Shift Operator Finite-difference Time-domain Research Articles

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 modificatory algorithm for electrically thin dispersive layers base on shift operator finite-difference time-domain method

A novel technique for treating electrically thin dispersive layer with the finite difference time domain (FDTD) method is introduced. The proposed model is based on modifying the node update equations to account for the layer, where the electric and magnetic flux densities are locally averaged in the FDTD grid. Then, based on the characteristics that the complex permittivity and complex permeability of three kinds of general dispersive media model, i.e. Debye model, Lorentz model, and Drude model, may be described by rational polynomial fraction in jω, the shift operator method is then applied to obtain the recursive formulation for D and E, B and H available for FDTD computation is obtained. The model is validated with several numerical examples. The computed results illustrate the generality, memory and time step economy and the precision of presented scheme.

New FDTD-based method for computing the Lorentz dispersive media

We apply the shift-operator finite-difference time-domain (SO-FDTD) method to the calculation of the Lorentz dispersive media. The Lorentz-medium permittivity is written as a rational fractional function, and the relation between D and E is derived in a time domain. The high efficiency and accuracy of the method is demonstrated by calculating the reflection and transmission of the electromagnetic plane wave impinging on a Lorentz-dispersive-medium slab. The results obtained with the help of the SOFDTD method are compared with analytical results. The SO-FDTD method is proved to have high efficiency and accuracy in computing the Lorentz dispersive media.

Analysis on the Calculation of Plasma Medium with Parallel SO-FDTD Method

This paper introduces a novel parallel shift operator finite-difference time-domain (SO-FDTD) method for plasma in the dispersive media. We calculate the interaction between the electromagnetic wave of various frequencies and non-magnetized plasma by using the parallel SO-FDTD method. Then, we compare the results, which are calculated with serial and parallel SO-FDTD executions to obtain the speedup ratio and validate the parallel execution. We conclude that the parallel SO method has almost the same precision as the serial SO method, while the parallel approach expands the scope of memory and reduces the CPU time.

An improved shift operator finite-difference time-domain method based on digital signal processing technique for general dispersive medium

An improved shift operator finite-difference time-domain （SO-FDTD） method for general dispersive medium based on the implementation of infinite impulse response filter in digital signal processing technique is presented. Compared with the commonly used SO-FDTD, the storage variables in the improved SO-FDTD are reduced by 33% and computational efficiency is also increased. Finally, the generality and the feasibility of the presented scheme are validated by calculations of scattering by first order and second order dispersive objects.

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.

Calculation of the Effect on the Reflection of the Plane Electromagnetic Wave for Non-Magnetized Plasma with Different Electron Density Distributions

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a non-magnetized plasma slab with different electron density distributions. The results show that the average electron density only determines overall trends of the reflection, and different distributions affect the oscillating process of the reflection. If the average electron density maintains the same, the distribution of electron density with homogenous or inhomogeneous alternation will sharply take effects on the reflection. And magnitude of alternation of electron density affects the incident frequency directly when the reflection tends to uniform.

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.