Proposed Finite-difference Time-domain Method Research Articles

FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations

In this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced. Finally, one-dimensional signal propagation in such electromagnetic media is considered. The proposed FDTD method is derived based on a discrete approximation of the Grünwald–Letnikov definition of the fractional derivative and evaluated in a code. The stability condition is derived for the proposed FDTD method based on a numerical-dispersion relation. The obtained numerical results are compared with the outcomes of reference frequency-domain simulations, proving the accuracy of the proposed approach. However, high spatial resolution is required in order to obtain accurate results. The developed FDTD method is, unfortunately, computation and memory demanding when compared to the ordinary FDTD algorithm.

3-D FDTD Method for Fast Calculation of Geomagnetic Storm Electromagnetic Fields

In this article, a 3-D finite-difference time-domain (FDTD) method is proposed for rigorous modeling and fast calculation of ultralow frequency geomagnetic storm electromagnetic fields (GS-EMFs). The proposed FDTD approach enables modeling of large-scale and complex 3-D earth structure (e.g., multilayer ground and earth curvature). Unlike conventional FDTD methods, the proposed FDTD method does not require extensive computational resources when dealing with ultralow frequency problems. In this article, the ground surface GS-EMFs produced by an electrojet (line current and sheet current sources) are compared with those obtained using the classical 1-D approaches for case of uniform and horizontally stratified ground. The effect of horizontally vertically multilayer ground and earth curvature on the GS-EMFs is evaluated by the proposed FDTD method. The presented results fully support the adequacy and efficiency of the proposed FDTD method for modeling of large-scale and complex 3-D earth structures for calculation of GS-EMFs.

A Drude-Two-CP-FDTD method for Drude-critical points model of metal nanofilms

Based on Drude-critical points (Drude-Two-CP) model for a dispersive media, a finite-difference time-domain (FDTD) method for metal nanofilms is proposed. By establishing the corresponding relationship between Drude-Two-CP model and Drude–Lorentz model, the conversion coefficients between the two models are calculated. And we modify the Drude-Two-CP model into the form of standard Lorentz model. The transformation relationship between the two models is conducive to the modular programming of FDTD. Formula deduction and calculation results show that Drude-Two-CP model has higher fitting accuracy and fitting formulas are more complex. Using the proposed FDTD method, we have calculated the reflection, transmission and extinction coefficients of gold and aluminium nanofilms. The results show that the FDTD results are in good agreement with those of Drude-Two-CP model, which are better than those of Drude–Lorentz model. Therefore, the Drude-Two-CP-FDTD method proposed in this paper is helpful for improving the accurate modelling and calculation of nano-optical structures.

Fast Calculation of Scattering in Planar Uniaxial Anisotropic Multilayers

In this paper, the generalized recursive formulations of the finite difference time domain (FDTD) for updating the electric and magnetic fields in the multi-layer anisotropic media are derived with a uniaxial perfectly matched layer. The stability condition of the proposed method is clearly analyzed and verified. Then this method is used to calculate the three-dimensional complex scattering fields in planar multilayered anisotropic microstructures with optical axis perpendicular to the layered interface and the scattering fields of arbitrary shape scatters in the anisotropic layered structures. The electric field induced by the sine dipole source is calculated in the spatial domain and the corresponding spectral domain results are achieved through Fourier transform. The scattering field of composite materials with submillimeter thicknesses used in the industrial engineering is calculated using a terahertz wave with operation frequency of 0.3 THz. Robustness of the derived formulations for the complex uniaxial anisotropic media is verified by comparing with the COMSOL software, which is based on FEM analysis. The comparison of memory and CPU time shows the efficiency of the proposed FDTD method. Finally, the scattering fields of different scatters buried in multilayer anisotropic media are studied. So it is expected to become an effective simulation tool for dealing with complex electromagnetic environment in the future, such as abnormal detection of aircraft coating materials and detection of hidden target and so on.

