Frequency-dependent Finite-difference Time-domain Research Articles

Computational Study on Air Film Approach in Reentry Blackout Mitigation

Communication blackouts during the atmospheric reentry phase are a significant challenge, as flight data are lost due to interruptions caused by plasma gas generated by aerodynamic heating. This study explores a novel mitigation method using an air film, a thin insulating coolant layer on the surface. The researchers successfully reduced the reentry blackout by employing a gas injection system. Through a coupled approach using computational fluid dynamics and a frequency-dependent finite-difference time-domain method, the plasma flow properties and electromagnetic propagation were analyzed around a test model in a wind tunnel in DLR (German Aerospace Center). The numerical results indicated that the injected nitrogen gas formed an insulating air film layer on the surface. The thin layer advected backward, maintaining a low temperature without ionization, and covered the object in the wake region. The electromagnetic waves propagated and reached a distant area because the electron density was low. It means that the air film layer acted as a propagation window for the telecommunication waves. Thus, communication blackouts will be avoidable because electromagnetic waves can transmit through the air-film layer. It concluded that the air film effect, developed as a thermal protection technique, is a novel mitigation scheme for reentry blackouts.

A Novel FDTD Approach Considering Frequency Dispersion of FR-4 Substrates for Signal Transmission Analyses at GHz Band

High-speed digital signaling can cause various signal integrity and electromagnetic interference problems. Signal attenuation and distortion can be observed in the gigahertz band owing to the frequency dispersion of substrates. In this article, we propose a frequency-dependent finite-difference time-domain (FDTD) approach for the numerical analyses of flame-retardant type-4 (FR-4) substrates. The proposed FDTD approach provides accurate broadband solutions because it can take into account the frequency dispersion of the substrate. First, the broadband complex permittivity of FR-4 substrates was measured using a balanced-type circular disk resonator and fitted into a Djordjevic model for the FR-4 substrates. Second, we adapted the fast inverse Laplace transform and Prony methods to find the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> -domain expressions and incorporate them into the FDTD formulation.The validity of the proposed approach was demonstrated by comparing the numerical and experimental results of the differential insertion loss and phase constant of differential microstrip lines. Both results were in good agreement, indicating the validity and usefulness of the proposed approach for simulations of broadband signal transmission in FR-4 substrates.

Ultrashort Laser Pulse Focusing by Amplitude and Phase Zone Plates

In this paper, using the frequency-dependent finite-difference time-domain method, a femtosecond cylindrical vector beam of second-order focusing binary zone plates (BZP) is investigated. It is shown that the relief material has a significant effect on the electromagnetic field formed in the focal plane. It is also shown that, in the case of tight focusing of a second-order cylindrically polarized laser pulse, a reverse energy flux is formed in the focus near the optical axis. For the quartz BZP, the energy backflow is maximum. For aluminum and chromium BZPs, the reverse energy flux is approximately two times less, and there is no energy backflow in the focus formed by the gold BZP. This study will be useful for surface nanostructuring applications where a focused short pulse is applied.

Analysis and perception of a viscoelastic, frequency-dependent Finite-Difference Time Domain damping model of a drum

This study investigates the influence of viscoelastic damping parameters in a Viscoelastic Finite Difference Time Domain (FDTD) model on the sound of a drum head. Due to the strong nonlinearity between the complex, frequency-dependent Young’s modulus as a model input parameter and resulting damping frequencies and damping strength, this relation can no longer be analyzed analytically. One reference and eight altered membranes are constructed. Integrating the sound into minor third bands, nonlinear mode couplings due to viscoelasticity are found, relating to the real part of the Young’s modulus as well as to the Laplace-Transform parameter of the FDTD model. Furthermore, the perception of the sounds was investigated. The results are compared to the physical observation, showing variations in brightness and pitch. Hereby, the perception can be described as proportional to the physical analysis, as long as the variation of the Laplace parameter in one or more damped frequencies does not lead to a huge difference in the sounds decay time, which seems to distract the attention from other acoustical characteristics.

