Total-field/scattered-field Research Articles

High-efficiency scattering field modeling in metallic components: a machine-learning-inspired approach

We present a highly efficient method for characterizing the scattering field distribution of surface plasmon polaritons in metallic components by combining the eXtended Pseudospectral Frequency-Domain (X-PSFD) method with an iterative, machine-learning-inspired procedure. Shifting away from traditional matrix operations, we utilize the “Adam” optimizer—an effective and swift machine learning algorithm—to solve the scattering field distribution. Our method encompasses the derivation of the associated cost function and gradient differentiation of the field, leveraging spectral accuracy at Legendre collocation points in the Helmholtz equation. We refine the total-field/scattered-field (TF/SF) formulation within the X-PSFD framework for optimized incident field management and employ Chebyshev–Lagrange interpolation polynomials for rapid, accurate computation of broad-band results. To ensure global accuracy, we introduce unique physical boundary conditions at subdomain interfaces. Demonstrating our method’s robustness and computational efficiency, we model perfect electric conductors (PECs) and silver nanocylinders, and we apply our approach to analyze the excited electric field on subtly distorted metallic surfaces, particularly plasmonic structures, thereby validating its wide-ranging effectiveness.

The Simulation of The Propagation of Electromagnetic Waves Through a Material with Various Thicknesses Using Finite Difference Time Domain (FDTD)

A finite difference time domain method in one dimension (1D-FDTD) is employed to study the properties of the propagation of electromagnetic waves across a medium with finite thicknesses. In this paper, we simulated the propagation of a Gaussian pulse. Since we simulated in one dimension, the absorbing boundary condition (ABC) can be applied to minimize undesirable reflection which generated at the numerical boundaries. We also implemented total field / scattering field (TF/SF) to ensure the source propagated in only one direction. The analysis performed by inserting the object with both relative permittivity and permeability values higher than one decreased the pulse’s amplitude.

Accurate modelling of the optics of high resolution liquid crystal devices: a reconfigurable liquid crystal grating

ABSTRACT An accurate method to model the optical behaviour of liquid crystal (LC) devices, particularly suited to devices where diffractive effects are present is described here. An accurate electromagnetic modelling programme that takes into account the full non-uniformity and anisotropy of the LC has been developed. This is combined with an existing in-house LC finite element modelling programme based on the Landau – De Gennes theory, that uses the order tensor representation of the LC orientation and allows an accurate descriptions of structures containing LC defects and small features. The electromagnetic model is based on the total field/scattered field (TF-SF) approach to electromagnetic scattering problems and is implemented using finite differences in the frequency domain (FDFD) in a form that can accommodate perfectly matched layers (PMLs) and periodic boundary conditions. The resultant matrix problem is solved efficiently using an especially adapted form of a sweeping preconditioner and the generalised minimum residual method (GMRes). This method has been implemented in 2D and is demonstrated here with the design and analysis of a reconfigurable blazed phase grating that utilises an LC defect to produce an abrupt fly-back, with the capability of short periods and high diffraction efficiency.

A time domain element differential method for solving electromagnetic wave scattering and radiation problems

In this paper, a simple and efficient numerical method named time domain element differential method (TD-EDM) is proposed to solve electromagnetic wave scattering and radiation problems. In the method, the governing equations as well as boundary conditions are directly solved in a strong-form formulation. The computational domain is discretized using isoparametric elements, and the spatial derivatives of basic variables appearing in the governing equations are calculated by a set of analytical expressions of partial derivatives of the element shape functions with respect to global coordinates, and time derivatives of the basic variable are computed using the Newmark time integration scheme. The absorbing boundary condition (ABC) is applied on the truncation boundary to absorb the outgoing waves, which realizes the numerical modeling of an open infinite region. The incident wave is induced in the total-field region by setting equivalent electromagnetic currents on the total-field/scattering-field (TF/SF) boundary. The TD-EDM equations at the nodes located near the total-field boundary are modified to satisfy the conditions that the electric field values of all nodes involved belong to either the total-field or the scattered field. The near-to-far-field transformation technique is used to calculate the far scattered field, and then the target's Radar Cross Section (RCS) is evaluated. Several numerical results including the radiation from a line current source and the target's Radar Cross Section (RCS) are given to validate correctness of the proposed method.

