Total-field/scattered-field Research Articles

Analytic Fields With Higher-Order Compensations for 3-D FDTD TF/SF Formulation With Application to Beam Excitations

The total-field/scattered-field (TF/SF) formulation is widely used to initiate incident waves for scattering problems in finite-difference time-domain (FDTD) simulations. An important aspect of the TF/SF formulation is the calculation of incident fields at the TF/SF boundary by methods that account for the numerical nature of the incident wave in the FDTD grid. Failure to do so can lead to high levels of field leakage errors across the TF/SF boundary. This paper presents an improved analytic time-domain method for accurately computing incident fields in the TF/SF formulation. Using analytic field expressions with higher-order dispersion and polarization compensations, the proposed method compensates for 1) the FDTD numerical dispersion; and 2) the lack of orthogonality between the frequency-dependent field polarizations and the wavevector, which was not accounted for in existing analytic time-domain methods. The higher-order compensations result in further suppression of field leakage errors in the SF region. In addition to exciting a plane wave, the proposed method can be employed to excite an incident beam. To demonstrate this, numerical experiments that source both 3-D plane wave and focused beam into a free space FDTD grid are presented and compared with existing methods.

Using a Two-Step Finite-Difference Time-Domain Method to Analyze Lightning-Induced Voltages on Transmission Lines

A novel high-efficient two-step finite-difference time-domain (FDTD) method is proposed to analyze the lightning-induced voltages on transmission lines (TLs) in this paper. The proposed method includes two steps. The first step is to calculate, using the 2-D FDTD method, electromagnetic fields that are radiated from a vertical lightning channel and illuminate the nearby TLs. The second step is to calculate, using the 3-D FDTD method, the electromagnetic response of the TL that is illuminated by the incident electromagnetic fields added at the total field-scattered field connecting the boundary of the 3-D space. To validate the proposed two-step FDTD method, the results calculated using the two-step FDTD method are compared with those calculated with Agrawal coupling model, and with those calculated using the 3-D FDTD method. The two-step FDTD method shows high computational efficiency in analyzing lightning-induced voltages on TLs.

Enhanced Total-Field/Scattered-Field Technique for Isotropic-Dispersion FDTD Scheme

A new total-field/scattered-field (TF/SF) technique is proposed for the isotropic-dispersion finite difference time domain (ID-FDTD) scheme. The proposed technique does not calculate incident fields on the TF/SF boundary by using a one-dimensional (1D) FDTD scheme as is used in the conventional technique or by using a fast Fourier transform (FFT) algorithm such as is used in the analytic field propagation (AFP) method, but proceeds instead by using an analytic expression of the incident field. Hence, the proposed technique does not require the interpolation procedure that must be used to simulate an oblique incident wave in the conventional technique. To verify the effectiveness of the proposed technique, the quality of the plane waves excited by the proposed and conventional techniques are compared and discussed. Also, the accuracy of the proposed method is numerically shown in a scattering problem.

Rigorous interference and diffraction analysis of diffractive optic elements using the finite-difference time-domain method

The Finite-Difference Time-Domain (FDTD) method has proven to be a useful tool to analyze electromagnetic scattering phenomena. In this work, the FDTD method is applied at optical wavelengths. More precisely, we present the results obtained using the FDTD algorithm to simulate the performance of optical devices such as volume diffraction gratings. The Perfectly Matched Layers (PML), Total-Field Scattered-Field formulation (TF/SF) and Near-Field to Far-Field transformation (NF/FF) are some add-ons included in order to correctly calculate the far field distribution obtained from the numerical near-field values computed in the simulation region. These values in the near-field region are computed by illuminating the grating with of a plane wave at the Bragg angle of incidence. In addition, we compare the results obtained by the FDTD method to those obtained using the Rigorous Coupled Wave Theory (RCWT) applied to diffraction gratings. As will be seen in this paper there is good agreement between the two approaches, thus validating our FDTD implementation.

FDTD Discrete Planewave (FDTD-DPW) Formulation for a Perfectly Matched Source in TFSF Simulations

A technique is proposed for the generation of planewaves in the total-field scattered-field (TFSF) formulation of the FDTD method. The method is developed using the 1D properties of a planewave and optimized projection of the 3D finite difference operators to the 1D domain. The result is an efficient and accurate planewave source that can be propagated on six 1D grids concurrent with the main simulation, and that is perfectly matched to the main 2D/3D FDTD domain for any source function. Numerical simulations show that the technique is valid for any angle of propagation, and for any gridcell aspect ratio, with non-physical reflections in the scattered field domain on the order of machine precision (-300 dB).

Optimized Analytic Field Propagator (O-AFP) for Plane Wave Injection in FDTD Simulations

Optimizations are proposed for the original frequency domain analytic field propagator (AFP) to source plane waves in a 1D/2D/3D total-field scattered-field (TF/SF) FDTD formulation. The proposed technique essentially produces no field leakage error (limited by-300 dB machine precision error) with finite sampling points dictated by temporal aliasing constraints. By taking advantage of the inherent 1D nature of a plane wave, the memory requirements for the original AFP are reduced significantly. The proposed optimized solution (O-AFP) greatly reduces the computational complexity by calculating a number of spatial fields of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) rather than <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), which then makes the technique practical enough to include fully 3D simulations.

