Shift 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.

Research on Transmission Characteristics of Two-Dimensional Superconducting Photonic Crystal in THz-Waves

In this paper, the transmission characteristics of two-dimensional photonic crystal with Hg-1223 cylindrical array in transverse magnetic mode are studied in terahertz-waves by shift operator finite-difference time-domain method. The effects of external temperature and pressure and the period and radius of the dielectric cylinders on the transmission properties of superconducting photonic crystal in terahertz-waves are studied. The simulation results show that external temperature and pressure can be used to change the plasma frequency of superconductor, thus adjusting band gap width of superconducting photonic crystal. The decreasing of the external temperature or the increasing of the pressure have resulted in the increasing of the band gap width of superconducting photonic crystal, while increasing external temperature or decreasing the pressure can decrease the band gap width, which gradually becomes apparent as temperature increases or pressure decreases. In addition, the increasing of the periods and radius of superconducting cylinders can also broaden the band gap of superconducting photonic crystal in terahertz-waves. The research in this paper is in terahertz-waves, and all the cutoff frequencies of band gap are between 0.1 and 6 THz, which provides references for practical application of superconducting photonic crystal.

Effect of the plasma sheath on the propagation of low frequency radio waves

The plasma sheath formed around a hypersonic vehicle traveling through the atmosphere will affect the quality of wireless signals. To fully grasp this effect, it is necessary to comprise the vehicle antennas in the investigations, which is considered in our work. Firstly, the discrete plasma sheath data is generated by using COMSOL. Then, combining the shift-operator Finite-Difference Time-Domain method and numerical methods such as the high-dimensional Lagrange interpolation, an electromagnetic algorithm designed for the discrete plasma sheath data is developed. Based on this, the influence of the plasma sheath on the radio wave propagation is studied under different flight condition. Results show that, due to the influence both of the plasma sheath and of the vehicle antenna, the radio waves exhibit rich propagation behaviors, such as the frequency-band shift and the tail diffraction, etc. Compared with other studies, the results in this paper more approximately reflect the propagation characteristics of radio waves in the hypersonic environment, and can provide a reference for the related applications.

Propagation characteristics of oblique incidence terahertz wave through non-uniform plasma**Project supported by the National Basic Research Program of China (Grant No. 2014CB340203), the National Natural Science Foundation of China (Grant Nos. 61431010 and 61501350), and the Natural Science Foundation of Shaanxi Province, China (Grant Nos. 2018JM6016 and 2016JM1001).

The propagation characteristics of oblique incidence terahertz (THz) waves through non-uniform plasma are investigated by the shift-operator finite-difference time-domain (SO-FDTD) method combined with the phase matching condition. The electron density distribution of the non-uniform plasma is assumed to be in a Gaussian profile. Validation of the present method is performed by comparing the results with those obtained by an analytical method for a homogeneous plasma slab. Then the effects of parameters of THz wave and plasma layer on the propagation properties are analyzed. It is found that the transmission coefficients greatly depend on the incident angle as well as on the thickness of the plasma, while the polarization of the incident wave has little influence on the propagation process in the range of frequency considered in this paper. The results confirm that the THz wave can pass through the plasma sheath effectively under certain conditions, which makes it a potential candidate to overcome the ionization blackout problem.

An improved cascaded SO-FDTD method for high temperature magnetized plasma

An improved cascaded shift operator finite-difference time-domain method is put forward for high temperature magnetized plasma. The calculation formulas of iterative coefficients of this method are given. These results show that the improved method can let the mathematical formula reduce math order and the computational complexity. This is contributed to the derivation of the formula and the compilation of the calculation program. The absorption and reflection characteristics of high temperature magnetized plasma on electromagnetic wave are studied by using this improved CSO-FDTD method. The effects of external magnetic field and temperature on the attenuation coefficient and absorption coefficient of the plasma are discussed. A new phenomenon is found, namely, a sharp transmission peak emerged in the physics band formed by a terahertz wave passing through the monolayer plasma. By studying the effects of external magnetic field and temperature, the phenomenon can be simply produced by monolayer high temperature plasma.