Surface catalysis effects on mitigation of radio frequency blackout in orbital reentry

Radio frequency (RF) blackout during atmospheric reentry leads to the cutoff of communication with ground stations and/or data-relay satellites. This causes significant problems during reentry, and thus, mitigation methods have been in high demand. In this study, we numerically demonstrate a novel method for mitigating the RF blackout using surface catalysis effects. Plasma flow behavior and electromagnetic wave propagation around a reentry vehicle were investigated in detail. The approach couples computational fluid dynamics and a frequency-dependent finite-difference time-domain method. The computations were performed with a massive parallelization technique using a large computer. The computed results were compared for cases imposing low and full catalysis conditions on a surface boundary. The investigation revealed that the surface catalysis effects reduce the RF blackout. Atomic species, dissociated across a shock wave formed in front of the vehicle, were recombined on the vehicle surface through surface catalysis. These molecules, flowing into a wake region at the vehicle’s rear, caused recombinations of electrons, originally generated in the shock layer. Therefore, a decrease in electrons was observed in the wake region and a wake path, which allows the propagation of electromagnetic waves, was formed. This complicated behavior of the molecules and electrons, induced by the surface catalysis, resulted in mitigation of the RF blackout.

Investigation of the influence of amplitude spiral zone plate parameters on produced energy backflow

Investigation of the influence of parameters of silver, aluminum, gold, and chromium spiral zone plates on the longitudinal component of Umov-Pointing vector in produced optical vortices by using the frequency-dependent finite-difference time-domain method is presented. It is shown that the aluminum spiral zone plate with a relief height of 50 nm gives an optical vortex with the smallest longitudinal component of Umov-Pointing vector on the optical axis. The gold spiral zone plate is the least effective for the formation of vortex beams with a reverse energy flow.

Numerical Dosimetry of Electromagnetic Pulse Exposures Using FDTD Method

A novel frequency-dependent finite-difference time-domain (FDTD) method, previously proposed by the author, is applied to numerical dosimetry of exposures by an electromagnetic (EM) pulse incident to biological bodies, which are characterized by four Cole–Cole relaxation terms. The proposed method applies the fast inverse Laplace transform to determine the time-domain impulse responses of the complex permittivity function and utilizes Prony’s method to determine the infinite impulse response representation in the $z$ -domain. The FDTD formulation for the update of the electric field is then directly derived by using the $z$ -transformation. The validity of the method is demonstrated by the 3-D analyses of a homogeneous dielectric sphere and a multilayer sphere illuminated by an EM pulse. It is demonstrated that the numerical results of induced electric field distributions inside the spheres are in good agreement with those derived from Mie’s theory over a broad frequency range, proving the validity of the proposed method. Finally, numerical dosimetry of a heterogeneous human head excited by an EM pulse is performed and specific energy absorption due to the pulse illumination is calculated by using the proposed method.

Reentry blackout prediction for atmospheric reentry demonstrator mission considering uncertainty in chemical reaction rate model

A numerical simulation model of plasma flows and electromagnetic waves around a vehicle was developed to predict a radio frequency blackout. Plasma flows in the shock layer and the wake region were calculated using a computational fluid dynamics technique with a three-dimensional model. A finite-catalytic wall condition known to affect plasma properties, such as the number density of electrons, was considered for accurate prediction. A parametric study was performed to investigate the effect of uncertainty in the chemical reaction rate model on evaluating a radio frequency blackout. The behavior of electromagnetic waves in plasma was investigated using a frequency-dependent finite-difference time-domain method. Numerical simulations of reentry blackout were performed for the Atmospheric Reentry Demonstrator mission at various altitudes. The plasma flows and the complex movement of electromagnetic waves around the Atmospheric Reentry Demonstrator vehicle were clarified. The predicted signal loss profile was then directly compared with the experimental flight data to validate the present models. The numerical results generally reproduced the trends over altitudes of the measured data. It is suggested that the present simulation model can be used to investigate the radio frequency blackout and signal loss of electromagnetic waves in the communication of a reentry vehicle. It was confirmed that high associative ionization reaction rates contribute to reducing the electron density in the wake region and radio frequency blackout. It is suggested that the accuracy of predicting the signal loss improved when considering the uncertainty in the chemical reaction model for associative ionizations.

Analysis of Radio Frequency Blackout for a Blunt-Body Capsule in Atmospheric Reentry Missions

A numerical analysis of electromagnetic waves around the atmospheric reentry demonstrator (ARD) of the European Space Agency (ESA) in an atmospheric reentry mission was conducted. During the ARD mission, which involves a 70% scaled-down configuration capsule of the Apollo command module, radio frequency blackout and strong plasma attenuation of radio waves in communications with data relay satellites and air planes were observed. The electromagnetic interference was caused by highly dense plasma derived from a strong shock wave generated in front of the capsule because of orbital speed during reentry. In this study, the physical properties of the plasma flow in the shock layer and wake region of the ESA ARD were obtained using a computational fluid dynamics technique. Then, electromagnetic waves were expressed using a frequency-dependent finite-difference time-domain method using the plasma properties. The analysis model was validated based on experimental flight data. A comparison of the measured and predicted results showed good agreement. The distribution of charged particles around the ESA ARD and the complicated behavior of electromagnetic waves, with attenuation and reflection, are clarified in detail. It is suggested that the analysis model could be an effective tool for investigating radio frequency blackout and plasma attenuation in radio wave communication.