Incident Plane-Wave Source Formulations for Leapfrog Complying-Divergence Implicit FDTD Method

The commonly used unconditionally stable finite-difference time-domain (FDTD) methods such as alternating direction implicit (ADI)-FDTD, and its one-step formulation, leapfrog ADI-FDTD, have been found to violate the divergence condition of Gauss's law. The recently proposed leapfrog complying-divergence implicit (CDI)-FDTD not only addresses this problem, but also features many advantages, including unconditional stability, minimal floating-point operations and one-step leapfrog update. To further expand its application, this paper presents the incident plane-wave source formulations for leapfrog CDI-FDTD. Two stable and efficient formulations with different advantages are presented for introducing the far-zone plane-wave source into the FDTD problem space, namely, the scattered-field (SF) formulation and total-field / scattered field (TF/SF) formulation. To deal with the discontinuity and inconsistency across TF/SF boundaries, the fields on the boundaries need special treatments with careful modifications to ensure stability and proper plane-wave injection. Numerical results show that the incident fields can be effectively injected into the problem space with the stability of leapfrog CDI-FDTD maintained in both formulations. In addition, comparisons of radar cross sections computed using leapfrog CDI-FDTD, leapfrog ADI-FDTD and explicit FDTD with both SF and TF/SF formulations are presented. These demonstrate the advantages of leapfrog CDI-FDTD method in solving far-zone plane-wave source problems, including high efficiency, unconditional stability and complying divergence.

Enhanced light extraction from organic light emitting diodes using a flexible polymer-nanoparticle scattering layer

Efficient optical outcoupling from organic light emitting diodes (OLEDs) is an important challenge in solid state lighting technology. In this work, the effect of an external light extraction layer, prepared using polydimethylsiloxane (PDMS) and zinc oxide (ZnO) nanoparticles, was studied on the performance of red, green, blue and white OLEDs. The self-standing flexible film can effectively address the loss modes at the substrate-air interface. With the application of the layer, a maximum enhancement of about 80% in light outcoupling was observed in white OLEDs. Monochrome OLEDs also showed appreciable enhancement in emission with green having the highest improvement (102%), followed by red (56%) and blue (35%). Finite-difference time-domain (FDTD) simulations were performed for elucidating the mechanism behind the improvement in light extraction due to nanoparticle scattering layer. Total-Field Scattered-Field (TFSF) source was used to simulate the scattering cross-section for different wavelengths. Reduced Fresnel reflections at the air-glass interface and advantageous Mie scattering by ZnO nanoparticles seem to increase the optical outcoupling. This film could be a potential candidate for light extraction in OLEDs because of its facile fabrication, economical precursors, and adaptability to flexible substrates and absence of any possible optical artefacts to the emission.

Automated adaptive TFSF method for solving time domain Maxwell's equations

AbstractThe total field–scattered field (TFSF) formulation is quite popular for solving Maxwell's equations in finite difference time domain (FDTD) and finite volume time domain (FVTD) methods. Here a fixed TFSF interface around the scattering body is employed to separate the total field (TF) cells and scattered field (SF) cells. This interface is selected based on experience as it is assigned prior to the solution, and, therefore, the solution accuracy may not be optimal. In the present work, a novel automated adaptive total field–scattered field (ATFSF) method is proposed for accurately computing the electromagnetic scattering by complex‐shaped metal objects excited by an external plane wave. In the proposed method, an algorithm is devised to dynamically identify the TF cells and the SF cells, to be solved using TF and SF methods, respectively, using intensity of electromagnetic (EM) wave. The algorithm is tested in a 2‐D spectral volume time domain (SVTD) framework for solving electromagnetic scattering, and the predicted surface current/radar cross section is compared against the SF, TF, and the conventional TFSF methods. It is seen that the present method improves the solution accuracy significantly.

Adaptable Nonstandard FDTD Schemes for the Precise Evaluation of Electrostatic Fields

The reduction of the total computational overhead in the design of complex geometries, such as modern aircrafts, is a very challenging problem, particularly when electrostatic fields (ESF) for lightning protection, are considered. To this aim, an efficient ESF evaluation scheme, based on the nonstandard finite-difference time-domain (NS-FDTD) method, is proposed. Combining the total-field/scattered-field (TF/SF) concept with a distinct sine-wave form, the novel technique cancels the accumulative errors caused by the static field component. Numerical results reveal that the featured method enables the use of high-frequency discretization models to ESF problems, with notable accuracy and seriously decreased design costs.

Finite-difference time-domain analyses of active cloaking for electrically-large objects.

