Classical FDTD Research Articles

Disclosing transverse spin angular momentum of surface plasmon polaritons through independent spatiotemporal imaging of its in-plane and out-of-plane electric field components

The comprehensive capture of near-field spatiotemporal information of surface plasmon polaritons (SPPs) is a prerequisite for revealing their physical nature. In this study, we first performed an independent, spatiotemporal imaging of the out-of-plane and in-plane components of SPP near-fields in a femtosecond light-excited trench using an obliquely incident time-resolved photoemission electron microscopy (TR-PEEM). We did the capture by imaging of the interference patterns induced by a superposition of the p - or s -polarized probe light, with the out-plane or in-plane components of SPP near-fields, under the noncollinear excitation mode. The method may be used to reconstruct a 3D SPP spatiotemporal field. Moreover, we demonstrated that the fringe shift of the interference patterns between the captured in-plane and out-of-plane components of the SPP field in PEEM images corresponds to the 1/4 fringe period, which is attributed to π / 2 out of phase of the out-of-plane and in-plane near-field components of SPP. The resulting TR-PEEM images are supported by a classical wave mode and FDTD simulations. Essentially, the measured π / 2 phase difference between the in-plane and out-of-plane components of the SPP indicated a rotating field component in the propagation plane, i.e., that the SPP exhibits an elliptically polarized electric field in the propagation plane. The experimental results presented herein provide direct evidence of SPP having the inherent attributes of transverse spin angular momentum.

Comparison of FDTD and TDWP Methods for Simulating Electromagnetic Wave Propagation above Terrains

Abstract — Researchers have always been in favor of path loss calculation in different media for applications such as telecommunication link design. Wave propagation calculations in large spaces using the FDTD method is time-consuming and imposes a great computational burden. For this reason, to replace the classical FDTD method for wave propagation simulation and path loss calculation in large spaces, optimized methods, namely TDWP, have been provided. In this paper, the use of the TDWP method for wave propagation simulation and path loss calculation above a terrain is investigated. Longitudinal components of ground-waves are taken into account (including direct waves, ground reflections, and surface waves). Propagation space is longitudinally divided into smaller FDTD windows with finite length. The electromagnetic pulse travels through these windows from left to right to the desired point. But despite its capability in reducing computational burden and increasing processing speed, TDWP has lower precision in instantaneous field simulation and calculation of propagation coefficients, so that results obtained from FDTD and TDWP are clearly different. In this paper, some efficient methods are proposed, which yield an increase in method accuracy.

Imaging the scattering field of a single GaN nanowire

In this work, a single gallium nitride (GaN) nanowire has been examined by our previously reported technique parametric indirect microscopic imaging (PIMI). Mapping of the nanoscale scattering signals from GaN nanowire has been achieved with PIMI system. A comparison with classical far field microscopy and FDTD simulations is included to show the relevant differences and the strength of this technique. In PIMI, highly defined modulated illumination, far field variation quantification, and filtering process resolve the nanoscale scattering field distribution in the form of polarization parameters. We believe that our system provides us a platform to understand the physics of these nanoscale scattering fields from optical nanoantennas.

Recursively Convolutional CFS-PML in 3-D Laguerre-FDTD Scheme for Arbitrary Media

Weighted Laguerre finite-difference time-domain (Laguerre-FDTD) method is an efficient and unconditionally stable time-domain numerical method. The complex frequency-shifted perfectly matched layer (CFS-PML) is the main absorbing boundary condition in the Laguerre-FDTD method. The implementations of CFS-PML in the Laguerre-FDTD method, which have been reported, include the use of auxiliary variables and auxiliary differential equations. These implementations make CFS-PML sensitive to its parameters and timescale parameter s of weighted Laguerre polynomials and result in potential instability and poor absorption issues in numerical simulations. In this paper, we proposed an efficient and stable implementation of CFS-PML based on recursive convolution in the Laguerre-FDTD method. The accuracy of the proposed implementation is theoretically validated. Its numerical dispersion is theoretically derived for choosing the key parameters of CFS-PML in the Laguerre-FDTD scheme. The numerical dispersion demonstrates that the timescale factor s needs to match the simulated signal frequency and the CFS-PML parameter $\alpha $ is chosen as $0.5s\varepsilon _{0}$ to obtain the minimum dispersive error. Numerical examples validate the theoretical predictions and verify that the proposed implementation of CFS-PML is robust and retains the advantages of CFS-PML in classical FDTD method, such as effectively absorbing evanescent as well as guided waves. It requires nonsplits of electromagnetic field components, no auxiliary variables, and no modifications when applying it to inhomogeneous, lossy, and dispersive media. The CFS-PML formulas can directly be converted into computer codes of the Laguerre-FDTD method.

