Finite Difference Time Domain Method Method Research Articles

Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor

Breast cancer is the most common cancer in women, and non-destructive detection of the tumor is vital. The interaction of electromagnetic waves with breast tissue and the behavior of waves after interaction are used to model tumor detection mathematically. The behavior of electromagnetic waves in a medium is described using Maxwell's equations. Electromagnetic waves propagate according to the electrical properties of a medium. Since the electrical properties of tumor tissue are different from those of normal breast tissue, it is assumed that the tumor is a lossy dielectric sphere, and the breast is a lossy dielectric medium. Under this assumption, Maxwell's equations are used to calculate the scattered field from the tumor. The field scattered by the tumor is different from other tissues because their dielectric properties are different. The location and size of the tumor can be determined by utilizing the difference in scattering from the tissues. While the scattering field from the tumor in spherical geometric form is analytically calculated, it is not analytically possible to calculate the scattering field from the tumor in different geometric shapes. In addition to non-destructive detection of the tumor, an efficient numerical method, the finite difference time domain method (FDTD), is used to simulate the field distribution. After the location of the tumor is determined, the Alternating Direction Implicit (ADI) FDTD method, which gives simulation results by dividing the computation domain into smaller sub-intervals, can be used. Scattered fields are calculated analytically in the geometry where the tumor is in the form of a smooth sphere, and in more complex geometry, the field distributions are successfully obtained with the help of MATLAB using FDTD and ADI-FDTD algorithms.

Lumped-Network FDTD Method for Simulating Transient Responses of RF Amplifiers Excited by Intentional Electromagnetic Interference Signals

Unintentional as well as intentional electromagnetic interference can cause interference and performance degradation of microwave circuits or systems. In this article, a modified multiport lumped-network finite-difference time-domain method (FDTD) method based on Y-matrix is proposed, where bilinear transform is used to incorporate the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V–I</i> relation of the lumped-network into FDTD iteration. It is further used for simulating transient responses of <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mesfet</small> -based amplifiers, which are often used in many radar and communication systems. The excitation of such an RF amplifier is assumed to be an intentional electromagnetic interference (IEMI) signal but with different waveforms and magnitudes. Parametric studies are performed to show hybrid effects of waveforms and magnitudes of the IEMI signals on the transient coupled voltages at the output port of such <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mesfet</small> -based amplifier, with useful information obtained for understanding the interaction process between the intentional electromagnetic interference signals and active components.

Plasmonic enhancement of light to improve the parameters of solar cells

Surface plasmon resonance (SPR) can be generated in metal nanostructures such as gold, silver, copper and aluminium, which are promising materials in the fields of optoelectronics and plasmonics. The SPR in periodic arrays has aroused great interest because of its uniform optical properties which can be applied in integrated optoelectronics device, including solar cells (SC). The optical spectra of structures with Ag nanoparticles on the surface of Si wafer were calculated. The simulation was carried out using finite-difference time-domain method (FDTD). The FDTD method is a powerful numerical algorithm for the direct solution of Maxwell's equations. As a source of radiation, a plane wave with a range of wavelengths 300–1240 nm is used. The enhancement of solar light absorption of structures with Ag nanoparticles has been demonstrated. The Localized Surface Plasmon Resonance peaks have been obtained in the wavelength range of 830–865 nm that is in good agreement with experimentally revealed one. It was shown that the period of Ag nanoparticles replacement significantly influences on the spectra and LSPR peak position. The measurement of current–voltage characteristics of solar cells with and without Ag nanoparticles demonstrated significant enhancement of short current density in case of AgNPs on SCs surface.

Analysis of GPR Wave Propagation in Complex Underground Structures Using CUDA-Implemented Conformal FDTD Method

Ground penetrating radar (GPR), as a kind of fast, effective, and nondestructive tool, has been widely applied to nondestructive testing of road quality. The finite-difference time-domain method (FDTD) is the common numerical method studying the GPR wave propagation law in layered structure. However, the numerical accuracy and computational efficiency are not high because of the Courant-Friedrichs-Lewy (CFL) stability condition. In order to improve the accuracy and efficiency of FDTD simulation model, a parallel conformal FDTD algorithm based on graphics processor unit (GPU) acceleration technology and surface conformal technique was developed. The numerical simulation results showed that CUDA-implemented conformal FDTD method could greatly reduce computational time and the pseudo-waves generated by the ladder approximation. And the efficiency and accuracy of the proposed method are higher than the traditional FDTD method in simulating GPR wave propagation in two-dimensional (2D) complex underground structures.

