial subwavelength structures exhibit extraordinary properties that cannot be found in nature. Designing artificial structures having exceptional properties plays a pivotal role in current metamaterial research. We present a new numerical simulation scheme for metamaterial research. The scheme is based on a graphic processing unit (GPU)-accelerated finite-difference time-domain (FDTD) method. The FDTD computation can be significantly accelerated when GPUs are used instead of only central processing units (CPUs). We explain how the fast FDTD simulation of large-scale metamaterials can be achieved through communication optimization in a heterogeneous CPU/GPU-based computer cluster. Our method also includes various advanced FDTD techniques: the non-uniform grid technique, the total-field/scattered-field (TFSF) technique, the auxiliary field technique for dispersive materials, the running discrete Fourier transform, and the complex structure setting. We demonstrate the power of our new FDTD simulation scheme by simulating the negative refraction of light in a coaxial waveguide metamaterial.

UPML‐ABC and TF/SF boundary for unconditionally stable AH‐FDTD method in conductive medium

For analysing the scattering problem in conductive medium with the new unconditionally stable associated Hermite (AH) finite-difference time-domain (FDTD) method, the formulation of uniaxial anisotropic perfectly matched layer absorbing boundary condition (UPML-ABC) and the total-field/scattered-field (TF/SF) implementation scheme are deduced. By virtue of AH differential transformation matrix and the eigenvalue transformation, frequency-dependent parameters of the lossy medium can be well treated in AH-UPML, without using any additional auxiliary variables. Numerical verification for the scattering of buried conductor in lossy half-space is performed. Compared with Mur's ABC, UPML increases the absorbing performance by more than 80 dB in AH-FDTD analysis.

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme**Project supported by the National Natural Science Foundation of China (Grant Nos. 61331007 and 61471105).

An efficient conformal locally one-dimensional finite-difference time-domain (LOD-CFDTD) method is presented for solving two-dimensional (2D) electromagnetic (EM) scattering problems. The formulation for the 2D transverse-electric (TE) case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit (ADI) CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field (TF/SF) boundary and the perfectly matched layer (PML), the radar cross section (RCS) of two 2D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

Estimation of Radar Cross-Section in Rayleigh, MIE, and Optical Regions by the 2-D-FDTD Simulation

In this paper, the far-field electromagnetic fields were calculated by using near-field/far-field (NF/FF) transformation technique from the near field finite-difference time domain (FDTD) data obtained by total field/scattering field (TF/SF) formulation. To evaluate the effectiveness of scattering mechanisms depending on the frequency used, the target geometry and the electrical properties, first of all simple shapes such as a square cylinder, a circular cylinder, and an equilateral triangle, were studied. It has been shown that the radar cross section (RCS) calculations can be done in Rayleigh, Mie, and optical regions by the 2-D FDTD simulation. Finally, the RCS behavior of an aircraft model composed of simple shapes as ellipse and triangle are investigated for different illuminations and different frequencies.

Application of the discrete Green's function-based antenna simulations for excitation of the total-field/scattered-field interface in the FDTD method

In this article, the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) method is proposed for simulation of wire antennas irradiating inhomogeneous dielectric scatterers. Surface equivalence theorem in the discrete domain is used to separate the problem into an inhomogeneous domain and a wire antenna that are simulated with the use of FDTD and DGF-FDTD, respectively. Then, the excitation of the total-field/scattered-field (TFSF) interface within the FDTD domain is computed as a convolution of antenna currents with DGF. Such a radiation is compatible with the grid and can excite the FDTD domain without the erroneous field leakage across the TFSF interface. The developed method is illustrated by canonical problems involving wire antennas that irradiate scatterers. If the DGF length is equal to the number of iterations in a simulation, the developed method perfectly introduces irradiation from wire antennas into the TFSF FDTD domain (assuming infinite numerical precision of computations). © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1949–1953, 2014

Application of Symplectic Partitioned Runge-Kutta Method and Total-Field Scattered-Field Formulation to Simulation of GPR Data

The second-order Lobatto IIIA-IIIB symplectic partitioned RungeKutta (SPRK) method, combining with the first-order Mur absorbing boundary condition, is developed for the simulation of ground penetrating radar wave propagation in layered pavement structure. For 2-dimetional case, a significant advantage of this method is that only two functions need to be calculated at each time step. The total-field/scattered-field technique is used for plane wave excitation. Numerical examples are presented to verify the accuracy and efficiency of the proposed algorithm. The results illustrate that the reflected signal calculated by the SPRK method is in good agreement with that obtained using the finite difference time domain (FDTD) scheme, but the CPU time consumed by proposed algorithm is reduce about 20% of the FDTD scheme. In addition, an actual field test is conducted to evaluate the further performance of the SPRK method. It is found that the simulated waveform fits well with the measured signal in many aspects, especially in the peak amplitude and time delay.