Implicit Local Refinement for Evanescent Layers Combined With Classical FDTD

In this letter we hybridize the well-known FDTD method with the fully implicit method of . In effect, this enables local space refinement without necessitating a smaller time step. In particular, this is very useful for thin layers of highly conducting material or to treat complex media, such as plasma, allowing evanescent waves.

Development of a Self-Consistent Truly Multiphysics Algorithm Based Upon the Courant-Insensitive Space–Time Conservation-Element Solution-Element Method

This paper reports on the theoretical aspects and current development status of a self-consistent truly multiphysics algorithm. The algorithm is based upon the Courant-insensitive space-time conservation-element solution-element methodology. Previous attempts for electromagnetic solutions have applicability only in constant material domains with PEC boundary conditions. This paper reports on the extension of this algorithm for the solution of the generalized Maxwell equations, including linear-dispersive materials. The numerical solution is shown to be extremely accurate on highly nonuniform meshes and reduces to the classical Yee FDTD error properties in the uniform Cartesian grid limit. Validation problems and comparison with the ubiquitous baseline FDTD algorithm will be presented in 1-D (2-D space-time). Results show that the second-order CESE method has an accuracy equivalent to fourth-sixth order FDTD for equal grids with highly discontinuous coefficients (e.g., permittivity).

On the Accuracy of Three Different Six Stages SS-FDTD Methods for Modeling Narrow-Band Electromagnetic Applications

Recently, three different six stages split-step finite difference time domain (SS-FDTD) methods introduced for removing the FDTD Courant-Friedrichs-Levy (CFL) stability limit. Accuracy performance of these methods for modeling narrow-band electromagnetic applications is studied. Numerical example carried out in two-dimensional domain shows that when the CFL stability limit is exceeded, the accuracy of the classical FDTD scheme is maintained only with the splitting scheme that solves the field equations at each FDTD sub-stage alternatively between the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> directions.

3D Crank-Nicolson finite difference time domain method for dispersive media

The unconditionally stable Crank-Nicolson finite difference time domain (CN-FDTD) method is extended to incorporate frequency-dependent media in three dimensions. A Gaussian-elimination-based direct sparse solver is used to deal with the large sparse matrix system arising from the formulation. Numerical results validate and confirm that the scheme is unconditionally stable for time steps over the Courant-Friedrich-Lewy limit of classical FDTD.

On the dispersion relation of ADI-FDTD

In this letter, we analyze the alternating direction implicit finite-difference time-domain (ADI-FDTD) dispersion relation and find the numerical plane-wave relationship between the magnetic and electric fields, showing that the scheme is not divergence-free. We also show that negative-group-velocity modes with positive phase velocities may appear for high Courant numbers. A parallel comparison is made with the behavior of the classical Yee FDTD and the Crank-Nicolson schemes.

Analysis of two dimensions sparse multicylinder scattering problem using DD-FDTD method

An algorithm of two-dimensional (2-D) domain decomposition finite-difference time-domain (DD-FDTD) using in sparse multicylinders scattering problem is proposed in this paper. The idea of domain decomposition is introduced to divide the sparse problem domain into several subdomains. All of subdomains are connected by means of the 2-D time domain Green's function. As a result, a great deal of meshes memory between cylinders is removed, especially when the distances between cylinders become large. Furthermore, the coupling between cylinders can be regarded as the equivalent cylindrical wave irradiations. The incident signals of the equivalent cylindrical waves are expressed as cylindrical wave input field array (CWIFA) according to Huygens principle. Then the calculation time is significantly reduced. The near-field to far-field transformation is used to obtain the equivalent cylindrical wave; as a result, the calculation time can be reduced further. The new method has been demonstrated in 2-D multicylinders scattering problem. Numerical results are in good agreement with the results obtained using classical FDTD method and moment of methods (MM).

Three-dimensional FDTD modeling of a ground-penetrating experiment

This paper deals with a numerical FDTD approach to solve a particular ground-penetrating problem. Classical Yee FDTD formulation is used to simulate layered media on a perfectly electrically conductive plate (PEC). It is shown that an alternative of the step 3-D PML formulated by Sullivan is well adaptated to surround the computational domain. In particular, the PEC can be easily extended to the PML medium without any extra reflection error.