Invisibility cloaking devices constitute a unique and potentially disruptive technology, but only if they can work over broad bandwidths for electrically-large objects. So far, the only known scheme that allows for broadband scattering cancellation from an electrically-large object is based on an active implementation where electric and magnetic sources are deployed over a surface surrounding the object, but whose 'switching on' and other characteristics need to be known (determined) a priori, before the incident wave hits the surface. However, until now, the performance (and potentially surprising) characteristics of these devices have not been thoroughly analysed computationally, ideally directly in the time domain, owing mainly to numerical accuracy issues and the computational overhead associated with simulations of electrically-large objects. Here, on the basis of a finite-difference time-domain (FDTD) method that is combined with a perfect (for FDTD's discretized space) implementation of the total-field/scattered-field (TFSF) interface, we present detailed, time- and frequency-domain analyses of the performance and characteristics of active cloaking devices. The proposed technique guarantees the isolation between scattered- and total-field regions at the numerical noise level (around -300 dB), thereby also allowing for accurate evaluations of the scattering levels from imperfect (non-ideal) active cloaks. Our results reveal several key features, not pointed out previously, such as the suppression of scattering at certain frequencies even for imperfect (time-delayed) sources on the surface of the active cloak, the broadband suppression of back-scattering even for imperfect sources and insufficiently long predetermination times, but also the sensitivity of the scheme on the accurate switching on of the active sources and on the predetermination times if broadband scattering suppression from all angles is required for the electrically-large object.

Realizing accurate simulations by embedding input and output layers in unclosed TF/SF boundary to eliminate leakage.

ABSTRACT The total-field/scattered-field (TF/SF) boundary can be considered as a special source in the finite-difference time-domain method (FDTD). In contrast, to the direct addition of a current source, simulations can be performed by adding excitations in the waveform by setting the TF/SF boundary. However, certain leakage always occurs when loading the closed TF/SF boundary, which leads to an error in both the total-field and scattered-field regions. To overcome this limitation, this paper proposes a novel technique to eliminate the leakage in the TF/SF boundary. In particular, the causes for the leakage are analyzed, and a new structure involving input and output layers is established and perfectly embedded in the classical TF/SF boundary. The new boundary can eliminate the leakage generated between the total-field and scatter-field regions. Numerical simulations in two dimensions involving excitations via Gaussian pulses and a sinusoidal signal indicate that a zero-leakage state can be attained, as opposed to the minimum leakage of −300 dB attained using existing approaches, both in the total-field and scattered-field regions, irrespective of the occurrence of scattering.

A 3-D Total-Field/Scattered-Field Plane-Wave Source for the FDTD Analysis of Reentry Plasma Sheath

A 3-D total-field/scattered-field (TF/SF) plane-wave source was developed for the analysis of the plane wave propagation characteristics in the reentry plasma sheath. Owing to the dynamic variation in the surrounding flow field, the plasma sheath during the reentry process presents various 3-D inhomogeneous structures, such as dynamic plasma turbulence and considerable metal ablation particles. The proposed 3-D model can be efficiently applied to simulate the scattering effects of the 3-D inhomogeneous structures on the electro-magnetic (EM) signals. The proposed model utilizes a 3-D TF/SF boundary to introduce the plane wave source into the simulation domain, and six pairs of 2-D auxiliary propagators are created to generate the incident field on the TF/SF boundary based on the phase matching and the current density convolution finite-difference time-domain (JEC-FDTD) method. The uniaxial anisotropy perfectly matched layer (UPML) is modified as the absorbing boundary condition of the 2-D propagators. Implementation issues such as stability and dispersion are also discussed. The accuracy and efficiency of the proposed scheme are validated by admirable numerical simulation results and excellent agreement with the transmission line analogy method.

Efficient one‐step leapfrog ADI‐FDTD for far‐field scattering calculation of lossy media

AbstractFree from the Courant‐Friedrichs‐Lewy (CFL) stability condition and sub‐step computations, the one‐step leapfrog alternative‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD) method is very efficient in dealing with fine grid problems. In this letter, a one‐step leapfrog ADI‐FDTD method for three‐dimensional far‐field scattering simulation method for lossy media is proposed. A novel total field/scattering field (TF/SF) implementation is derived for the one‐step leapfrog ADI‐FDTD, providing the computational flexibility in far‐field electromagnetic (EM) scattering calculation. The auxiliary matrices are introduced to further improve its efficiency for lossy media. The simulation results show that there is a good agreement between the proposed one‐step leapfrog ADI‐FDTD method and Yee's FDTD in solving the far‐field scattering problem and benefits in performance were encountered when using the proposed method.