Analytical Expression for the Time-Domain Discrete Green's Function of a Plane Wave Propagating in the 2-D FDTD Grid

In this letter, a new closed-form expression for the time-domain discrete Green's function (DGF) of a plane wave propagating in the 2-D finite-difference time-domain (FDTD) grid is derived. For the sake of its verification, the time-domain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2-D total-field/scattered-field (TFSF) FDTD simulations. Such an implementation of AFP requires computations of time-domain DGF for the plane wave with the use of multiple-precision arithmetic. Then, excitations at the TFSF interface can be computed as a time-domain convolution of a source function with DGF. The developed time-domain implementation of AFP demonstrates the leakage error across the TFSF interface around the numerical noise level that validates the correctness of the DGF derivation.

FDTD Application of Targets Electromagnetic Scattering in Layered Space

Finite Difference Time Domain (FDTD) was used to characterize the electromagnetic scattering (EMS) for targets in layered space. A new set of 1D modified Maxwell equations and auxiliary equations with incident angle was derived from 2D Maxwell equations and was used to compute the electromagnetic field in vertical boundary in 2D total field-scattered field (TF/SF), and thus incidence of uniform plane wave in time domain can be directly realized. In order to avoid complex Somerfield integration, the reciprocity theorem was used to simplify an extrapolation algorithm. Then the proposed algorithm and program in this paper were validated by applying them to compute the electromagnetic scattered field for targets in half-space and the radiation field for line current in layered lossy space. Finally this algorithm was used to characterize EMS for a tunnel in multi-layered space, for a tunnel open to vehicle, and for a tunnel and vehicle in lossless layered space. The results show the vehicle has a great impact on the scattering field, and the layered media surrounded the target can shield the scattering field. DOI: http://dx.doi.org/10.11591/telkomnika.v11i12.3699 Full Text: PDF

Electromagnetic Scattering From 3-D Targets in a Random Medium Using Finite Difference Frequency Domain

In this paper a three-dimensional (3-D) numerical technique based on the finite difference frequency domain (FDFD) is implemented to calculate the scattering from arbitrary shaped objects embedded in a continuous random medium. The total field/scattered field (TF/SF) algorithm is integrated with the FDFD to minimize the memory consumption and speed up the calculations. For validation purposes, the radar cross-section of a 2-D conducting cylinder in random medium is calculated using the FDFD technique and compared to previously published data based on the current generator method. An upgrade to a 3-D solver was then inspired once the idea of using the multi-grid technique was introduced to accelerate the convergence rate of the BICGSTAB iterative solver. Thus, allowing the FDFD technique to become a robust method to solve the scattering problem from large targets embedded in random medium. Therefore, using the introduced simulating scheme, one can easily elucidate any scattering information out of real life targets surrounded by random environmental effects.

Rigorous analysis of axisymmetric transformation optics lenses embedded in layered media illuminated by obliquely incident plane waves

ABSTRACTA body of revolution, finite‐difference time‐domain (BOR‐FDTD) method is developed for rigorous analysis of axisymmetric transformation optics (TO) lens devices. For normal incidence, a one dimensional (1‐D) FDTD method based on the total‐field scattered‐field (TFSF) technique was proposed to model the propagation of a plane wave launched from the top of a layered medium in cylindrical coordinates. The 1‐D FDTD solutions were employed to efficiently inject normally incident plane waves into the BOR‐FDTD method. For oblique incidence, analytical formulations were derived and presented by expanding the plane wave into a series of cylindrical modes via Fourier series expansion of the ϕ‐dependent variables, which were then used to introduce obliquely incident plane waves into the TFSF formulas associated with the BOR‐FDTD method. These procedures allowed for accurate simulations of BOR TO lenses embedded in layered media illuminated by obliquely incident waves. The accuracy and efficiency of the proposed method were verified by comparing numerical results with either analytical solutions or a commercial software (COMSOL) package. Thereafter, the developed BOR‐FDTD code was utilized to study the imaging properties of (a) radial gradient‐index (GRIN) lenses with a parabolic index profile, (b) a flat TO GRIN lens, (c) a spherical Luneburg lens, and (d) a cylindrical TO Luneburg lens both in free space and on top of a substrate. Here the TO GRIN lenses were designed by using the quasi‐conformal transformation optics (QCTO) technique. It was found that the flat TO lens was able to provide identical focusing properties as a cemented doublet in both free space and over a dielectric substrate. Moreover, the numerical results demonstrated that the flattened TO Luneburg lens possessed the desired imaging properties under different illuminations for both polarizations.