A New Hybrid Method Combining the ADI-FDTD and the MOMTD Techniques

This paper describes a new hybrid technique, combining the alternating direction implicit finite difference time domain (ADI-FDTD) method and the method of moments in the time domain (MoMTD) to analyze problems involving thin-wire antennas close to inhomogeneous dielectric bodies. The unconditionally stable ADI-FDTD formulation presents computational advantages over the explicit Yee FDTD scheme in cases that require a fine mesh to accurately model their electromagnetic characteristics. The hybrid procedure has been found stable in the examples analyzed so far, which was not always the case in the previous approach based on the classical Yee FDTD.

New multiple‐region schemes with multiresolution capabilities for the FDTD analysis of radiating structures

AbstractIn this Letter multiple‐region FDTD (MR/FDTD) with compressed near‐field to near‐field transform is presented and compared to classical FDTD. Different MR/FDTD simulation strategies are proposed. The suitability of MR/FDTD for the simulation of surrounded antennas in an array configuration is discussed. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 268–273, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10294

Hybrid time domain solvers for the Maxwell equations in 2D

AbstractWe present a new approach to time domain hybrid schemes for the Maxwell equations. By combining the classical FD‐TD scheme with two unstructured solvers, one explicit finite volume solver and one implicit finite element solver, we achieve a very efficient and flexible second‐order scheme. The second‐order accuracy of the hybrid scheme is verified through convergence studies on perfectly conducting as well as dielectric and diamagnetic circular cylinders. The numerical results also show its superiority to the FD‐TD scheme. Copyright © 2002 John Wiley &amp; Sons, Ltd.

A discrete wavelet transform (DWT)‐based compression technique for the computation of Kirchhoff integrals in MR/FDTD

The multiple-region FDTD (MR/FDTD) has recently been introduced as an extension of the classical FDTD to multiple subregions within a problem domain. In MR/FDTD, the problem domain is broken down into several volumes interacting with each other by means of a near-field to near-field transformation. One of the available methods is the Kirchhoff integrals, a method that has been successfully applied to FDTD, but that suffers from a high demand for computation resources. In this paper, a new discrete wavelet transform (DWT)-based compression technique for the computation of Kirchhoff integrals is presented that leads to important savings both in memory size and computation time, while combining excellent accuracy and ease of implementation. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 312–316, 2000.

Fast modal ABC's in the hybrid PEE-FDTD analysis of waveguide discontinuities

The authors discuss the application of two types of fast modal absorbing boundary conditions (ABC's) to the analysis of waveguide discontinuities by means of the hybrid partial eigen-function expansion finite-difference time-domain (PEE-FDTD) method. For low-order modes, ARX digital filters are used while higher order modes are terminated with simplified ABC's based on the evanescent nature of modes below cutoff. Numerical tests show that this approach gives a very good absorption of modes while allowing one to achieve significant acceleration of numerical computation compared to classical FDTD scheme.

MR/FDTD: A multiple-region finite-difference--time-domain method

Multiple-region FDTD (MR/FDTD), an extension of classical FDTD to multiple subregions within a problem domain, is introduced. In MR/FDTD the problem domain is broken into several independent FDTD subregion lattices. The subregions lattices are terminated with the use of a surface integrated radiation boundary condition applied simultaneously to all subregions providing mutual interaction between the subregions. The advantages of MR/FDTD for sparse modeling problems include computation and memory efficiencies that result from confirming the FDTD lattices to the space near objects and from the ability to use different lattices and/or lattice orientations within each subregion. MR/FDTD also eliminates the need for local absorbing boundary conditions. Comparison between MR/FDTD and classical FDTD is provided through numerical examples. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 14, 101–105, 1997

Electromagnetic wave diffraction using a finitevolume method

The authors describe a finite volume time domain (FVTD) method for the resolution of electromagnetic diffraction by ‘complex’ structures. Results obtained for an aircraft by this technique which allow a conformal meshing are compared with results from a classical FDTD code.

Surface impedance boundary conditions at oblique incidence in FDTD

Surface impedance formalism permits to reduce the discretization volume in a finite difference time domain (FDTD) code. The method based on the definition of surface impedances for plane waves at horizontal or vertical polarizations, is introduced in fdtd algorithm, to model interfaces between two media. In this paper, two dimensional and three dimensional results are compared to those computed with classical fdtd or Fresnel reflection coefficients involving a Fourier transform.