A systematic and topologically stable conformal finite-difference time-domain algorithm for modeling curved dielectric interfaces in three dimensions

A systematic conformal finite-difference time-domain (FDTD) algorithm for the direct modeling of dielectric interfaces in three dimensions is presented in this paper. The straightforward procedure is based on the proper reformation of the grid cells in the vicinity of the dielectric surface, leading thus to the creation of five-faced prisms on the primary grid, apart from the standard hexagonal ones. The new scheme overcomes any topological deficiency that forbids the contour path FDTD and conformal FDTD technique to directly simulate dielectric boundaries, since it maintains the lattice duality. Therefore, no instabilities, even late-time ones, are observed. On the other hand, the accuracy obtained, even with very coarse meshes, is very good as is proved by the numerical analysis of various resonance problems.     

Equivalence of propagation characteristics for thetransmission-line matrix and finite-difference time-domain methods intwo dimensions

The equivalence of propagation characteristics for the transmission line matrix (TLM) and finite-difference-time-domain (FD-TD) methods in two dimensions is discussed. A propagation analysis of a TLM shunt node complete with permittivity and loss stubs and a dispersion analysis of the two-dimensional FD-TD method in an arbitrary medium are performed and yield dispersion relations. The relations are identical when the FD-TD method is operated at the upper limit of its stability range     

Computer-aided design of two dimensional electric-type hyperthermiaapplicators using the finite-difference time-domain method

A hyperthermia applicator design tool consisting of a finite-difference time-domain (FDTD) technique in combination with a graphical display of electric fields and normalized linear temperature rise is described. This technique calculates, rather than assumes, antenna current distributions; it includes mutual interactions between the body and the applicator, and it calculates driving-point impedance and power delivered to the applicator. Results show that the fundamental limitation of 2-D electric-type applicators is overheating of the fat by normal components of the electric field, which exist because of near fields and capacitive coupling with the muscle. Two factors which contribute to the capacitance are the muscle conductivity and the small antenna size in air. Two examples of applicators designed to avoid fat overheating are described: a 27-MHz segmented dipole for heating large tumors to 7 cm depth, and a 100-MHz dipole for small tumors to 5 cm depth. The first uses a water bolus, and the second uses a water bolus with low-permittivity strips to reduce normal fields at the antenna ends. The results of this study describe fundamental limitations of electric field applicators, and illustrate the use of a powerful applicator design tool that allows rapid evaluation of a wide range of ideas for applicators which would require months and years to test experimentally.     

金属透镜的色散时域有限差分法研究

为克服传统时域有限差分法(FDTD)不能计算色散材料的困难,给出了一种基于Drude模型的色散FDTD算法,并推导出具体的差分公式。将该方法用于模拟金属透镜的聚焦功能,结果与已有理论吻合。本文方法完全适用于分析电导率与频率有关的各种色散材料所构建的光波导。     

Space-domain finite-difference and time-domain moment method for electromagnetic simulation

A hybrid time-domain numerical method based on finite-difference technique and moment method is proposed. Starting from Maxwell's differential equations, our method uses Yee's finite difference scheme in the space domain, but does not utilize the customary explicit leap-frog time scheme. Instead, in the time domain, the fields are expanded in a series of basis functions and treated by a moment method procedure. By choosing appropriate basis functions and testing functions, the conventional finite-difference time-domain (FDTD) formulation and the order-marching unconditionally stable FDTD scheme can be derived from our method as two special cases. Finally, we use triangle basis functions and Galerkin's testing procedure to get an implicit formulation. To verify the accuracy and efficiency of the new formulation, we compare the results with the FDTD method. Our method improves computational efficiency notably, especially for multiscale problems with fine geometric structures, which is restricted by stability constrain in the FDTD method.     

A selective survey of the finite-difference time-domain literature

The finite-difference time-domain (FDTD) method is arguably the most popular numerical method for the solution of problems in electromagnetics. Although the FDTD method has existed for nearly 30 years, its popularity continues to grow as computing costs continue to decline. Furthermore, extensions and enhancements to the method are continually being published, which further broaden its appeal. Because of the tremendous amount of FDTD-related research activity, tracking the FDTD literature can be a daunting task. We present a selective survey of FDTD publications. This survey presents some of the significant works that made the FDTD method so popular, and tracks its development up to the present-day state-of-the-art in several areas. An “on-line” BibT_EX database, which contains bibliographic information about many FDTD publications, is also presented     

Analysis of the accuracy of the numerical reflection coefficient of the finite-difference time-domain method at planar material interfaces

This paper presents a rigorous analysis of the numerical error of the reflection coefficient of the finite-difference time-domain (FDTD) algorithm at planar material boundaries. The derived expressions show that the numerical reflection depends on a large number of parameters, such as the grid resolution and the time step, the frequency, the angle, and the polarization of the incident wave. In conclusion, the FDTD algorithm does not accurately fulfil the boundary conditions for the continuity of the fields. The theoretical findings enable the detailed characterization of the field behavior in the grid at material interfaces. The numerical total reflection and the Brewster angle are studied as well as the discretization influences on the specific absorption rate (SAR).     