A high-precision electromagnetic technique for modeling and simulation in inhomogeneous media

ABSTRACTThe high-precision method for modeling inhomogeneous media and the precision limit of finite-difference time-domain (FDTD) are studied theoretically and numerically. Firstly, based on the transform-domain idea, a new layered modeling technique for inhomogeneous media is developed, with the control equation of the modeling precision given. Compared with other modeling methods, the paramount advantage of this method is that the modeling process is not restrained by the magnitude range of the data, and that the modeling precision can be controlled easily. Then, the shift operator finite-difference time-domain is adopted to determine the field values in inhomogeneous media, and a high-precision computational method is proposed. This method theoretically proves that the relationship between the FDTD grid size and the calculated field value satisfies a definite function, which is then verified by numerical examples. The significance of the results is that this relationship will provide an effective approach to predict field values during the modeling grid size tending to zero, which can be regarded in theory as an approximation to the true value of the electromagnetic (EM) fields. The advantages of this approach are that it not only inherits the advantages of the FDTD method, but also gives a way out of the difficulty that the EM algorithms available are difficult to provide a high-precision prediction of radio propagation; and it can be seen from the validation process in this paper that this approach could also be used in the algorithms based on the mesh modeling and in the inhomogeneous media for improving their calculation precision.

Plasma Passive Jamming for SAR Based on the Resonant Absorption Effect

The resonant absorption effect between plasma and electromagnetic waves makes the plasma a potential efficient passive jamming method for synthetic aperture radar. In this paper, the validity of plasma passive jamming is verified by comparing the echoes with and without plasma. First, the shift operator finite-difference time-domain method is utilized to numerically calculate the echoes from different plasma parameters. Then, the images of point target with and without plasma are obtained and compared. The image of point target with plasma is partly focused and the geometry character of point target is destructed. The simulation and analysis results validate the effectiveness of the proposed plasma passive jamming method.

Research on the scattering characteristics of electromagnetic waves in time‐varying and weakly collisional and fully ionized dusty in plasma

In this study, a three-dimensional (3D) time-varying dusty plasma iterative finite-difference time-domain (FDTD) algorithm is deduced by combining the relative permittivity of fully ionised dusty plasma and the shift-operator FDTD method. Then, a 3D time-varying dusty plasma model is established. The scattering characteristics of electromagnetic (EM) waves are analysed by calculating the backward radar cross-sections (RCSs) of different parameters in time-varying dusty plasma. The results show that the RCS will increase when the dust particles are considered in plasma. The values of RCS increase with the dust radius dust concentration relaxation time of charge and electron density increasing. In dusty plasma, the electron temperature has a different effect on the incident wave frequency bands. Finally, the effects of dust to electron density ratio on RCS are analysed and as the increase of the incident frequency, the absorption of dusty plasma on EM wave will reduce.

Evaluations of Plasma Stealth Effectiveness Based on the Probability of Radar Detection

To overcome the limitations of radar cross section characteristic, a method using detection probability as an indicator to evaluate plasma stealth effectiveness is proposed in this paper. Based on shift operator finite-difference time-domain method, the distorted waveform of linear frequency modulation radar echo is obtained when the targets coated with plasma. Then, by making a comparison between outputs of pulse compression with and without plasma, the peak instantaneous signal-to-noise ratio (SNR) loss is calculated. According to the signal detection theory, the relationship between plasma parameters and radar detection probability is built up through the SNR loss, in which the attenuation of radar echo and the mismatch loss of pulse compression are both considered. Finally, effects of plasma parameters including electron density, collision frequency, and radar frequency on the probability of detection have been studied systematically. By adopting detection probability $P_{d }\le 0.1$ as a valid criterion, the effective plasma parameters for different radar frequencies are given as a guide when using plasma for stealth application.

Propagation characteristics of terahertz waves in temporally and spatially inhomogeneous plasma sheath

The plasma sheath is produced by high-temperature heating during the reentry of a hypersonic vehicle to the Earth atmosphere. Temperature around the vehicle rises rapidly because of severe friction with air. The vehicle temperature behind friction is high enough to excite various real gas effects including chemical reactions of air, which contains ablation particles of vehicle, free electrons, and ions. The plasma sheath greatly affects the transmission of electromagnetic waves and has very strong interference on the communication signals, which results in interrupt between the target and the ground station, namely, blackout. The electron density of plasma sheath surrounding the aircraft is inhomogeneous and varies with time. Temperature and pressure will also change at different altitudes. Therefore, it is meaningful to investigate the propagation characteristics of electromagnetic waves in temporally and spatially inhomogeneous plasma sheath. The temporally and spatially inhomogeneous plasma sheath model is introduced and the electron density data of the National Aeronautics and Space Administration (NASA) reentry vehicle is employed. The relationships among temperature, pressure, and collision frequency are obtained with the empirical formula of collision frequency. Then, the reflection coefficient and transmission coefficient of time-varying single layer plasma are calculated with the shift operator finite-difference time-domain (SO-FDTD) method. These results are compared to verify the correctness of the proposed method. Finally, the LTJEC-FDTD method is used to calculate the reflection coefficient, transmission coefficient and absorptivity at different relaxation time, temperature, and pressure in the terahertz (THz) band. The results show that the higher temperature and pressure will enable the electromagnetic wave to penetrate the plasma sheath at high relaxation time of electron density. If the incident wave frequency is lower than the cut-off frequency of plasma, the reflection of electromagnetic wave will be more obvious. However, when the incident wave frequency is in the THz band, the effects of temperature and pressure on the propagation of electromagnetic wave are obviously weakened. The absorption of electromagnetic wave by plasma will be more obvious when the relaxation time, temperature, and pressure decrease. If the relaxation time of electron density is shorter than or equal to the period of THz wave, more energy of electromagnetic wave will be absorbed by the plasma sheath. Contrarily, if the relaxation time of electron density is much longer than the period of THz wave, the absorption of electromagnetic energy will decrease. This study gives some insight into the temporally and spatially inhomogeneous plasma sheath, and provides a theoretical basis for solving the blackout problem.

