Time Domain Electric Field Research Articles

Finite difference delay modelling for analysis of shielding effectiveness of perforated conductive enclosure

AbstractThis paper introduces finite difference delay modelling (FDDM) for computing the shielding effectiveness (SE) of a conductive enclosure with an aperture against electromagnetic pulses. FDDM offers optimal accuracy and stability for analysing complex structures. The time domain electric field integral equation (TD‐EFIE) for the conductive enclosure is derived by imposing boundary conditions on the perfect electrical conductor (PEC) surface in the Laplace domain. Time discretization is based on finite differences, and the Laplace‐to‐Z transform mapping is utilized. Fast Fourier Transform (FFT) is employed to expedite the FDDM solution process. Both frequency domain shielding effectiveness (FD‐SE) and time domain shielding effectiveness (TD‐SE) are evaluated using this approach. Finally, to validate the accuracy of the proposed method, results are compared with simulations using CST‐MWS software and the frequency domain moment method.

Time-domain electric field analysis of few-cycle pulse damage behavior in ultra-broadband chirped mirrors

The laser-induced damage resistance performance of ultra-broadband chirped mirrors (UBCM) is a critical factor influencing the generation of petawatt or exawatt laser pulses in thin film compression techniques. In this study, a few-cycle pulse damage testing platform was set up, and two UBCMs with different designs were fabricated for a comparative study of their laser-induced damage. Because light of varying wavelengths forms an electric field at different times within UBCMs under few-cycle pulse irradiation, a time-domain electric field model was developed to obtain transient electric field variations and explain the damage behavior. The model successfully elucidated the origin of the damage and discrepancy between the two UBCMs in terms of damage thresholds, showcasing its potential applications in designing high-threshold UBCMs for high-power laser systems.

Acousto-optic-based time domain electric field sensor for magnetic resonance imaging applications.

An acousto-optic (AO)-based electric field sensor is presented for time domain measurement under magnetic resonance imaging (MRI). A fully MR-compatible sensor is designed and fabricated using a phase-shifted fiber Bragg grating mechanically coupled to a piezoelectric transducer. Mechanical resonance of the piezoelectric transducer is matched to the operating frequencies of commonly used MRI systems to increase the sensitivity of the sensor. Sensitivity of the sensor is measured as 1.27 mV/V/m, with a minimum detectable electric field of 4.4 mV/m/√/Hz. Directivity of the sensor is measured with a 18 dB orthogonal component rejection. The dynamic range of the sensor is calculated as 117 dB/Hz, which allows the measurement of electric fields up to 3.2 kV/m. In MRI studies, the AO sensor was able detect local hot spots around a reference implant accurately with high signal-to-noise ratio. AO sensor exhibited similar or better performance when compared with commercially available MRI compatible electric field sensors. Furthermore, the small size of the sensor with the flexible fiber optic link could allow in situ measurements of electric fields during critical interventional procedures such as pacemaker lead or deep brain stimulator placement as an MRI dosimeter during diagnostic scans.

Three-Dimensional Forward Modeling of Transient Electromagnetic Method Considering Induced Polarization Effect Based on Spectral Element Method

The transient electromagnetic method (TEM) is widely used in the exploration of mineral, petroleum, and geothermal resources due to its sensitivity to low-resistivity bodies, limited site constraints, and strong resistance to interference. In practical applications, the TEM often uses a long wire source instead of an idealized horizontal electric dipole (HED) source as the excitation source. This is due to the complex external conditions and the relatively large distance between the receiving zone and the transmitter source. Compared to the HED, the long wire source can provide a larger excitation current, generating stronger signals to meet the requirements of a higher signal-to-noise ratio or deeper exploration. It also produces longer-duration signals, thereby providing better resolution. Additionally, for the interpretation of TEM data, three-dimensional forward modeling plays a crucial role. However, the mature traditional TEM forward method is based on a simple, sometimes inappropriate model, as it is well established that the induced polarization (IP) effect is widely present in the deep earth, especially in oil and gas reservoirs. The presence of the IP effect results in negative responses in field data that do not conform to the traditional theoretical decay law of TEM, which can significantly impact data processing and inversion results. To address this issue, a TEM forward modeling method considering the IP effect based on the spectral element method (SEM) has been developed in this study. Firstly, starting from the Helmholtz equation satisfied by the time domain electric field, we introduce the Debye model with polarization information into the forward modeling by utilizing the differential form of Ohm’s law. As a result, we derive the boundary value problem for the time domain electric field that considers the induced polarization effect. Using Gauss–Lobatto–Legendre (GLL) polynomials as the basis functions, the SEM is employed to discretize the governing equations at each time step and obtain spectral element discretization equations. Then, temporal discretization equations are derived using the second-order backward Euler formula, and the linear system of equations is solved using the Pardiso direct solver. Finally, the electromagnetic responses at any time channel are obtained via SEM interpolation and numerical integration, thereby achieving three-dimensional TEM forward modeling considering the IP effect. The results indicate that this method can effectively reflect the spatial distribution of polarizable subsurface media. It provides valuable references for studying the polarization parameters of subsurface media and performing a three-dimensional inversion of TEM data considering the induced polarization effect.