Steady-state response by finite-difference time-domain method and lanczos algorithm

A hybrid method combining the finite-difference time-domain (FDTD) method and Lanczos algorithm is proposed for efficiently obtaining the steady-state response for closed systems. With the Lanczos algorithm, modes of the FDTD operator can be easily extracted to reconstruct the steady-state response at any time by an analytic formula. With the aid of the time-reversal technique, existing FDTD codes are preserved. Numerical results show that with only very few Lanczos iterations, results of good agreement can be achieved between the proposed method and brute-force FDTD.     

Proposal and finite-difference time-domain simulation of whisperinggallery mode microgear cavity

The existence of many high Q whispering gallery modes in microdisk and microcylinder lasers seriously affects the internal efficiency in lasing operation and disturbs the enhancement of the spontaneous emission factor. To suppress these modes except for one lasing mode, we propose the microgear cavity having a grating with the same period as that of the mode standing wave. A finite-difference time-domain simulation theoretically demonstrates that the microgear selects one resonant mode that satisfies the unique condition regarding the mode order and the phase. This paper describes the dependence of the mode behavior on some structural parameters, and concludes that a deep grating, which seems to be possible in an experiment, allows for sufficient suppression of any types of nonlasing modes and the enhancement of the Q factor of the lasing mode     

电磁计算中辛时域有限差分算法研究进展

辛时域有限差分（symplectic finite-difference time-domain,SFDTD）算法作为一种高精度、高稳定、高保真度的时域数值算法,在多个学科领域得到了广泛的应用,并已发展成为一种较为成熟的数值计算方法.本文主要对SFDTD算法的构建、数值优化以及相关关键技术处理进行了介绍.重点总结了基于时间和空间上的差分近似优化处理方法,处理不连续边界及金属曲面时的局部修正方法,以及时域电磁仿真中不可或缺的三大关键技术:总场/散射场技术、完全匹配层（perfect matched layer,PML）、近远场变换技术.最后,介绍了SFDTD算法在电磁仿真、量子力学求解、多物理问题建模与分析中的具体应用.     

A finite-difference time-domain beam-propagation method for TE- and TM-wave analyses

The application of the existing time-domain beam-propagation method (TD-BPM) based on the finite-difference (FD) formula has been limited to the TE-mode analysis. To treat the TM mode as well as the TE mode, an improved TD-BPM is developed using a low-truncation-error FD formula with the aid of the alternating-direction implicit scheme. To improve the accuracy in time, a Pade (2,2) approximant is applied to the time axis. Although the truncation error in time is found to be O(/spl Delta/t/sup 2/), as in the case of the Pade (1,1) approximant, this method allows us to use a large time step. A substantial reduction in CPU time is found when compared to the conventional method in which a broadly banded matrix is solved by the Bi-CGSTAB. The effectiveness in evaluating the TE- and TM-mode waves is shown through the analysis of the power reflectivity from a waveguide facet. This method is also applied to the analysis of a waveguide grating. The accuracy and efficiency of the TD-BPM are assessed in comparison with the finite-difference time-domain method.     

Treating late-time instability of hybridfinite-element/finite-difference time-domain method

The hybrid finite element/finite-difference time-domain (FETD/FDTD) method previously proposed to handle arbitrarily shaped dielectric objects is employed to investigate electromagnetic problems of high Q systems for which the transient response over a very long duration is necessary. To begin with, the paper demonstrates that this hybrid method may suffer from late-time instability and spurious DC modes. Then an approach which combines the temporal filtering and frequency shifting techniques is presented to overcome sequentially and, respectively, the two drawbacks. Its accuracy is validated by the favorable comparison with several different methods for the analysis of resonant frequencies and and factors of the various modes in an isolated dielectric resonator. Finally, the present method is applied to calculate the scattering parameters on the microstrip line due to the presence of the cylindrical dielectric resonator     

Characterization of microstrip discontinuities using conformalmapping and the finite-difference time-domain method

Microstrip discontinuities are analyzed using Wheeler's waveguide model and the finite-difference time-domain (FDTD) method. Wheeler's model employs a conformal transformation to convert a microstrip into an enclosed waveguide structure. This permits the mapping of a discontinuous microstrip into a discontinuous, but enclosed, waveguide. The enclosed waveguide eliminates the difficulties usually associated with analysis of an open domain geometry. The FDTD technique is then used to calculate the scattering coefficients of the discontinuous waveguide. The features of this approach are: (1) it yields a smaller computational domain than that required to analyze the untransformed geometry; (2) it yields results over a band of frequencies; and (3) it is simple to implement. Results obtained using this scheme show good agreement with previously published results     

Fast single-mode characterization of optical fiber by finite-difference time-domain method

Usually, although not always, manufacturers producing optical fiber state that the functioning will be single mode in most cases without specifying the wavelengths to be worked with. A rapid method of light simulation within the optical fibers was developed for a single-mode characterization, which avoids errors and problems in transmitting the signals through the fiber. The method was validated with two optical fibers, in which the intensity patterns are well known in theory, and a rather good fit between the theoretic intensity curves at the endface of the fibers was achieved. In order to characterize the monomodal regime, the method was applied to two optical fibers with different refractive-index profiles, using the finite-difference time-domain (FDTD) for the body of revolution (BOR).     