Advanced validation of CFD-FDTD combined method using highly applicable solver for reentry blackout prediction

An analysis model of plasma flow and electromagnetic waves around a reentry vehicle for radio frequency blackout prediction during aerodynamic heating was developed in this study. The model was validated based on experimental results from the radio attenuation measurement program. The plasma flow properties, such as electron number density, in the shock layer and wake region were obtained using a newly developed unstructured grid solver that incorporated real gas effect models and could treat thermochemically non-equilibrium flow. To predict the electromagnetic waves in plasma, a frequency-dependent finite-difference time-domain method was used. Moreover, the complicated behaviour of electromagnetic waves in the plasma layer during atmospheric reentry was clarified at several altitudes. The prediction performance of the combined model was evaluated with profiles and peak values of the electron number density in the plasma layer. In addition, to validate the models, the signal losses measured during communication with the reentry vehicle were directly compared with the predicted results. Based on the study, it was suggested that the present analysis model accurately predicts the radio frequency blackout and plasma attenuation of electromagnetic waves in plasma in communication.

Prediction Performance of Blackout and Plasma Attenuation in Atmospheric Reentry Demonstrator Mission

A numerical simulation model that combines the plasma flows and electromagnetic waves around a reentry vehicle during atmospheric reentry was developed to evaluate the radio frequency blackout and plasma attenuation. The physical properties of the plasma flow in the shock layer and wake region were obtained using a computational fluid dynamics technique. The electromagnetic waves were expressed using a frequency-dependent finite difference time domain method with the plasma properties. Combined simulations were performed for the atmospheric reentry demonstrator of the ESA at various altitudes based on reentry orbit data. The electromagnetic wave behaviors around the vehicle during atmospheric reentry were investigated in detail. Moreover, a parametric analysis with different ionization reaction models was performed. It was confirmed that the vehicle is surrounded by the plasma and the propagation of the electromagnetic waves is prevented at high altitude. Then, the plasma is dissipated and the propagation recovers at low altitude. Validation of the simulation model was performed based on the plasma attenuation history of the experimental flight data. A comparison of the measured and predicted results showed good agreement. It was concluded that the combined simulation model could be an effective tool for investigating the radio frequency blackout and the plasma attenuation of radio wave communication.

Examination of Radio Frequency Blackout for an Inflatable Vehicle During Atmospheric Reentry

Numerical simulations of the plasma flow and electromagnetic wave around a membrane-aeroshell type reentry vehicle were performed using various physical model combinations, and the possibility of radio frequency blackout of transceiver antenna embedded at the rear of the vehicle was investigated. The flowfield was assumed to be in thermochemical nonequilibrium, and it was described by the Navier–Stokes equations with a multitemperature model and the equation of state. The simulations were performed for several altitudes, including the highest heat flux point according to reentry orbit data. Through these computations, the detailed distributions of the flowfield properties in the shock layer and wake region were successfully obtained. To evaluate the possibility of radio frequency blackout during atmospheric reentry, the distribution of the electron number density around the inflatable vehicle was clarified. A frequency-dependent finite-difference time-domain method was used for simulations of electromagnetic waves, and the physical properties were obtained from the computational results of the plasma flow calculation. Electromagnetic wave behaviors in an ionized gas region behind the inflatable vehicle were investigated. It was found that the number density of electrons was sufficiently small and that the electromagnetic waves can propagate with no reflection and less attenuation. These results suggest that radio frequency blackout may not occur during the atmospheric reentry of the inflatable vehicle.

Circuit-Oriented Solution of Drude Dispersion Relations by the ${\rm FD}^{2}{\rm TD}$ Method

This paper deals with the time-domain numerical calculation of electromagnetic fields in media described by linear Drude dispersive models. The frequency-dependent finite-difference time-domain method is applied to solve multipole Drude equations using equivalent circuit models. Two new different circuit methods, named CIRC and PCRC, are proposed. The dispersion analysis and the stability conditions are carried out for these methods. Finally, illustrative examples are provided.