Total-Field/Scattered-Field Formulation for FDTD Analysis of Plane-Wave Propagation Through Cold Magnetized Plasma Sheath

Modeling wideband plane-wave propagation through a stratified magnetized plasma sheath is important toward predicting the quality of communications during re-entry, scattering caused by electron density perturbations, and many other applications. When using the finite-difference time-domain (FDTD) method to solve the problem, modeling the incident field in the simulation domain is difficult if the incident field travels obliquely to the grid axes. In this article, a total-field/scattered-field (TF/SF) formulation whereby a plane-wave source is introduced into cold layered magnetized plasma has been developed for the FDTD method. Based on phase matching theory, twelve auxiliary 1-D propagators are specified to calculate the correction field values for the TF/SF boundary. A modified convolution perfect match layer (CPML) is implemented to terminate the 1-D propagators. Numerical results are also presented to show the accuracy and effectiveness of the method. Although this method is developed for magnetized plasma, the extension to other anisotropic dispersive layered media is straightforward.

A Novel P–N Transparent Source for Waveguide Ports in the FDTD Method

Sources are important in the finite-difference time domain (FDTD) method. There are several types of sources, such as the hard source (applied field), the transparent current source (impressed current), the total field/scattered field (TF/SF) source, and the transparent field source. These sources have certain drawbacks in the simulation of waveguide structures. A novel positive–negative (P–N) source is proposed in this letter. It is transparent and can excite the same field as the hard source. For no auxiliary FDTD calculation is required, the P–N source is more efficient than the transparent current source and the transparent field source in the simulation of waveguide structures.

Generation of Bessel beam sources in FDTD.

In this paper, a straightforward approach is presented to generate Bessel beam sources in three-dimensional finite-difference time-domain (FDTD) method. Based on the angular spectrum representation (ASR), the incident Bessel beam is described as a superposition of plane waves whose wavevectors covering a conical surface. This decomposition of Bessel beam is then approximated by a finite collection of plane waves, which are injected into FDTD simulation domain using the total-field/scattered-field (TF/ST) method. The present method's correctness and accuracy are verified by comparing the reconstructed field in FDTD with the original field. Far-field scattered diagrams of a dielectric sphere and a spheroid particle illuminated by a zero-order or a higher-order Bessel beam are calculated using FDTD. The results are compared with those calculated using the generalized Lorenz-Mie theory (GLMT) and surface integral equation method (SIEM). Very good agreements have been achieved, which partially indicate the correctness of our method. Internal and near-surface field distributions for a two-layer hemisphere particle, which are illuminated by Bessel beams, are also displayed to show the potentials of this approach in solving scattering problems of complex particles. This approach can also be applied to generate other structured beam sources in FDTD, which provides an access to solve structured beam scattering by complex particles using FDTD.

Light-scattering model for aerosol particles with irregular shapes and inhomogeneous compositions using a parallelized pseudo-spectral time-domain technique**Project supported by the National Natural Science Foundation of China (Grant Nos. 41575025 and 41575024).

To improve the modeling accuracy of radiative transfer, the scattering properties of aerosol particles with irregular shapes and inhomogeneous compositions should be simulated accurately. To this end, a light-scattering model for nonspherical particles is established based on the pseudo-spectral time domain (PSTD) technique. In this model, the perfectly matched layer with auxiliary differential equation (ADE-PML), an excellent absorption boundary condition (ABC) in the finite difference time domain generalized for the PSTD, and the weighted total field/scattered field (TF/SF) technique is employed to introduce the incident light into 3D computational domain. To improve computational efficiency, the model is further parallelized using the OpenMP technique. The modeling accuracy of the PSTD scheme is validated against Lorenz–Mie, Aden–Kerker, T-matrix theory and DDA for spheres, inhomogeneous particles and nonspherical particles, and the influence of the spatial resolution and thickness of ADE-PML on the modeling accuracy is discussed as well. Finally, the parallel computational efficiency of the model is also analyzed. The results show that an excellent agreement is achieved between the results of PSTD and well-tested scattering models, where the simulation errors of extinction efficiencies are generally smaller than 1%, indicating the high accuracy of our model. Despite its low spatial resolution, reliable modeling precision can still be achieved by using the PSTD technique, especially for large particles. To suppress the electromagnetic wave reflected by the absorption layers, a six-layer ADE-PML should be set in the computational domain at least.