FDTD scattered field formulation for scatterers in stratified dispersive media

We introduce a simple scattered field (SF) technique that enables finite difference time domain (FDTD) modeling of light scattering from dispersive objects residing in stratified dispersive media. The introduced SF technique is verified against the total field scattered field (TFSF) technique. As an application example, we study surface plasmon polariton enhanced light transmission through a 100 nm wide slit in a silver film.

Optical waveguide grating couplers: 2nd-order and 4th-order finite-difference time-domain analysis

Output optical waveguide grating couplers are rigorously analyzed using the 2-order and the 4-order finite-difference time-domain (FDTD) method in conjunction with the total field/scattered field (TF-SF) approach and special averaging and regularization techniques for the mitigation of permittivity discontinuities. Volume-holographic and surface-relief grating couplers are analyzed for both TE and TM polarizations. The 2- and 4-order FDTD results are compared in terms of computational efficiency and accuracy. In addition, the FDTD results are compared to the approximate ones obtained by the rigorous coupled-wave analysis in conjunction with the leaky modes.

Excitation of Plane Waves for FDTD Analysis of Anisotropic Layered Media

The use of total-field/scattered-field (TF/SF) technique to excite plane waves is extended to anisotropic layered media. A split-field form one-dimensional (1-D) auxiliary finite-difference time-domain (FDTD) method is proposed to generate the incident fields required by total-field/scattered-field technique. The use of split-field technique enables the separate discretization of the field components that propagate in the direction either parallel with or perpendicular to the planar interface during the derivation of 1-D auxiliary FDTD. Simulation results show that maximum leakage errors into the scattered-field region are in the order of -44.6 dB less than the maximum incident field at 30deg incidence for a three-layered medium. The method is proved to be effective for the introduction of plane waves for the FDTD analysis of anisotropic layered media.

Analysis of Scattering from Multiple Objects by the Finite-Difference Frequency-Domain Method With an Iteration-Free Multiregion Technique

An iteration-free multiregion (IFMR) technique was proposed and applied to finite-difference frequency-domain (FDFD) analysis of electromagnetic scattering from multiple objects in open space. The entire computational domain is divided into several small subdomains. The mutual coupling effect among subdomains is introduced through combining total-field/scattered-field (TF/SF) formulation and mode series of scattered field. The final matrix equation is a Schur complement system, so the computation for each subdomain is relatively independent. The numerical results obtained by the FDFD method with IFMR are in a good agreement with those by the full-domain FDFD method, but both the amount of unknowns and the computational time are reduced. Additionally, compared to the iterative process based on multiple scattering, the computational time is reduced, and the truncation error of the iteration is avoided, as IFMR is the limit of the iterative process.

Generation of an incident focused light pulse in FDTD.

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is introduced into the FDTD simulation grid using the total-field/scattered-field (TF/SF) approach. The accuracy of our results is demonstrated by comparison with exact theoretical formulas.

A Nearly Perfect Total-Field/Scattered-Field Boundary for the One-Dimensional CIP Method

A total-field/scattered-field (TF/SF) boundary which is commonly used in the finite-difference time-domain (FDTD) method to illuminate scatterers by plane waves, is developed for use in the constrained interpolation profile (CIP) method. By taking the numerical dispersion into account, the nearly perfect TF/SF boundary can be achieved, which allows us to calculate incident fields containing high frequency components without fictitious scattered fields. First of all, we formulate the TF/SF boundary in the CIP scheme. The numerical dispersion relation is then reviewed. Finally the numerical dispersion is implemented in the TF/SF boundary to estimate deformed incident fields. The performance of the nearly perfect TF/SF boundary is examined by measuring leaked fields in the SF region, and the proposed method drastically diminish the leakage compared with the simple TF/SF boundary.

Mathematical simulation of nonlinear waveguiding systems based on 2D photonic crystals

A mathematical model of nonlinear two-dimensional waveguiding systems based on photonic crystals was constructed using the finite-difference time-domain method (FDTD), the total field/scattered field (TF/SF) method, and the perfectly matched layer method (PML). The constructed numerical algorithm can also be used for investigation of other two-dimensional waveguiding systems. The results of simulating the elements of particular waveguiding systems are presented.