A high efficient SO-FDTD method for magnetized collisional plasma

Based on the Maxwell formulae and the auxiliary differential equation of polarized current density, this paper presents a high efficient shift-operator finite difference time-domain (SO-FDTD) method for simulating magnetized cold plasma, which combines time-domain shift operators with a memory-minimized algorithm. This method is applied to calculate the reflection and transmission of the electromagnetic waves incidence in a magnetized plasma layer, and its accuracy is validated by the analytical method. The bistatic radar cross section of magnetized plasma sphere is also calculated by this method. Numerical experiment demonstrates that the new method is more efficient than the improved SO-FDTD methods proposed in the recent references based on the same accuracy. Moreover, the recursion formulae of the new SO-FDTD method avoid huge expenses of computer resource arising from complicated convolutions and complex or exponential variables, so the computations for magnetized plasma are simpler than other FDTD methods based on recursive convolution or transformation principle such as piecewise-linear current density recursive convolution-FDTD method and Z-transformation-FDTD method proposed in former references.

SO-FDTD analysis on the stealth effect of magnetized plasma with Epstein distribution

Shift operator finite-difference time-domain (SO-FDTD) method is developed to study the stealth technology of inhomogeneous magnetized plasma in this paper. The high accuracy and efficiency of this method is verified by computing the reflection and transmission coefficients of electromagnetic wave through a collisional magnetized plasma slab in one dimension. The stealth effect of radar targets covered with Epstein distribution inhomogeneous magnetized plasma is studied. The results show that the stealth effect of radar targets covered with Epstein distribution inhomogeneous magnetized plasma is better than that of radar targets covered with homogeneous magnetized plasma.

SO-FDTD method of analyzing the reflection and transmission coefficient of weakly ionized dusty plasma layer

The complex permittivity of weakly ionized dusty plasma is presented as a fractional polynomial in j. A frequency-domain constitutive relation of weakly ionized dusty plasma is given by shift operator finite-difference time-domain (SO-FDTD) method in time domain. Also the recurrence relation on the electromagnetic properties of weakly ionized dusty plasma is deduced by the SO-FDTD. The reflection and transmission coefficients of the weakly ionized dusty plasma layer are calculated, and the influences which is caused by the change of the dust particle concentration and radius on reflection and transmission coefficients are also analyzed by the SO-FDTD method. The result shows that the reflection coefficient in the presence of dust particles is smaller than in the absence of dust particles, while the transmission coefficient in the former case is larger than in the latter case. Besides, it is found that the reflection coefficient decreases as the concentration or radius of dust particle increases.

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 FDTD formulation for high order dispersive media of muscle-equivalent

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 muscle slab. For human tissues where multiterm Debye relaxation equations must generally be used. We describe a new differential equation approach, which can be used for general dispersive media. In this method D( t) is expressed in terms of E( t) by means of a differential equation involving D, E, and their time derivatives. The method is illustrated by means of example of media for which relative permittivity is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body.

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.

The comparison of the CPU time between SO-FDTD method and PLCDRC method for dispersive media

The precision and computational efficiency of the shift operator finite-difference time-domain (SO-FDTD) method are compared with those of the piecewise linear current density recursive convolution (PLCDRC) method by simulating the electromagnetic wave at different frequency propagation in homogeneous unmagnetized plasma in this paper. The results show that the two methods almost have the same precision, but the CPU time of the SO-FDTD method is less than that of the PLCDRC method, this is because the SO-FDTD method eliminates many convolution operations of the PLCDRC method.

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.