Unconditionally Stable CNAD- and BT-Based CFS-PML Implementation for Truncating Anisotropic Magnetic Plasma

In this letter, an unconditionally stable and efficient implementation of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the Crank–Nicolson-approximate-decoupling (CNAD) finite-difference time-domain method (FDTD) scheme and the bilinear transform method is developed for terminating anisotropic magnetic plasma. The dispersive and anisotropic magnetic plasma can be simulated by the auxiliary differential equation method. The proposed CFS-PML implementation can not only attenuate evanescent waves but also reduce late-time reflections. Furthermore, the proposed algorithm not only has the advantage of the conventional FDTD method in terms of absorbing electromagnetic waves but also takes advantage of the unconditional stability of the origin CN-FDTD scheme in terms of reducing the computational time. A numerical example is provided in the 2-D computational domain to indicate the effectiveness of the proposed CFS-PML scheme. The results show that the proposed CFS-PML is unconditionally stable for the time step, which surpasses the Courant limit, and it is suitable for truncating the anisotropic magnetic plasma.

Chromatic analysis of harmonic Fresnel lenses by FDTD and angular spectrum methods.

In this paper, we present a detailed and rigorous study of cylindrical harmonic Fresnel lenses (HFLs) using the finite difference time domain method (FDTD) and angular spectrum method (ASM). The HFL is a kind of diffractive lens that can have maximum diffraction efficiency at several discrete harmonic wavelengths, which is suitable for some broadband applications. Previous studies on HFLs were investigated mainly in the domain of paraxial approximation. By using our proposed calculation method, we have determined the efficiency, focal length, maximum focus intensity, and full width at half maximum (FWHM) of the focal spot for several harmonic numbers and for F-numbers of 0.5, 1, and 3. To compare with the paraxial approximation, we have presented the response to both s-polarized and p-polarized light with constant refractive index and real dispersive material, BK7. Moreover, we have also analyzed the cases with oblique illumination. We have shown that the harmonic wavelengths do not change with F/# and that the diffraction efficiency and FWHM of the focus increase as F/# increases. New results on harmonic wavelengths shift and oblique angle of incidence response have been detailed.

Trapezoid 2D photonic crystal nanoring resonator-based channel drop filter for WDM systems

In the present work, a nanostructure of trapezoid photonic crystal ring resonator-based channel drop filter is designed for wavelength division multiplexing systems (WDM) to drop a channel at a center peak wavelength of 1543 nm. The proposed channel drop filter is composed of bus waveguide, drop waveguide, trapezoid nanoring resonator and reflector in a two-dimensional (2D) hexagonal lattice with circular rods arranged in air host. The trapezoid nanoring resonator is playing a very important role in WDM systems for dropping a single channel over a wide wavelength range. The photonic band gaps of perfect lattice structure and non-perfect lattice structure are absolutely calculated by plane wave expansion method. The functional properties of the designed filter are evaluated by finite difference time domain method (FDTD). The functional properties are center peak wavelength, dropping efficiency, passband width and quality factor. The FDTD method results show dropping efficiency is 100%, and quality factor is about 514.33 which are highly suitable for WDM systems. Further, lattice constant, inner and outer rod radius and refractive index difference of the structure are varied to tune the filter center peak wavelength and its corresponding functional parameters effects are investigated. The proposed nanoring resonator-based optical filter is ultra-compact size around $$14\, \upmu \hbox {m} \times 8.4\, \upmu \hbox {m}$$ ; hence, it is extremely suitable for WDM-based photonic communication systems and photonic integrated circuits.