FDTD algorithm to achieve absolute stability in performance analysis of SWCNT interconnects

Crosstalk analysis in very-large-scale (VLSI) interconnects is usually carried out using finite-difference time-domain (FDTD) methods. However, the stability of FDTD is limited by the Courant–Friedrichs–Lewy (CFL) stability criteria. In this work, we propose an innovative FDTD algorithm to overcome the stability limitations due to the CFL criteria and make the analysis absolutely stable for all times. Using the proposed FDTD method, we analyze the response of coupled interconnects for symmetric and asymmetric inputs with both in-phase and out-of-phase switching. We further analyzed the functional switching and determined how to reduce noise peaks due to crosstalk. For all responses, we compared our new algorithm with HSPICE results, revealing greatly enhanced accuracy and central processing unit (CPU) runtime compared with conventional FDTD. Finally, relative and absolute stability analyses of the proposed FDTD method were carried out using Nyquist and Routh–Hurwitz (R–H) criteria.

Performance analysis of VCSEL using finite difference time domain method

Vertical Cavity Surface Emitting Laser (VCSEL) with significantly diverse structures has evolved with time for a different type of applications. A number of researchers used Finite Element Method (FEM) solver for computation of optical resonance modes in VCSEL but this method has a limitation of accuracy because it uses an approximate solution of partial differential equationsand integral equations. Furthermore, FEM is based either on eliminating the time derivatives completely or by rendering the partial differential equations into an equivalent ordinary differential equations. In this research work, we have used Finite Difference Time Domain (FDTD) method which elaborates the fine features of VCSEL and the accuracy of the VCSEL results got improved.The proposed approach is also beneficial for calculating reflectance for multiple wavelengths of light per simulation which is the major advantage over FEM. In this research paper, a new VCSEL structure is modeled and also numerically investigated by using proposed FDTD method. A complete analysis of VCSEL light emission, its electric field and Poynting vector are also evaluated at different points of light in thesecond window of optical communication. A rigorous evaluation in terms of spectrum analysis, transmission analysis and farfield projection analysis is done for wavelength ranging from 1310 nm to 1350 nm. Results show that the maximum power of 0.81 W is obtained at a wavelength of 1320 nm with maximum peak voltage of 1.4 V/m and 0.006 W/m2 Poynting vector.

Lightning Surge Propagation Analysis in OHGW of Electrified High Speed Railway

This paper proposes the analysis of the lightning surge propagation along overhead ground wires based on the telegraph equations which describe the voltage and current on a power transmission line and the finite difference time-domain (FDTD) method. The proposed FDTD method was tested with the 25-kV power transmission system of a high-speed railway in comparison with the solution obtained by using the Bewley method. From the results, after the travelling surge reaches the contact point between the overhead ground wire and the transmission pole, the surge is partially reflected and partially passes through. If the grounding resistance at a transmission pole is small, the peak of the reflected voltage surge is greater than that of the surge passing through. However, the higher value of grounding resistance causes the higher peak of the surge that passes through than the peak of the reflected surge. The computations show that the FDTD method is one of the most accurate methods to analyze lightning surge propagation in power transmission lines.

A New Approach for Solving Inverse Scattering Problems with Overset Grid Generation Method

This paper presents a new approach of Forward-Backward Time-Stepping (FBTS) utilizing Finite-Difference Time-Domain (FDTD) method with Overset Grid Generation (OGG) method to solve the inverse scattering problems for electromagnetic (EM) waves. The proposed FDTD method is combined with OGG method to reduce the geometrically complex problem to a simple set of grids. The grids can be modified easily without the need to regenerate the grid system, thus, it provide an efficient approach to integrate with the FBTS technique. Here, the characteristics of the EM waves are analyzed. For the research mentioned in this paper, the ‘measured’ signals are syntactic data generated by FDTD simulations. While the ‘simulated’ signals are the calculated data. The accuracy of the proposed approach is validated. Good agreements are obtained between simulation data and measured data. The proposed approach has the potential to provide useful quantitative information of the unknown object particularly for shape reconstruction, object detection and others.

Second-Order Accurate FDTD Method for Nonuniform Plasma at Multilayer Interfaces

The second-order accurate finite-difference time domain (FDTD) method for nonuniform nonmagnetized plasma at multilayer interfaces is proposed based on the PLJERC scheme and Taylor series. The definition of the accuracy order of difference equations is given and a brief demonstration is presented to illustrate that the FDTD equations at the discontinuous interface based on the reflection coefficient theory is only first-order accurate. Second-order accurate FDTD equations are deduced according to the effective electron density at the interface both for the H-i-E case and the E-i-H case. A reflection coefficient test is done on a PEC slab covered by multilayer nonmagnetized plasma to validate the accuracy of the proposed FDTD method. Calculation results show that the reflection coefficient obtained by the proposed method coincides with that of the analytic methods well and the proposed method has higher accuracy than the conventional FDTD method. The reflection characteristics of the multilayer plasma with four typical electron density distribution profiles and versus incident angle, frequency, and electron collision frequency are analyzed by the proposed method.

