Symplectic Finite-difference Time-domain Research Articles

Plasma photonic crystals numerical and filter characteristics analysis based on symplectic algorithm

From the Maxwell equation, the method of symplectic finite-difference time-domain is applied in analyzing one-dimensional plasma photonic crystal. The propagation process of electromagnetic pulse in one-dimensional vacuum plasma photonic crystal structure is simulated by symplectic algorithm discrete in 2nd order time 2nd order space (T2S2), and 2nd order time 4th order space (T2S4) respectively. Then, from the perspective of frequency domain, the reflection coefficient of the plasma–vacuum photonic crystals is analyzed. The results show that the symplectic finite-difference time-domain method is accuracy and correctness. In the end, the filter characteristics of the plasma photonic crystals (PPCs) are analyzed in different thickness of plasma.

Symplectic FDTD algorithm for the simulations of double dispersive materials

Combined with the Lossy Drude-Lorentz dispersive model, a symplectic finite-difference time-domain (SFDTD) algorithm is proposed to deal with the double dispersive model. Based on matrix splitting, symplectic integrator propagator and the auxiliary differential equation (ADE) technique, with the rigorous and artful formula derivation, the algorithm is constructed, and detailed formulations are provided. Excellent agreement is achieved between the SFDTD-calculated and exact theoretical results when transmittance coefficient in simulation of double dispersive film in one dimension is calculated. As to numerical results for a more realistic structure in three dimensions, the simulation of periodic arrays of silver split-ring resonators using the Drude dispersion model are also included. The transmittance, reflectance, and absorptance of the structure are presented to test the efficiency of the proposed method. Our method can be used as an efficiency simulation tool for checking the experimental data.

A symplectic FDTD algorithm for the simulations of lossy dispersive materials

A high-order symplectic finite-difference time-domain (SFDTD) algorithm, based on the matrix splitting, the symplectic integrator propagator and the auxiliary differential equation (ADE) technique, is presented. The algorithm is applied to the lossy Lorentz–Drude dispersive model. With the rigorous and artful formula derivation, the detailed formulations are provided. Moreover, the present algorithm can also be applicable to the lossy Drude and Lorentz dispersive model in a straightforward manner. An excellent agreement is achieved between the SFDTD-calculated and exact theoretical results when calculating the transmission coefficient in simulation of metal films. Focusing action of the matched left-handed materials (LHMs) slab is also achieved as the second example in the two-dimensional space. Numerical results for a more realistic structure, the simulation of periodic arrays of silver split-ring resonators (SRRs) using the Drude dispersion model, are also included, and the results agree well with those obtained by the finite element method (FEM).

A Parameter-Optimized Symplectic FDTD Method Based on the (4,4) Stencil

A parameter-optimized (4,4) stencil-based symplectic finite-difference time-domain method [PO-SFDTD(4,4)] is proposed to tailor the numerical dispersion behavior according to different specifications such as zero dispersion error at designated directions or zero dispersion anisotropy, either at a certain frequency or for a given bandwidth. The effect of the proposed parameter optimization on numerical stability is also discussed. Compared to the conventional higher-order symplectic methods, the proposed PO-SFDTD(4,4) method yields better flexibility in handling dispersion and anisotropy errors.

High-order symplectic FDTD scheme for solving a time-dependent Schrödinger equation

Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrödinger equation. First, the high-order symplectic framework for discretizing a Schrödinger equation is described. Then the numerical stability and dispersion analyses are provided for the FDTD(2, 2), higher-order FDTD(2, 4) and SFDTD(3, 4) schemes. Next, to implement the Dirichlet boundary condition encountered in the quantum eigenvalue problem, the image theory and one-sided difference technique are manipulated particularly for high-order collocated differences. Finally, a detailed numerical study on 1D and 2D quantum eigenvalue problems is carried out. The simulation results of quantum wells and harmonic oscillators strongly confirm the advantages of the SFDTD scheme over the traditional FDTD method and other high-order approaches. The explicit SFDTD scheme, which is high-order-accurate and energy-conserving, is well suited for a long-term simulation and can save computer resources with large time step and coarse spatial grids.

Symplectic FDTD method study left-handed material electromagnetic characteristics

A symplectic finite-difference time-domain (SFDTD) method is used. The method is based on expressing the dynamical system in Hamiltonian form, it can maintain the energy conservation (i.e. Hamiton volume conservation), and the corresponding mathematical formulation for the evolution of the system state is symplectic transformation. This method has better stability and accuracy than the general FDTD method. This is the first use of the method to study the electromagnetic properties of left-handed materials. Using the Drude dispersion medium model to describe the dispersion characteristics of left-handed materials, and left-handed materials with negative refractive index, the collection effect and phase compensation effect are simulated.