New scheme for introducing an oblique incidence plane wave to layered media in finite-difference time-domain

In the application of two-dimensional finite-difference time-domain (2D-FDTD) method to the analysis of scattering by an object embedded in layered media，the obliquely incident wave along the total field-scattered field (TF-SF) contains the incidence pulse and the reflected and multiple-reflected wave，which can not be introduced by use of the traditional method. To solve this problem，a hybrid scheme using different ways to treat the four TF-SF boundaries is presented. The modified 1D-FDTD including oblique incidence angle is used to treat the longitudinal side boundaries，which can produce the reflected and multiple-reflected wave to layered interface automatically. The longitudinal side boundaries are extended downwards，such that the TF-SF lower boundary is located in the perfectly matched layer (PML) completely，thus the transmission wave and scattered wave are both outward-going waves in the lowest PML layer，and are absorbed by PML. The TF-SF upper boundary is located in free space; the incidence wave along it is in fact a properly time-delayed duplication of the waveform at the corner of TF-SF upper longitudinal boundary. The computational results show the reliability and applicability of the presented hybrid scheme.

ANALYSIS OF TF-SF BOUNDARY FOR 2D-FDTD WITH PLANE P-WAVE PROPAGATION IN LAYERED DISPERSIVE AND LOSSY MEDIA

In the application of two-dimension (2D) finite-difference time-domain (FDTD) to scattering analysis of object embedded in layered media, the incident electromagnetic wave propagation is much more complicated, it can not inject the plane wave source by traditional method. To solve this problem, the Π-shape total-field/scattering- field (TF-SF) boundary scheme is presented. The side TF-SF boundaries are governed by the modified 1D Maxwell's equations, but the discretization for which to p-wave is more difficult than n- wave. Then an auxiliary magnetic variable is used, which can develop the modified 1D-FDTD to p-wave without any approximately. To truncate the modified 1D-FDTD, the convolutional perfectly matched layer (CPML) absorbing boundary condition (ABC) is also given. Examples showthe feasibility and applicability of proposed Π-shape TF/SF boundaries scheme.

A Total-Field/Scattered-Field Plane-Wave Source for the FDTD Analysis of Layered Media

A total-field/scattered-field (TF/SF) plane-wave source is developed for the finite-difference time-domain analysis of general (possibly lossy) planar layered media. A 1-D auxiliary grid is created to generate the incident field in the presence of the layered medium. Inhomogeneous plane waves are also allowed for lossless layers and narrowband excitation.

Longitudinal gradient coil optimization in the presence of transient eddy currents

The switching of magnetic field gradient coils in magnetic resonance imaging (MRI) inevitably induces transient eddy currents in conducting system components, such as the cryostat vessel. These secondary currents degrade the spatial and temporal performance of the gradient coils, and compensation methods are commonly employed to correct for these distortions. This theoretical study shows that by incorporating the eddy currents into the coil optimization process, it is possible to modify a gradient coil design so that the fields created by the coil and the eddy currents combine together to generate a spatially homogeneous gradient that follows the input pulse. Shielded and unshielded longitudinal gradient coils are used to exemplify this novel approach. To assist in the evaluation of transient eddy currents induced within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using the total-field scattered-field (TFSF) scheme was performed. The simulations demonstrate the effectiveness of the proposed method for optimizing longitudinal gradient fields while taking into account the spatial and temporal behavior of the eddy currents.

TF/SF Boundary and PML–ABC for an Unconditionally Stable FDTD Method

This letter proposes a total-field/scattered-field (TF/SF) formulation and perfectly matched layer (PML) absorbing boundary condition for the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials (WLPs). This approach provides the computational flexibility in electromagnetic scattering and improved performance yet maintains unconditional stable. Numerical results show the TF/SF connecting boundary and PML are effective in the WLP-FDTD method for scattering

Coupled Field Inside Shielding Enclosure With an Aperture Due to Nearby Lightning

Due to a nearby lightning return stroke, the coupled electromagnetic (EM) fields inside a rectangular shielding enclosure, on the finitely conducting ground, with an aperture in one wall are calculated numerically by using the finite-difference time-domain (FDTD) method. First, the near fields generated by the return stroke are obtained in two-dimensional (2-D) cylindrical coordinates by the FDTD method. Then, the coupled fields inside a rectangular shielding enclosure are calculated in three-dimensional (3-D) rectangular coordinates through the total field-scattered field connecting boundary, with the sources obtained by coordinates transformations of the return stroke near fields

Application of the finite-difference time-domain method and total-field/scattered field formulation to scattering phenomena in solids

The finite-difference time-domain (FDTD) numerical method has the unique characteristic that it can separately calculate the far-field scattered waves and near-field total waves at the same time, where total waves refer to a mixture of incident plane waves and scattered waves. This formulation is called the total-field/scattered-field (TF/SF) formulation and is very effective for the analysis of scattering problems in nondestructive evaluation (NDE). In this report, a TF/SF formulation of the elastic wave fields in solids is described. Specifically, scalar and vector potentials are used for the formulation. Using these potentials is beneficial for two reasons. First, the longitudinal waves and shear waves are initially separated. Therefore, the scattering phenomenon can be clearly recognized. Second, it is facile to use the potentials for setting the absorbing boundaries. The FDTD TF/SF formulation using potentials has been proved effective in the analysis of the scattering of a longitudinal plane wave incident to a square hole.