Reverse Time Migration of Elastic Waves Using the Pseudospectral Time-Domain Method

Reverse time migration (RTM), especially that for elastic waves, consumes massive computation resources which limit its wide applications in industry. We suggest to use the pseudospectral time-domain (PSTD) method in elastic wave RTM. RTM using PSTD can significantly reduce the computational requirements compared with RTM using the traditional finite difference time domain method (FDTD). In addition to the advantage of low sampling rate with high accuracy, the PSTD method also eliminates the periodicity (or wraparound) limitation caused by fast Fourier transform in the conventional pseudospectral method. To achieve accurate results, the PSTD method needs only about half the spatial sampling rate of the twelfth-order FDTD method. Thus, the PSTD method can save up to 87.5% storage memory and 90% computation time over the twelfth-order FDTD method. We implement RTM using PSTD for elastic wave equations and accelerate it by Open Multi-Processing technology. To keep the computational load balance in parallel computation, we design a new PML layout which merges the PML in both ends of an axis together. The efficiency and imaging quality of the proposed RTM is verified by imaging on 2D and 3D models.

Reverse Time Migration of Elastic Waves Using the Pseudospectral Time-Domain Method

Reverse time migration (RTM), especially that for elastic waves, consumes massive computation resources which limit its wide applications in industry. We suggest to use the pseudospectral time-domain (PSTD) method in elastic wave RTM. RTM using PSTD can significantly reduce the computational requirements compared with RTM using the traditional finite difference time domain method (FDTD). In addition to the advantage of low sampling rate with high accuracy, the PSTD method also eliminates the periodicity (or wraparround) limitation caused by fast Fourier transform in the conventional pseudospectral method. To achieve accurate results, the PSTD method needs only about half the spatial sampling rate of the twelfth-order FDTD method. Thus, the PSTD method can save up to 87.5% storage memory and 90% computation time over the twelfth-order FDTD method. We implement RTM using PSTD for elastic wave equations and accelerate it by Open Multi-Processing technology. To keep the computational load balance in parallel ...

A Dissipative Systems Theory for FDTD With Application to Stability Analysis and Subgridding

This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the magnetic and electric fields on the boundary as inputs and outputs. Suitable expressions for the energy stored in the region and the energy absorbed from the boundaries are introduced, and used to show that the FDTD system is dissipative under a generalized Courant-Friedrichs-Lewy condition. Based on the concept of dissipation, a powerful theoretical framework to investigate the stability of FDTD methods is devised. The new method makes FDTD stability proofs simpler, more intuitive, and modular. Stability conditions can indeed be given on the individual components (e.g. boundary conditions, meshes, embedded models) instead of the whole coupled setup. As an example of application, we derive a new subgridding method with material traverse, arbitrary grid refinement, and guaranteed stability. The method is easy to implement and has a straightforward stability proof. Numerical results confirm its stability, low reflections, and ability to handle material traverse.

Finite difference time domain model of ultrasound propagation in agarose scaffold containing collagen or chondrocytes.

Measurement of ultrasound backscattering is a promising diagnostic technique for arthroscopic evaluation of articular cartilage. However, contribution of collagen and chondrocytes on ultrasound backscattering and speed of sound in cartilage is not fully understood and is experimentally difficult to study. Agarose hydrogels have been used in tissue engineering applications of cartilage. Therefore, the aim of this study was to simulate the propagation of high frequency ultrasound (40 MHz) in agarose scaffolds with varying concentrations of chondrocytes (1 to 32 × 10(6) cells/ml) and collagen (1.56-200 mg/ml) using transversely isotropic two-dimensional finite difference time domain method (FDTD). Backscatter and speed of sound were evaluated from the simulated pulse-echo and through transmission measurements, respectively. Ultrasound backscatter increased with increasing collagen and chondrocyte concentrations. Furthermore, speed of sound increased with increasing collagen concentration. However, this was not observed with increasing chondrocyte concentrations. The present study suggests that the FDTD method may have some applicability in simulations of ultrasound scattering and propagation in constructs containing collagen and chondrocytes. Findings of this study indicate the significant role of collagen and chondrocytes as ultrasound scatterers and can aid in development of modeling approaches for understanding how cartilage architecture affects to the propagation of high frequency ultrasound.