High-order unified symplectic FDTD scheme for the metamaterials

A high-order unified symplectic finite-difference time-domain (US-FDTD) method, which is energy conserved, for modeling the metamaterials is proposed. The lossless Drude dispersive model is taken into account in US-FDTD scheme, and the detailed formulations of the proposed US-FDTD method are also provided. The high-order split perfectly matched layers (SPML) are used as the absorbing boundary conditions (ABCs) to terminate the computational domain. The analysis of Courant stability and numerical dispersion demonstrate that US-FDTD scheme is more efficient than the traditional time domain numerical methods. Focusing and refocusing of the electromagnetic wave in target detection is validated using the normal incident Gaussian beam with a matched slab. Oblique incidence results associated with the inverse Snell effect and the phase compensation effect of the composite slab further demonstrated the efficiency of the method. Numerical results for a more realistic structure are also included. All the results agree well with the theoretical prediction. The method proposed here can be directly put into using as a time-domain full-wave simulation tool for applications in metamaterials.

High-oder symplectic FDTD scheme for solving time-dependent Schrdinger equation

Using three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD(3, 4)) scheme is proposed to solve the time-dependent Schrdinger equation. First, high-order symplectic framework for discretizing the Schrdinger equation is described. The numerical stability and dispersion analyses are provided for the FDTD(2, 2), FDTD(2, 4) and SFDTD(3, 4) schemes. The results are demonstrated in terms of theoretical analyses and numerical simulations. The spatial high-order collocated difference reduces the stability that can be improved by the high-order symplectic integrators. The SFDTD(3, 4) scheme and FDTD(2, 4) approach show better numerical dispersion than the traditional FDTD(2, 2) method. The simulation results of a two-dimensional quantum well and harmonic oscillator strongly confirm the advantages of the SFDTD(3, 4) scheme over the traditional FDTD(2, 2) method and other high-order approaches. The explicit SFDTD(3, 4) scheme, which is high-order-accurate and energy-conserving, is well suited for long-term simulation.

The Stability and Numerical Dispersion Study of the ADI-SFDTD Algorithm

In this letter, the alternating-direction-implicit (ADI) technique is applied to Symplectic finite-difference time-domain (SFDTD) method, the curl operator is endued with two different styles when doing computation from the th progression to th progression. It holds the advantages of both ADI-FDTD and SFDTD, not only eliminating the restriction of the Courant-Friedrich-Levy (CFL), but also holding the inner characteristics of Maxwell’s equations. The analytical accuracy and efficiency of the proposed method is verified good.

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order symplectic finite-difference time-domain (SFDTD) scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain (FDTD), the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to −300 dB.

Analysis of numerical dispersion properties of SFDTD and MRTD schemes

In this paper, the Maxwell's equations are written as Hamilton canonical equations by using Hamilton functional variation method. Maxwell's equations can be discretized with symplectic propagation technique combined with high-order difference schemes approximations to construct symplectic finite difference time domain (SFDTD) method. The high-order dispersion equations of the scheme for space is deduced. The numerical dispersion analysis is included, and it is compared with the multiresolution time-domain (MRTD) method based on the Daubechies scaling functions. Numerical results show high efficiency and accuracy of the SFDTD method.

A Compact Symplectic High-Order Scheme for Time-Domain Maxwell's Equations

A fourth-order compact symplectic finite-difference time-domain (CS-FDTD) method for modeling long-range propagation is proposed. Theoretical analyses of numerical stability and dispersion are presented, and the comparisons to Fang's high-order FDTD and symplectic FDTD (S-FDTD) method are provided. One-dimensional (1-D) numerical simulation is performed to investigate the distortion of the long-range pulse propagation. It indicates the improved performance of the CS-FDTD approach compared to the S-FDTD method.

Survey on Symplectic Finite-Difference Time-Domain Schemes for Maxwell's Equations

To discretize Maxwell's equations, a variety of high-order symplectic finite-difference time-domain schemes, which use th-order symplectic integration time stepping and th-order staggered space differencing, are surveyed. First, the order conditions for the symplectic integrators are derived. Second, the comparisons of numerical stability, dispersion, and energy-conservation are provided between the high-order symplectic schemes and other high-order time approaches. Finally, these symplectic schemes are studied by using different space and time strategies. According to our survey, high-order time schemes for matching high-order space schemes are required for optimum electromagnetic simulation. Numerical experiments have been conducted on radiation of electric dipole and wideband S-parameter extraction of dielectric-filled waveguide. The results demonstrate that the high-order symplectic scheme can obtain satisfying numerical solutions under high Courant-Friedrichs-Levy number and coarse grid conditions.

