Standard Finite-difference Time-domain Research Articles

Implementation of ADI-FDTD subgrids in ground penetrating radar FDTD models

Realistic numerical modeling of ground penetrating radar (GPR) using the finite-difference time-domain (FDTD) method could greatly benefit from the implementation of subgrids – supporting finer spatial resolution – into the conventional FDTD mesh. This is particularly important, when parts of the computational domain need to be modeled in detail or when there are features or regions in the overall computational mesh with values of high dielectric constant supporting propagation of waves at very short wavelengths. A scheme that simplifies the process of implementing these subgrids into the traditional FDTD method is presented. This scheme is based on the combination of the standard FDTD method and the unconditionally stable alternating-direction implicit (ADI) FDTD technique. Because ADI-FDTD is unconditionally stable its time-step can be set to any value that facilitates the accurate calculation of the fields. By doing so, the two grids can efficiently communicate information across their boundary without requiring to use a costly time-interpolation scheme. This paper discusses the performance of ADI-FDTD subgrids when implemented into the traditional FDTD method, using different communication schemes for the information exchange at the boundary of the two grids. The developed algorithm, can handle cases where the subgrid crosses dielectrically inhomogeneous media. In addition, results from the comparison between the proposed scheme and a commonly employed purely FDTD subgridding technique are presented.

Combined analytical-finite difference time-domain full wave simulation of mode-locked vertical-extended-cavity semiconductor lasers

A time-domain approach based on the finite difference time-domain (FDTD) method is described for vertical-extended-cavity surface-emitting lasers (VECSELs). To permit the simulation of realistic devices with large extended cavities a combined analytical-FDTD model is developed. This approach uses plane wave propagation in the linear extended cavity to couple the active mirror and the semiconductor saturable absorber mirror (SESAM) in which the standard FDTD method is applied. This allows for a significant computational time reduction. The material response in the active quantum wells (QWs) and the absorber is incorporated by an infinite impulse response digital filter. The model is validated by the simulation of a passively mode-locked VECSEL with a multiple QW active region and a single QW SESAM.

Alternative approach for modeling material interfaces in FDTD

AbstractA simple alternative way to position dielectric materials in the finite‐difference time‐domain (FDTD) Yee cell grid is proposed. Plane‐wave illuminated spheres are used as examples to study the performance of the alternative method compared to the standard FDTD method. Although the performances are generally equally good, the alternative method may sometimes give significantly improved accuracy. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1211–1214, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23309

An efficient approach toward guided mode extraction in two-dimensional photonic crystals

A rigorous, fast and efficient method is proposed for analytical extraction of guided defect modes in two-dimensional photonic crystals, where each Bloch spatial harmonic is expanded in terms of Hermite–Gauss functions. This expansion, after being substituted in Maxwell’s equations, is analytically projected in the Hilbert space spanned by the Hermite–Gauss basis functions, and then a new set of first order coupled linear ordinary differential equations with non-constant coefficients is obtained. This set of equations is solved by employing successive differential transfer matrices, whereupon defect modes, i.e. the guided modes propagating in the straight line-defect photonic crystal waveguides and coupled resonator optical waveguides, are analytically derived. In this fashion, the governing differential equations are converted into an algebraic and easy to solve matrix eigenvalue problem. Thanks to the analyticity of the proposed approach, the eigenmodes of these structures can be extracted very quickly. The validity of the obtained results is however justified by comparing them to those derived by using the standard finite-difference time-domain method.

Numerical modelling and experimental verification of GPR to investigate ring separation in brick masonry arch bridges

The application of ground-penetrating radar (GPR) as a non-destructive technique for the monitoring of ring separation in masonry arch bridges was studied. Numerical modelling techniques were used to simulate tests using GPR—these numerical experiments were backed up and calibrated using laboratory experiments. Due to the heterogeneity of these structures, the signals coming from the interaction between the GPR system and the bridge are often complex, and hence hard to interpret. This defined the need to create a GPR numerical model that will allow the study of the attributes of reflected signals from various targets within the structure of the bridge. The GPR numerical analysis was undertaken using the finite-difference time-domain (FDTD) method. Since “micro regions” in the structure need to be modelled, subgrids were introduced into the standard FDTD method, in order to economize on the required memory and the calculation time. Good correlations were obtained between the numerical experiments and actual GPR experiments. It was shown both numerically and experimentally that significant mortar loss between the masonry arch rings can be detected. However, hairline delaminations between the mortar and the brick masonry cannot be detected using GPR.

Computation of Electromagnetic Fields in Assemblages of Biological Cells Using a Modified Finite-Difference Time-Domain Scheme

When modeling objects that are small compared with the wavelength, e.g., biological cells at radio frequencies, the standard finite-difference time-domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating a generic lumped-element membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900,1800, and 2450 MHz. This method will facilitate deeper investigation of the phenomena in the interaction between electromagnetic fields and biological systems.