A new high order dispersive FDTD method for Drude material with complex interfaces

In this paper, motivated by the needs of tracking the transient change in the regularity of the electromagnetic fields across a Drude interface, we propose a new Maxwell–Drude formulation for transverse magnetic problems with inhomogeneous Drude dispersive materials. Based on the auxiliary differential equation approach, the proposed formulation couples the wave equation for the electric component with Maxwell’s equations for the magnetic components. A new finite-difference time-domain (FDTD) algorithm is introduced for solving the proposed Maxwell–Drude system, in which the time dependent jump conditions across the Drude interface are enforced through the matched interface and boundary (MIB) method. The proposed FDTD method achieves a second order of accuracy in solving Drude interfaces with fluctuating curvatures and non-smooth corners based on a simple Yee lattice, while it can be generalized to up to sixth order in dealing with a straight Drude interface. Therefore, the proposed FDTD method is more accurate and cost-efficient than the classical FDTD methods for Drude material with complex interfaces.

Finite-Difference Time-Domain Study of Guided Modes in Nano-Plasmonic Waveguides

A conformal dispersive finite-difference time-domain (FDTD) method is developed for the study of one-dimensional (1-D) plasmonic waveguides formed by an array of periodic infinite-long silver cylinders at optical frequencies. The curved surfaces of circular and elliptical inclusions are modelled in orthogonal FDTD grid using effective permittivities (EPs) and the material frequency dispersion is taken into account using an auxiliary differential equation (ADE) method. The proposed FDTD method does not introduce numerical instability but it requires a fourth-order discretisation procedure. To the authors' knowledge, it is the first time that the modelling of curved structures using a conformal scheme is combined with the dispersive FDTD method. The dispersion diagrams obtained using EPs and staircase approximations are compared with those from the frequency domain embedding method. It is shown that the dispersion diagram can be modified by adding additional elements or changing geometry of inclusions. Numerical simulations of plasmonic waveguides formed by seven elements show that row(s) of silver nanoscale cylinders can guide the propagation of light due to the coupling of surface plasmons.

Novel FDTD Simulation Method Using Multiple-Analysis-Space for Electromagnetic Far Field

Wide-band undesired electromagnetic noise near electronic systems, which includes small noise source like the printed circuit board (PCB), is a current problem in the field of electromagnetic interference. However, the estimation method for the electromagnetic noise near a system under test has not been established. This paper proposes a newly developed estimation method of the electromagnetic noise for a wide area, from near to far field, using the finite difference time-domain (FDTD) method. The proposed FDTD simulation method is an estimation technique for near to far field with multiple analysis spaces (MAS). The MAS has an internal analysis space (IAS) and an external analysis space (EAS). The analysis near a radiation source can be calculated in the IAS. The EAS is the outside space from IAS, which is for calculation of the far field. It is expected that the proposed FDTD method by MAS (FDTD-MAS) decrease in the calculation cost in terms of computational time and memory costs, especially for estimation of radiation from PCB. The principle procedure of the FDTD-MAS method is described in the first part of this paper. As example of advantages of the calculation and confirmation of the calculation accuracy, the electric field distributions radiated from a 1-GHz half-wavelength dipole antenna in an IAS of 0.3/spl times/0.3 m/sup 2/ area and an EAS of 7/spl times/7 m/sup 2/ area are used as examples. When the cell size ratio of IAS to EAS is changed from 6 to 20, the FDTD and theoretical values show good agreement. It is indicated that the FDTD-MAS simulation method is one of the most powerful tools for the estimation of electromagnetic noise from near field to far field from small and thin source.

A fourth-order accurate FDTD scheme with long-time stability

This letter presents a new finite-difference time-domain (FDTD) scheme with fourth-order accuracy in time and space. A combination of staggered backward differentiation time integrator and high-order spatial discretization is used to derive fourth-order accurate FDTD equations. The fourth-order accuracy of the proposed FDTD method is verified by monitoring L/sub 2/ norm errors in a two-dimensional partially-filled cavity. Furthermore, the computational cost study shows that the proposed fourth-order scheme is much more efficient than Yee's second-order FDTD scheme in solving the inhomogeneous cavity problem.