Accurate modeling of dielectric interfaces by the effective permittivities for the fourth-order symplectic finite-difference time-domain method

The fourth-order finite-difference time-domain (FDTD) method using a symplectic integrator propagator can calculate the propagation of the electromagnetic waves with very low dispersion error in the region of a constant or smoothly varying index profile. An additional technique is required for the problem with the discontinuous dielectric interfaces. We derived the third-order effective permittivities at dielectric interfaces for the fourth-order FDTD method in the case of 2D TE polarization. As the required accuracy level is increased, the memory resources used by the fourth-order FDTD method with the effective permittivities are reduced severalfold or more compared with the standard FDTD method. The accurate performance of the proposed method is demonstrated through numerical examples.

Application of the high‐order symplectic FDTD scheme to the curved three‐dimensional perfectly conducting objects

AbstractA high‐order symplectic finite‐difference time‐domain (SFDTD) scheme using the diagonal split‐cell model is presented to analyze electromagnetic scattering of the curved three‐dimensional perfectly conducting objects. On the one hand, for the undistorted cells, the fourth‐order accurate spatial difference is employed. On the other hand, for the completely distorted cells, the treatment of the curved surfaces is based on the diagonal split‐cell model. Finally, for the partially distorted cells, the interpolation strategy is proposed to keep the field components continuous. The numerical experiments suggest that the diagonal SFDTD scheme can obtain more accurate results than both the staircased SFDTD scheme and the traditional diagonal FDTD method. Furthermore, in view of the high numerical stability, the improved symplectic scheme does not need to decrease time increment to comply with the stability criterion. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 931–934, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22306

Radar cross section computation using symplectic Runge-Kutta-Nystrom method

In this paper, a high-order symplectic finite difference time domain schemes is constructed for Hamilton system, using the symplectic Runge-Kutta-Nystrom (SYRKN) method. On the basis of fixed phase space and total energy in the Hamilton system, a formula of iterative algorithm is proposed which can be used to calculate the radar cross section of a metal cylinder. Calculation results have shown that the SYRKN method is accurate and fast.

Higher Stability Limits for the Symplectic FDTD Method by Making Use of Chebyshev Polynomials

A new scheme is introduced for obtaining higher stability performance for the symplectic finite-difference time-domain (FDTD) method. Both the stability limit and the numerical dispersion of the symplectic FDTD are determined by a function zeta. It is shown that when the zeta function is a Chebyshev polynomial the stability limit is linearly proportional to the number of the exponential operators. Thus, the stability limit can be increased as much as possible at the cost of increased number of operators. For example, the stability limit of the four-exponential operator scheme is 0.989 and of the eight-exponential operator scheme it is 1.979 for fourth-order space discretization in three dimensions, which is almost three times the stability limit of previously published symplectic FDTD schemes with a similar number of operators. This study also shows that the numerical dispersion errors for this new scheme are less than those of the previously reported symplectic FDTD schemes

Symplectic finite-difference time-domain method for maxwell equations

We introduce a symplectic finite-difference time-domain method for electromagnetic field simulation. Our method can successfully solve Maxwell equations involving conductor loss, which cannot be solved by the symplectic integration methods that have been presented in previous works. A class of high-order symplectic schemes for computing the time-dependent electric and magnetic fields are derived on the basis of an s-stage symplectic partitioned Runge???Kutta method.We present numerical results to illustrate the validity and accuracy of the algorithm.

Total Field and Scattered Field Technique for Fourth-OrderSymplectic Finite Difference Time Domain Method

Using symplectic integrator propagator, a three-dimensionalfourth-order symplectic finite difference time domain (SFDTD) method isstudied, which is of the fourth order in both the time and spacedomains. The method is nondissipative and can save more memory comparedwith the traditional FDTD method. The total field and scattered field(TF-SF) technique is derived for the SFDTD method to provide theincident wave source conditions. The bistatic radar cross section (RCS)of a dielectric sphere is computed by using the SFDTD method for thefirst time. Numerical results suggest that the SFDTD algorithm acquiresbetter stability and accuracy compared with the traditional FDTDmethod.

A Diagonal Split-cell Model for the High-order Symplectic FDTD Scheme

A high-order symplectic FDTD (SFDTD) scheme using the diagonal split-cell model is presented to analyze electromagnetic scattering of the curved three-dimensional perfectly conducting objects. One the one hand, for the undistorted cells, the fourth-order accurate spatial difierence is employed. On the other hand, for the completely distorted cells, the treatment of the curved surfaces is based on the diagonal split-cell model. Finally, for the partially distorted cells, the interpolation strategy is proposed to keep the fleld components continuous. The numerical experiments suggest that the diagonal SFDTD scheme can obtain more accurate results than both the staircased SFDTD scheme and the traditional diagonal FDTD method. Furthermore, in view of the high numerical stability, the improved symplectic scheme does not need to decrease time increment to comply with the stability criterion.