1D trilayer films grating with W/SiO2/W structure as a wavelength-selective emitter for thermophotovoltaic applications

Wavelength selectivity of emitters is of great importance for thermophotovoltaic applications. In this paper, a modified 1D trilayer films grating with a silica (SiO2) layer sandwiched between two tungsten (W) layers to form the W/SiO2/W structure is proposed to obtain high spectral selective emittance. High average emittance of 0.95 is obtained for TM waves from about 600nm to 1900nm, and a broadband emission peak with emittance close to unity occurs between 900nm and 1800nm. Simultaneously, the emittance decreases sharply when λ>1800nm, which can minimize the thermal loss. The finite-difference time-domain method (FDTD) is utilized to analyze the radiative properties of the grating. The inductance–capacitance (LC) circuit model for this trilayer grating structure is presented to predict the magnetic polaritons (MPs) resonance location compared with the results obtained by FDTD method. The effects of the geometric parameters and emission angles on the emittance of the proposed grating are also investigated. The broadband emittance peak is considered as the combined results of the surface plasmon polaritons (SPPs) and several fundamental modes of magnetic polaritons (MPs) resonance at neighboring wavelengths.

Structure-Preserving Reduction of Finite-Difference Time-Domain Equations With Controllable Stability Beyond the CFL Limit

The timestep of the finite-difference time-domain method (FDTD) is constrained by the stability limit known as the Courant-Friedrichs-Lewy (CFL) condition. This limit can make FDTD simulations quite time consuming for structures containing small geometrical details. Several methods have been proposed in the literature to extend the CFL limit, including implicit FDTD methods and filtering techniques. In this paper, we propose a novel approach, which combines model-order reduction and a perturbation algorithm to accelerate FDTD simulations beyond the CFL barrier. We compare the proposed algorithm against existing implicit and explicit CFL extension techniques, demonstrating increased accuracy and performance on a large number of test cases, including resonant cavities, a waveguide structure, a focusing metascreen, and a microstrip filter.

Broadband surface impedance boundary conditions for higher order time domain discontinuous Galerkin method

Purpose – The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions. Design/methodology/approach – The paper solves the Maxwellian initial value problem in a computational domain, which is spatially discretized by the higher order DG method. On the boundary of the computational domain the paper applies a suitable impedance boundary condition (IBC). The frequency dependency of the impedance function is modeled by auxiliary differential equations (ADE). Findings – The authors will study the resonance frequency and the Q factor of different types of cavity resonators including lossy materials. The lossy materials are modeled by means of IBCs. The authors will compare the results with analytical results, as well as numerical results obtained by direct calculations where lossy materials are included explicitly into the numerical model. Several convergence studies are performed which demonstrate the accuracy of the approach. Originality/value – Modeling of frequency dependent boundary conditions in time domain with finite difference time domain method (FDTD) method is considered in numerous papers, as well as in frequency domain finite element method (FEM), and in a few papers also time domain FEM. However, FDTD method is only first order accurate and fails in modeling of complicated surfaces. FEM allows for high order accuracy, but time domain modeling is numerically extremely expensive. In frequency domain, broadband modeling of frequency dependent boundary conditions requires several simulations as opposed to the time domain, where a single simulation is needed. The time domain DG method proposed in this paper allows to overcome the difficulties. The authors introduce a broadband surface impedance formulation based on the ADE approach for the higher order DG method.

Analysis of near-field radiation transfer within nano-gaps using FDTD method

Enhancement of near-field radiative emission via coupling of surface plasmons in nano-gaps formed between thin films is important for understanding and implementation of energy harvesting using nano-thermophotovoltaic cells. Design and construction of such cells need to be carried out along with detailed modeling studies, necessitating accurate calculation of near-field emission within thin films. The objective of this paper is to provide a methodology based on finite difference time domain analysis for the calculation of the near-field thermal radiation emission based on local density of electromagnetic states. Near-field thermal emission is investigated within the nano-gap formed between thin silicon carbide layers where both support surface phonon polaritons. Modeling of this problem with the FDTD method is not trivial particularly for establishing the Drude–Lorentz permittivity model and the selection of the right boundary conditions. We present an effective boundary condition, for calculation of Local Density Of electromagnetic States (LDOS) via Finite Difference Time Domain Method (FDTD) for applications to nano-scale geometries. We conclude that Convolutional Perfectly Matched Layer (CPML) is the optimum boundary condition that gives the most accurate results compared against the other methodologies for parallel plates separated by nano-gaps. This boundary condition allows more streamlined simulations to be carried out when working with sub-wavelength structures. The challenges and the possible solutions to overcome these difficulties are discussed in detail.