The finite-difference time-domain solution of lossy MTL networkswith nonlinear junctions

We describe a numerical technique to solve lossy multiconductor transmission line (MTL) networks, also known as tube/junction networks, which contain nonlinear lumped circuits in the junctions. The method is based on using a finite-difference technique to solve the time-domain MTL equations on the tubes, as well as the modified nodal analysis (MNA) formulation of the nonlinear lumped circuits in the junctions. The important consideration is the interface between the MTL and MNA regimes. This interface is accomplished via the first and last finite-difference current/voltage pair on each MTL of the network and, except for this, the two regimes are solved independently of each other. The advantage of the FDTD method is that the MTL equations may contain distributed source terms representing the coupling with an external field. We apply the method to previously published examples of multiconductor networks solved by other numerical methods, and the results agree exceptionally well. The case of an externally coupled field is also considered     

Toward the development of a three-dimensional unconditionallystable finite-difference time-domain method

In this paper, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formulating an unconditionally stable two-dimensional FDTD is applied. Unlike the conventional ADI algorithms, however, the alternation is performed in respect to mixed coordinates rather than to each respective coordinate direction, Consequently, only two alternations in solution marching are required in the 3-D formulations. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method. It is found that the number of iterations with the proposed FDTD can be at least four times less than that with the conventional FDTD at the same level of accuracy     

Characterization of three-dimensional open dielectric structuresusing the finite-difference time-domain method

Millimeter and submillimeter wave three-dimensional (3-D) open dielectric structures are characterized using the finite-difference time-domain (FDTD) technique. The use of FDTD method allows for the accurate characterization of these components in a very wide frequency range. The first structure characterized through FDTD for validation purposes is a mm-wave image guide coupler. The derived theoretical results for this structure are compared to experimental data and show good agreement. Following this validation, a sub-mm wave transition from a strip-ridge line to a layered ridge dielectric waveguide (LRDW) in open environment is analyzed, and the effects of parasitic radiation on electrical performance are studied. The transition is found to be very efficient over a wide sub-mm frequency band which makes it useful for a variety of applications. In addition to the transition, a sub-mm wave distributed directional coupler made of the LRDW is extensively studied using the FDTD method as an analysis tool. Furthermore, an iterative procedure based on the FDTD models is used to design a 3-dB coupler with a center frequency of 650 GHz and negligible radiation loss. This successful design shows that the FDTD technique can be used not only as an analysis method, but also as a design tool to provide designs which take into account all high frequency parasitic effects     

Hybrid finite-difference time-domain modeling of curved surfacesusing tetrahedral edge elements

A hybrid finite-difference time-domain (FDTD) method is proposed for solving transient electromagnetic problems associated with structures of curved surfaces. The method employs the conventional FDTD method for most of the regular region but introduces the tetrahedral edge-based finite-element scheme to model the region near the curved surfaces. Without any interpolation for the fields on the curved surface, nor any additional stability constraint due to the finer division near the curved surfaces, the novel finite-element scheme is found to have second-order accuracy, unconditional stability, programming ease, and computational efficiency. The hybrid method is applied to solve the electromagnetic scattering of three-dimensional (3-D) arbitrarily shaped dielectric objects to demonstrate its superior performance     

Efficient body of revolution finite-difference time-domain modelingof integrated lens antennas

An efficient body of revolution finite-difference time-domain (BOR-FDTD) method for the analysis of the radiation properties of integrated lens antennas is presented in this paper. By neglecting most of the reactive power of the planar feed and by expanding the filtered source currents into azimuthal modes, lenses with both rotationally and nonrotationally symmetric planar feeds can be handled. It appears that three to four azimuthal modes are sufficient to adequately model the magnetic currents of a double-slot feed. Therefore, compared to a full three-dimensional (3-D) numerical method, the implementation of the proposed method is very time and memory efficient. If only the radiation properties are required, the model described here can also be applied efficiently to other axially symmetric geometries with an asymmetric feeding structure     

Analysis of arbitrarily shaped two-dimensional microwave circuitsby finite-difference time-domain method

A version of the finite-difference time-domain method adapted to the needs of S-matrix calculations of microwave two-dimensional circuits is presented. The analysis is conducted by simulating the wave propagation in the circuit terminated by matched loads and excited by a matched pulse source. Various aspects of the method's accuracy are investigated. Practical computer implementation of the method is discussed, and an example of its application to an arbitrarily shaped microstrip circuit is presented. It is shown that the method in the proposed form is an effective tool of circuit analysis in engineering applications. The method is compared to two other methods used for a similar purpose, namely the contour integral method and the transmission-line matrix method