Total-Field/Scattered-Field Separation Based on $H$ -field Correction for the Nonstandard Finite-Difference Time-Domain

The nonstandard finite-difference time-domain (NS-FDTD) methodology is a very competent numerical tool for the radar cross section (RCS) analysis of scattering objects with complicated geometries and electrically large sizes, due to its high accuracy at fixed frequencies. During the RCS calculation via the typical FDTD scheme, the total-field/scattered-field (TF/SF) approach is generally used to separate the SF from TF simulation region. However, existing TF/SF separation algorithms for the NS-FDTD method are rather laborious for practical arrangements. Therefore, we develop a new TF/SF separation technique, solely based on H-field correction, and apply it in both cubic- and rectangular-cell computational domains, which discretize demanding structures. In all scenarios, the proposed algorithm is found to be superior over previously derived procedures, while, concurrently, remaining much simpler in its overall NS-FDTD implementation.

Application of the weighted total field-scattering field technique to 3D-PSTD light scattering model

PSTD (Pseudo Spectral Time Domain) is an excellent model for the light scattering simulation of nonspherical aerosol particles. However, due to the particularity of its discretization form of the Maxwell's equations, the traditional Total Field/Scattering Field (TF/SF) technique for FDTD (Finite Differential Time Domain) is not applicable to PSTD, and the time-consuming pure scattering field technique is mainly applied to introduce the incident wave. To this end, the weighted TF/SF technique proposed by X. Gao is generalized and applied to the 3D-PSTD scattering model. Using this technique, the incident light can be effectively introduced by modifying the electromagnetic components in an inserted connecting region between the total field and the scattering field region with incident terms, where the incident terms are obtained by weighting the incident field by a window function. To optimally determine the thickness of connection region and the window function type for PSTD calculations, their influence on the modeling accuracy is firstly analyzed. To further verify the effectiveness and advantages of the weighted TF/SF technique, the improved PSTD model is validated against the PSTD model equipped with pure scattering field technique in both calculation accuracy and efficiency. The results show that, the performance of PSTD seems to be not sensitive to variation of window functions. The number of the connection layer required decreases with the increasing of spatial resolution, where for spatial resolution of 24 grids per wavelength, a 6-layer region is thick enough. The scattering phase matrices and integral scattering parameters obtained by the improved PSTD show an excellent consistency with those well-tested models for spherical and nonspherical particles, illustrating that the weighted TF/SF technique can introduce the incident precisely. The weighted TF/SF technique shows higher computational efficiency than pure scattering technique.

A 2-D FDTD Model for Analysis of Plane Wave Propagation Through the Reentry Plasma Sheath

A 2-D finite-difference time domain model was developed to analyze the wideband plane wave propagation characteristics in the reentry plasma sheath at the receiving antenna position. Because of the variation of the flow field, various inhomogeneous structures exist in the plasma sheath, such as electron density irregularities, large-scale ablation particles, and vortex electron density structures, which play important roles in refracting and distorting the electromagnetic wave signals. The proposed model directly included the effects of these inhomogeneous structures. The model used a $\pi $ -shaped total-field/scattered-field (TF/SF) boundary to introduce the plane wave source to the simulation domain. Based on the current density convolution (JEC) method and the phase matching principle, six 1-D auxiliary propagators were generated to obtain field values at the TF/SF boundary. The convolutional perfectly matched layer was implemented as the absorbing boundary condition of the auxiliary propagator. The efficiency and accuracy of the proposed method were validated by numerical examples.

Analytical Expression for the Time-Domain Green’s Function of a Discrete Plane Wave Propagating in a 3-D FDTD Grid

In this paper, a closed-form expression for the time-domain dyadic Green’s function of a discrete plane wave (DPW) propagating in a 3-D finite-difference time-domain (FDTD) grid is derived. In order to verify our findings, the time-domain implementation of the DPW-injection technique is developed with the use of the derived expression for 3-D total-field/scattered-field (TFSF) FDTD simulations. This implementation requires computations of the time-domain Green’s function of DPW 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 Green’s function of DPW. The developed time-domain implementation of the DPW-injection technique demonstrates the leakage error across the TFSF interface around the numerical noise level that verifies the correctness of the derivation.