Operator Finite-difference Time-domain Research Articles

Efficient Finite-Difference Time-Domain Modeling of Time-Varying Dusty Plasma

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic analysis of dusty plasma sheath in reentering hypersonic vehicles. The time-varying characteristics of dusty plasma should be considered to accurately analyze THz wave propagation in dusty plasma. In this work, we propose an efficient FDTD modeling of time-varying dusty plasma based on the combination of the bilinear transform and the state-space approach. The proposed FDTD formulation for time-varying dusty plasma can lead to a significant improvement in computational efficiency against the conventional shift operator FDTD counterpart while maintaining numerical accuracy. Numerical examples are performed to validate the proposed FDTD modeling of time-varying dusty plasma.

SO-FDTD analysis on transmission characteristics of terahertz wave in plasma

The propagation characteristics of terahertz waves in high-temperature magnetized inhomogeneous plasma sheath were investigated theoretically by the shift operator finite difference time domain method. Both the transmission characteristics of left and right circularly polarized terahertz waves propagating in uniform or non-uniform plasma were analyzed. Simulation results reveal that the transmission characteristics of terahertz waves in plasma will be influenced by plasma parameters and the external magnetic field. The plasma sheath has a high pass filtering characteristic to terahertz waves, which provides a significant theoretical basis, to a certain extent, for the “blackout” problem.

A general finite difference time domain method for hybrid dispersive media model

The shift operator finite difference time domain (SO-FDTD) method is developed to deal with a hybrid dispersive media model. First, we prove that the complex permittivity of the hybrid dispersive media model can be described by a rational polynomial fraction with respect to jω. Then, the relation between electric displacement D and electric field strength E is derived in the time domain by introducing zt as a shift operator. The constitutive relation in the discretized time domain and the recursive formulation of D and E available for FDTD computation are obtained. Finally, the reflection of the hybrid dispersive slab is computed. The computed results are in good agreement with that obtained by analytic method. This illustrates the generalization and the feasibility of the presented scheme.

Shift operator method and Runge-Kutta exponential time differencing method for plasma

In this paper, the shift operator finite difference time domain (SO-FDTD) method and Runge-Kutta exponential time differencing (RKETD) method are introduced. The high accuracy and efficiency of the two methods are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collisional plasma slab. A comparison of computational efficiency of the two methods is presented by simulating the electromagnetic wave propagation in homogeneous non-magnetized plasma. The numerical results indicate that the calculation time using SO-FDTD method is less than that using RKETD method with almost the same accuracy.

A novel UPML FDTD absorbing boundary condition for dispersive media

The dispersion relation and the reflectionless condition are obtained by Maxwell's curl equations in a uniaxial anisotropic medium and the phase-matching principle. On the basis of the shift operator finite difference time domain (SO-FDTD) method and the transform relation from the frequency domain to the time domain (jω replaced by ), an FDTD absorbing boundary condition available for three types of general dispersive medium models, i.e. Debye model, Lorentz model and Drude model, is given. Numerical results show that the presented scheme has good absorbing performance (the relative error is less than 10−3) for three typical dispersive models. This illustrates the generality and the high effectiveness of the presented scheme.

Finite-difference time-domain studies of low-frequency stop band in superconductor-dielectric superlattice

The transmission coefficients of electromagnetic (EM) waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain (SO-FDTD) method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.

Addendum to: “A FDTD analysis on magnetized plasma of Epstein distribution and reflection calculation” [Computer Physics Communications 180 (1) (2009) 55–60]: A short comment on the equivalence of the shift-operator FDTD method and the bilinear frequency approximation technique for modeling dispersive electromagnetic applications

Recently, the shift operator finite difference time domain (SO-FDTD) method has been introduced by Yang [Computer Physics Communications 180 (1) (2009) 55–60] for modeling dispersive electromagnetic applications. This letter discuss the equivalence of this scheme and the well-known bilinear frequency approximation technique used in the field of digital signal processing. Although the SO-FDTD scheme looks different at first glance, it has been observed that it is fully equivalent to the bilinear frequency approximation technique. Consequently, the SO-FDTD scheme is indeed a bilinear transform operation which is unfortunately not cited by the author.

A finite difference time domain absorbing boundary condition for general frequency-dispersive media

The dispersion relations and the reflectionless conditions are obtained by the Maxwell’s curl equations in a uniaxial anisotropic medium and the phase-matching. Using the shift operator finite difference time domain （SO-FDTD） method and the transform relationship of frequency domain to time domain （jω replaced by /t）, an FDTD absorbing boundary condition for three kinds of general dispersive media model, i.e. the Debye model, Lorentz model and Drude model, is given. The characteristics of our absorbing boundary condition are tested. The computed results illustrated the generality and the feasibility of the scheme.

A FDTD analysis on magnetized plasma of Epstein distribution and reflection calculation

A novel finite-difference time-domain (FDTD) method with recursive relationships among operators, developed for magnetized dispersive medium, is named shift operator FDTD (SO-FDTD) method. In this paper, the dielectric property of magnetized dispersive media is written as rational polynomial function, the relationship between D and E is deduced in time-domain. The high accuracy and efficiency of this method is verified by calculating the reflection and transmission coefficient of electromagnetic waves through a collisional plasma slab. As the electron density in plasma distributes as Epstein formula, the effect of the gradient coefficient σ and plasma thickness on the reflection coefficient is calculated. The results show that with different σ, the distribution between the reflection coefficient and the incidence frequency is same; but there is certain difference within some specific frequency range. And there are fewer effects of different thicknesses on the reflection coefficient under different conditions.

A general method for finite difference time domain modeling of wave propagation in frequency-dispersive media

The analysis of electromagnetic scattering and propagation in dispersive media is complicated in time domain，because its dielectric property is frequency-dependent. A disadvantage of the prevailing algorithms is the need to deduce different formulations for each dispersion model. In this paper，the shift operator finite difference time domain (SO-FDTD) method is developed. First，we prove that the complex permittivity of three kinds of general dispersive media models，i.e. Debye model，the Lorentz model and the Drude model, may be described by rational polynomial functions in jω. By introducing a shift operator zt，the constitutive relation between D and E is derived in discretised time domain. The shift operator method is then applied to the general dispersive medium case. The recursive formulation for D and E available for FDTD computation is obtained. Finally，the scatterings by a dispersive sphere and a PEC object covered with dispersive media are computed. The computed results are in good agreement with the literature and the one obtained by Mies series solution. This illustrates the generality and the feasibility of the presented scheme.

SO-FDTD Analysis on Magnetized Plasma

In this paper, a novel finite-difference time-domain (FDTD) method with recursive relationships among operators is developed for magnetized dispersive medium, named as the shift operator FDTD(SO-FDTD). The dielectric property of magnetized dispersive medium is written as rational polynomial function, the relationship between D and E is deduced in time-domain. And its high accuracy and efficiency are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collision plasma slab.

SO-FDTD analysis of anisotropic magnetized plasma

A novel finite-difference time-domain (FDTD) method, called shift operator FDTD (SO-FDTD) method is developed for anisotropic magnetized dispersive media. The recursive relation between operators is used. In this paper, some expressions containing the dielectric constants of magnetized dispersive media are written as rational polynomial function. The SO-FDTD formulation for anisotropic magnetized plasma is derived. The high efficiency and effectiveness of the method are confirmed by computing the reflection and transmission through a magnetized plasma layer, with the direction of the propagation parallel to the direction of the biasing field. A comparison with frequency domain analytic results is included. The CPU time was several times shorter than that of the JEC method.