Conservative and Provably Stable FDTD Subgridding

The finite difference time domain (FDTD) method is a common, robust simulation technique for transient electromagnetic interactions with complicated structures. However, the standard FDTD method is limited to cartesian grids everywhere in the computational grid. Many practitioners have extended FDTD to handle multiresolution problems by using finer grids near structures with small geometrical features abutted to coarse grids in regions of empty space. Unfortunately, subgridding implementations based on interpolation or extrapolation of neighboring field values can exhibit late time instabilities. Herein, a subgridding method based on multigrid finite element principles will be developed and its stability proven. Numerical results will assess its performance in 2-D and 3-D.

A Finite Volumes-Based 3-D Low Dispersion FDTD Algorithm

An algorithm extension to three dimensions is developed and presented for the highly phase-coherent modified second-order in time, fourth-order in space (or M24) finite-difference time-domain (FDTD) algorithm. A finite-volumes approach in conjunction with Yee's standard FDTD lattice is used for algorithm development. The corresponding dispersion relation is also developed, analyzed and compared to both the standard second-order and fourth-order FDTD algorithms as well as to two closely related high-order phase-coherent algorithms. Wideband algorithm attributes are also presented as well as sets of ready to use optimized algorithm coefficients.

Rigorous and Efficient Time-Domain Modeling of Electromagnetic Wave Propagation and Fading Statistics in Indoor Wireless Channels

Conventional numerical electromagnetic methods are known to provide accurate means of characterizing wireless channel transfer functions. However, their practical utilization is hampered by their typically large computational cost compared to empirical, measurement-based or ray-tracing techniques. In this paper, a full-wave, time-domain technique, stemming from the spatial expansion of electromagnetic field components in smooth, spline-type basis functions, is shown to provide a rigorous, yet efficient tool for site-specific indoor channel modeling. Based on this method, wireless propagation across indoor channel geometries can be accurately characterized and signal fading statistics can be extracted. Numerical examples, indicating the significantly improved efficiency of the proposed approach, compared to the standard finite-difference time-domain method, are given. Moreover, important wave propagation effects on indoor channel performance, readily accounted for by our full-wave analysis, are demonstrated.

The Treatment of Singularities at 90$^{\circ}$ and 270$^{\circ}$ Microstrip Corners in FDTD by the Modification of Assigned Material Parameters

It has been recently shown that the efficiency of the finite-difference time-domain (FDTD) method for structures containing thin wires and metal edges is much increased by using modified assigned material parameters (MAMPs). These parameters may be calculated empirically and in many cases analytically. In this contribution, the technique is extended to include the case of 90deg and 270deg corners in microstrip which may exist at an arbitrary position within the plane of the mesh. A semi-analytical method is presented and applied to the analysis of a complex patch antenna. Results are presented which show that the use of MAMPs allows a much larger cell size to be used than would be needed to achieve the same accuracy using standard FDTD.

Bandpass filters based on phase-shifted photonic crystal waveguide gratings

In this paper, a bandpass transmission filter realized in phase-shifted waveguide gratings based on photonic crystals (PCs) is proposed. Phase-shift regions each composed of one period of photonic crystal (PC) waveguide are incorporated into PC waveguide gratings. The magnitudes of the phase-shifts are modified by involving small changes in the size of the border rods in the phase-shift regions. Using standard coupled-mode theory and finite-difference time-domain (FDTD) method, we show that by properly choosing the magnitudes of phase-shifts and the lengths of waveguide gratings, a flat-top and sharp roll-off response with a narrow bandwidth is theoretically and numerically achieved by the designed filter. A further analysis shows that the center frequency of the transmission band can be changed by altering the magnitude of the phase-shift and the response performance exhibits relaxed sensitivity to the phase-shift variation. As a specific application, we theoretically demonstrate a third-order Chebyshev bandpass filter based on compound phase-shifted PC waveguide gratings. The filter performance is suitable for dense wavelength-division-multiplexed (DWDM) optical communication systems with a channel spacing of 100-GHz.

A new FDTD stencil for reduced numerical anisotropy in the computer modeling of wave phenomena

An isotropic finite difference scheme is utilized for the development of a new stencil for the finite-difference time-domain (FDTD) modeling of electromagnetic wave propagation. The key attribute of the new stencil is the improved isotropy of the numerical phase velocity at fairly moderate spatial sampling of the fields. More specifically, for a given phase velocity anisotropy error, the new stencil requires a much coarser grid than the one required by the standard, second-order accurate FDTD stencil. This, in turn, amounts to gains in computational resources when transient electromagnetic interactions in electrically-large domains are being modeled. The numerical attributes of the proposed stencil, namely, its dispersion, anisotropy and stability, are presented in the context of its application to the numerical simulation of two-dimensional transient electromagnetic wave propagation. Through a series of numerical studies, the enhanced isotropy provided by the proposed scheme is demonstrated and contrasted in a quantitative manner to that of the standard FDTD stencil. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.