Computation of tightly-focused laser beams in the FDTD method.

We demonstrate how a tightly-focused coherent TEMmn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field around the focus is decomposed into a plane-wave spectrum, and approximated by a finite number of plane waves injected into the FDTD grid using the total-field/scattered-field (TF/SF) method. We provide an error analysis, and guidelines for the discrete approximation. We analyze the scattering of the beam from layered spaces and individual scatterers. The described method should be useful for the simulation of confocal microscopy and optical data storage. An implementation of the method can be found in our free and open source FDTD software ("Angora").

Introduction of Oblique Incidence Plane Wave to Stratified Lossy Dispersive Media for FDTD Analysis

In the application of finite-difference time-domain (FDTD) method to the wideband plane wave scattering analysis of objects embedded in stratified lossy dispersive media, it is a challenge to solve the obliquely incident wave. In this work, a novel configuration of auxiliary one-dimensional (1-D) FDTD grids is proposed to provide the obliquely incident plane wave at the total-field scattered-field (TFSF) boundary in stratified lossy dispersive media. Thus a closed TFSF boundary is formed, where the incident waves are directly obtained from the auxiliary simulations without any interpolation. The formulations of the auxiliary simulations are presented by the modified 1-D Maxwell's equations. Given the dispersion characteristic, perfectly matched layer (PML) is implemented to the 1-D simulations. Examples demonstrate the effectiveness of the proposed technique of obliquely incident wave introduction.

A second-order scheme for Maxwell's equations with dielectric permittivity discontinuities and total field-scattered field boundaries

A finite volume scheme for numerical solution of Maxwell's equations in regions with dielectric permittivity discontinuities and total field-scattered field (TFSF) boundaries is proposed. The scheme is second-order accurate in space and time. The key idea is to choose stencils for approximation of derivatives used to increase the order of approximation so that they do not cross dielectric permittivity discontinuities or TFSF boundaries. Computational results verify second order of approximation of the proposed scheme.

A Total-Field/Scattered-Field Boundary for the Multi-Dimensional CIP Method

A total-field/scattered-field (TF/SF) boundary for the constrained interpolation profile (CIP) method is proposed for multi-dimensional electromagnetic problems. Incident fields are added to or subtracted from update equations in order to satisfy advection equations into which Maxwell's equations are reduced by means of the directional splitting. Modified incident fields are introduced to take into account electromagnetic fields after advection. The developed TF/SF boundary is examined numerically,and the results show that it operates with good performance. Finally, we apply the proposed TF/SF boundary to a scattering problem, and it can be solved successfully.

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order symplectic finite-difference time-domain (SFDTD) scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain (FDTD), the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to −300 dB.

Investigation of plasmonics resonance infrared bowtie metal antenna

An approximate resonance wavelength equation that varies with metal antenna structure size is developed to design a bowtie gold metal antenna working at near-infrared (IR) wavelength. Bowtie antenna structures with resonance wavelength of 1.06 μm, 1.55 μm and 10.6 μm are designed based on this equation. A finite-difference time domain (FDTD) algorithm with total field scattered field (TFSF) source simulation shows the resonance wavelength of the designed structures being precisely in agreement with the expected wavelengths from the equation. Planar integration of the metal bowtie antennas is discussed as well. Gold nanohole bowtie antenna arrays are fabricated and the near-field optical transmission properties of the nanohole array are investigated with a near-field scanning optical microscope (NSOM). Our experimental results verify the near-field optical transmission performance and further demonstrate that they are in agreement with the theoretical calculation results. The high enhancement efficiency and integration of the metal bowtie antennas open the possibility of a wide application in IR optoelectronics detection and imaging.