Finite-difference time domain method for the analysis of radar scattering characteristic of metal target coated with anisotropic ferrite

A metal cylinder coated with anisotropic ferrite material is analyzed using the finite-difference time-domain method (FDTD) in this paper, and the bistatic radar cross-section (RCS) is obtained. The new method of electromagnetic scattering by magnetized ferrite medium is analyzed in detail based on the FDTD. To exemplify the availability of the algorithm, bistatic RCS of a magnetized ferrite cylinder is computed, and the numerical results are the same as the shift operator FDTD (SO-FDTD), which shows that the proposed FDTD method is correct and efficient.

Performance analysis of the FDTD method applied to holographic volume gratings: Multi-core CPU versus GPU computing

The finite-difference time-domain method (FDTD) allows electromagnetic field distribution analysis as a function of time and space. The method is applied to analyze holographic volume gratings (HVGs) for the near-field distribution at optical wavelengths. Usually, this application requires the simulation of wide areas, which implies more memory and time processing. In this work, we propose a specific implementation of the FDTD method including several add-ons for a precise simulation of optical diffractive elements. Values in the near-field region are computed considering the illumination of the grating by means of a plane wave for different angles of incidence and including absorbing boundaries as well. We compare the results obtained by FDTD with those obtained using a matrix method (MM) applied to diffraction gratings. In addition, we have developed two optimized versions of the algorithm, for both CPU and GPU, in order to analyze the improvement of using the new NVIDIA Fermi GPU architecture versus highly tuned multi-core CPU as a function of the size simulation. In particular, the optimized CPU implementation takes advantage of the arithmetic and data transfer streaming SIMD (single instruction multiple data) extensions (SSE) included explicitly in the code and also of multi-threading by means of OpenMP directives. A good agreement between the results obtained using both FDTD and MM methods is obtained, thus validating our methodology. Moreover, the performance of the GPU is compared to the SSE+OpenMP CPU implementation, and it is quantitatively determined that a highly optimized CPU program can be competitive for a wider range of simulation sizes, whereas GPU computing becomes more powerful for large-scale simulations.

Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrödinger Equations using the FDTD Method

Maxwell and Schrödinger equations are coupled to incorporate quantum effects for the simulation of plasmonics nanodevices. Maxwell equations with Lorentz-Drude (LD) dispersive model are applied to large size plasmonics components, whereas coupled Maxwell and Schrödinger equations are applied to components where quantum effects are needed. The finite difference time domain method (FDTD) is applied to simulate these coupled equations.

Optical modeling of thin-film silicon solar cells by combination of the transfer-matrix method and the raytracer algorithm

We discuss an optical model which describes silicon thin-film solar cells with rough interfaces in a fast and easy way. In order to simulate thin layer stacks with rough interfaces diffuse scattering as well as interference effects have to be taken into account. Algorithms like the finite-difference time-domain method (FDTD) solve the Maxwell Equations, and therefore fulfil these demands; yet, they take a considerable amount of simulation time and computation capacity. To overcome these drawbacks, an optical model was developed which combines the transfer-matrix method (TMM) and the raytracer algorithm. The fraction of TMM and raytracer in the model is determined by a separating function which can be interpreted as the integral haze. In order to verify the combined optical model, a series of amorphous silicon single cells with varying intrinsic layer thicknesses was produced on two different kinds of textured substrates. The results of the combined optical model are compared to measured data and the simulation results of the FDTD method. We show that the combined optical model yields good results at low simulation time.

Computation of the acoustic radiation force using the finite-difference time-domain method

The computational details related to calculating the acoustic radiation force on an object using a 2-D grid finite-difference time-domain method (FDTD) are presented. The method is based on propagating the stress and velocity fields through the grid and determining the energy flow with and without the object. The axial and radial acoustic radiation forces predicted by FDTD method are in excellent agreement with the results obtained by analytical evaluation of the scattering method. In particular, the results indicate that it is possible to trap the steel cylinder in the radial direction by optimizing the width of Gaussian source and the operation frequency. As the sizes of the relating objects are smaller than or comparable to wavelength, the algorithm presented here can be easily extended to 3-D and include torque computation algorithms, thus providing a highly flexible and universally usable computation engine.