Novel Explicit 2-D FDTD Scheme With Isotropic Dispersion and Enhanced Stability

A two dimensional (2-D) finite-difference time-domain (FDTD) method based on a novel finite difference scheme is developed to eliminate the numerical dispersion errors. In this paper, the numerical dispersion and stability analysis of the new scheme are given; these show that the proposed method is nearly dispersionless and stable for a larger time step than the standard FDTD method for a monochromatic frequency. The new algorithm is also verified for two cases

Strong focusing properties and far-field focus in the two-dimensional photonic-crystal-based concave lens

We have demonstrated that the strong and far-field focusing of a point source and a plane wave in a two-dimensional photonic-crystal-based concave lens by the use of the standard finite-difference time-domain simulations. The effect of the distance between the point source and the lens on the focusing is discussed. The far-field focus of a plane wave is shown. In addition, a plane wave is formed with placing the source at the focus point. According to the calculation, the strong and good quality far-field focusing of the transmitted wave, explicitly following the well-known wave beam negative refraction law, can be realized. Moreover, the spatial frequencies information of the Bloch mode in multiple Brillouin zones is investigated in order to indicate the wave propagation in two different regions.

Design of optimized FDTD schemes for the accurate solution of electromagnetic problems

In this paper, we develop a set of two-dimensional finite-difference time-domain (FDTD) schemes, capable of minimizing dispersion errors according to problem-related requirements. Their performance is optimized within either a narrow or wide frequency band, by requiring the minimization of an error estimator at selected frequency points. By properly utilizing a series expansion of the estimator, accuracy improvement is ensured regardless of the propagation angle. Contrary to standard FDTD approaches, the design procedure is proven to efficiently exploit the potential of higher order operators, as the developed techniques attain significantly lower error levels, at no or low additional computational cost

Numerical and Analytical Formulizations of the Extended Mie Theory for Solving the Sphere Scattering Problem

For biomedical applications of numerical electromagnetics, the basic Mie theory is extended to the scenario where the spherical scatter and the surrounding medium are given electromagnetic properties of biological tissues. The numerical approach and the analytical approach to solve the six partial differential equations of the extended Mie theory are formulized in detail. Using two representative models, we validate the numerical and analytical solutions against the result from the standard finite-difference time-domain (FDTD) method and theoretical data. Both solutions are compared with respect to the accuracy and efficiency. The analytical solution provides more accurate results whereas the numerical solution is considerably more efficient. Therefore, the summarized analytical and numerical formulas of the extended Mie theory are both at choice for applications to numerical bioelectromagnetics.

Theory of directional pulse propagation

We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions, respectively, and use these to reformulate Maxwell's equations. These variables enable us to not only judge the effect and significance of backward-traveling field components, but also to discard them when appropriate. They thereby have the potential to simplify numerical simulations, leading to potential speed gains of up to 100% over standard finite difference time-domain (FDTD) or pseudospectral spatial-domain (PSSD) simulations. We present results for various illustrative situations, including an example application to second harmonic generation in periodically poled lithium niobate. These field variables are also used to derive both envelope equations useful for narrow-band pulse propagation, and a second order wave equation. Alternative definitions are also presented.

Smoothed Particle ElectroMagnetics: A mesh-free solver for transients

In this paper an advanced mesh-free particle method for electromagnetic transient analysis, is presented. The aim is to obtain efficient simulations by avoiding the use of a mesh such as in the most popular grid-based numerical methods. The basic idea is to obtain numerical solutions for partial differential equations describing the electromagnetic problem by using a set of particles arbitrarily placed in the problem domain. The mesh-free smoothed particle hydrodynamics method has been adopted to obtain numerical solution of time domain Maxwell's curl equations. An explicit finite difference scheme has been employed for time integration. Details about the numerical treatment of electromagnetic vector fields components are discussed. Two case studies in one and in two dimensions are reported. In order to validate the new proposed methodology, named as Smoothed Particle ElectroMagnetics, a comparison with the standard finite difference time domain method results is performed. The intrinsic adaptive capability of the proposed method, has been exploited by introducing irregular particles distribution.

Calculation of Diffraction Characteristics of Sub wavelength Conducting Gratings Using a High Accuracy Nonstandard Finite-Difference Time-Domain Method

Gratings with subwavelength groove depth and period are frequently used in optics for various purposes. The polarization dependent diffraction characteristics of subwavelength (high frequency) gratings can only be calculated by solving Maxwell’s equations of electromagnetism. In this paper, we calculate the classical diffraction characteristics of subwavelength conducting gratings numerically, using a new high accuracy version of nonstandard finite-difference time-domain (NS-FDTD) algorithm. For the purpose of analysis, we employ a gold sinusoidal grating with light incident at a large angle. We have compared high accuracy NS-FDTD simulation results with those obtained from standard finite-difference time-domain (S-FDTD), and the finite element method (FEM) simulations.

Off-grid perfect boundary conditions for the FDTD method

We implement off-grid boundary conditions within Yee's finite-difference time-domain (FDTD) method without disturbing the existing uniform mesh or changing the standard FDTD code. Both perfect electric conductor and perfect magnetic conductor walls are considered. Examples of straight, slanted, and curved walls are shown, the latter two being represented by an enhanced staircase approximation. We show that: 1) offsets comparable to the spatial step size lead to instabilities and 2) this issue is easily resolved by stepping into the neighboring cell. The method enhances the flexibility of the FDTD method with respect to complex geometrical domains without reducing the spatial step.