Improved and efficient unconditionally stable complex-envelope frequency-dependent FDTD formulations based on the implicit locally one-dimensional scheme

Improved and efficient unconditionally stable complex-envelope (CE) frequency-dependent finite-difference time-domain (FDTD) formulations, based on the implicit locally one-dimensional (LOD) scheme, are presented for modeling band-limited electromagnetic applications. The proposed formulations provide better accuracy performance than the CE implementations of previous classical LOD scheme while requiring less number of additional auxiliary variables and this will reduce both the CPU time and memory storage requirements. Moreover, the formulations allow modeling different frequency-dependent models in a straight forward manner. Numerical example carried out in a two-dimensional (2D) domain composed of Drude-Lorentz frequency-dependent material is included to show the validity of the formulations.

Computational fluid dynamics and frequency-dependent finite-difference time-domain method coupling for the interaction between microwaves and plasma in rocket plumes

Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.

Optimal Modeling of Infinite Graphene Sheets via a Class of Generalized FDTD Schemes

The accurate and fully 3-D analysis of graphene surface conductivity models by means of a frequency-dependent finite-difference time-domain method is introduced in this paper. For the infinite sheet to be consistently simulated, the novel technique uses a set of periodic boundary conditions that lead to a unit cell excited with a spectral scheme in terms of a total-field/scattered-field formulation. On the other hand, graphene itself is modeled through a subcell approach and a complex surface conductivity concept defined by quantum mechanical equations. This conductivity model is next converted to a volume one in order to permit a realistic time-domain study. Numerical outcomes, addressing a variety of applications, reveal a promising coincidence with those acquired from analytical closed-form expressions.

FD2TD ANALYSIS OF ELECTROMAGNETIC FIELD PROPAGATION IN MULTIPOLE DEBYE MEDIA WITH AND WITHOUT CONVOLUTION

This paper deals with the time-domain numerical calculation of electromagnetic (EM) fields in linearly dispersive media described by multipole Debye model. The frequency-dependent finite-difference time-domain (FD2TD) method is applied to solve Debye equations using convolution integrals or by direct integration. Original formulations of FD2TD methods are proposed using different approaches. In the first approach based on the solution of convolution equations, the exponential analytical behavior of the convolution integrand permits an efficient recursive FD2TD solution. In the second approach, derived by circuit theory, the transient equations are directly solved in time domain by the FD2TD method. A comparative analysis of several FD2TD methods in terms of stability, dispersion, computational time and memory is carried out.

Analysis of plasma photonic crystal with a tunable band gap using parallel method

This paper presents a parallel frequency-dependent finite-difference time-domain ((FD)2TD) method for plasma in the dispersive media. Results obtained with parallel and serial algorithms verify that parallel (FD)2TD has the same precision as the serial (FD)2TD, while the parallel approach could reduce the CPU time efficiently. A tunable filter is analyzed based on a one-dimensional photonic crystal containing a plasma defect by this method. The tunability of the photonic crystal filter can be achieved by adjusting the defect layer parameters instead of changing the dimension of photonic crystal.

Comment on “Photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic waves” [J. Appl. Phys. 101, 073304 (2007)

Recently, theoretical derivation of band structures of electromagnetic waves in two-dimensional microplasma array has been induced by Osamu Sakai et al. [J. Appl. Phys. 101, 073304 (2007)] using a modified plane wave expansion (PWE) method and a frequency-dependent finite difference time–domain (FDTD) method. This report reveals band diagrams with the effects of plasma electron collision frequency, especially focuses on the TE wave by nonmagnetized plasma. Although the band diagrams of TE wave and formulas of calculation look correct at first glance, there are some mistakes in the report which are unfortunately ignored by the authors. The correct formulas of the modified PWE method and FDTD method will be proposed.

Frequency-Dependent FDTD Simulation of the Interaction of Microwaves With Rocket-Plume

The ionized exhaust plumes of solid rocket motors may interfere with RF transmission under certain flight conditions. To understand the important physical processes involved, we measured microwave attenuation and phase delay due to the exhaust plume during sea-level static firing tests for a full-scale solid propellant rocket motor. The measured data were compared with the results of a detailed simulation performed using the frequency-dependent finite-difference time-domain ((FD) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> TD) method. The numerically derived microwave attenuation was in good agreement with experimental data. The results revealed that either the line-of-sight microwave transmission through ionized plumes or the diffracted path around the exhaust plume mainly affects the received RF level, which depends on the magnitude of the plasma-RF interaction.