A Time-Domain Volume Integral Equation Solver to Analyze Electromagnetic Scattering From Nonlinear Dielectric Objects

A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for analyzing electromagnetic scattering from dielectric objects with Kerr nonlinearity. The nonlinear constitutive relation that relates electric flux and electric field induced in the scatterer is used as an auxiliary equation that complements TD-EFVIE. The ordinary differential equation system that arises from TD-EFVIE’s Schaubert-Wilton-Glisson (SWG)-based discretization is integrated in time using a predictor-corrector method for the unknown expansion coefficients of the electric field. Matrix systems that arise from the SWG-based discretization of the nonlinear constitutive relation and its inverse obtained using the Padé approximant are used to carry out explicit updates of the electric field and the electric flux expansion coefficients at the predictor and the corrector stages of the time integration method. The resulting explicit marching-on-in-time (MOT) scheme does not call for any Newton-like nonlinear solver and only requires solution of sparse and well-conditioned Gram matrix systems at every step. Numerical results show that the proposed explicit MOT-based TD-EFVIE solver is more accurate than the finite-difference time-domain method that is traditionally used for analyzing transient electromagnetic scattering from nonlinear objects.

Induction mechanism and propagation characteristics of current in line conductors due to an electron avalanche

Transfer of bulk electric power required in the modern world can be realized only through Extra High Voltage and Ultra High Voltage transmission lines. The scenario is dominated by overhead lines in which electromagnetic noise generated by corona is an important concern. Corona-induced currents propagate along line conductors producing electromagnetic noise, which is essential to be quantified. Towards this end, the present work aims to investigate basic mechanism of current induction using an isolated avalanche developing under space charge modulated background field. Beginning with the complete electric field produced by an avalanche, the corresponding induced currents are quantified, and the structure of electric and magnetic fields is extracted. The well-known time-domain electric field integral equation is employed for the purpose. The basic issue with long transmission line modelling is amply demonstrated. Since single avalanche is the basic mechanism behind corona, general inferences drawn are applicable for corona on transmission lines.

Applying Loop-Star Functions With Multibranch Rao-Wilton-Glisson Basis Functions in the Time Domain Electric Field Integral Equation

In this paper, novel loop-star basis functions with the multibranch Rao-Wilton-Glisson (MB-RWG) basis functions are applied to obtain the low-frequency stable solution of the time domain electric field integral equation (TD-EFIE). With the help of the MB-RWG basis functions, it is possible to realize the quasi-Helmholtz decomposition in time domain between different regions that are discretized separately with nonconformal meshes, by modifying slightly the generation of the loop and star bases at the interfaces. Especially, the temporally differentiated form of the TD-EFIE is tested by the star basis, while the undifferentiated form of the TD-EFIE is tested by the loop basis. By means of the filtering technique, the components of the solution which have the potential of growing exponentially have been treated. Numerical results illustrate the accuracy and robustness of the proposed method in analyzing the transient scattering problems of perfectly electrical conducting (PEC) objects.

Modeling of Resonant Tunneling Diode Oscillators Based on the Time-Domain Boundary Element Method

We demonstrate how the coupling of a full-wave time-domain boundary element method (BEM) solver with a circuit solver can be used to model 1) the generation of high frequency oscillations in resonant tunneling diode (RTD) oscillators, and 2) the mutual coupling and synchronization of non-identical RTDs with significant differences in frequencies to achieve coherent power combination. Numerical simulations show a combined output power of up to 3.7 times a single oscillator in synchronized devices. The non-differential conductance of the RTD is modeled as a lumped component with a non-linear current-voltage relationship. The lumped element is coupled to the radiating structure using a finite-gap model in a consistent and discretisation independent manner. The resulting circuit equations are solved simultaneously and consistently with time-domain electric field integral equations that model the transient scattering of electromagnetic (EM) fields from conducting surfaces that make up the device. This paper introduces three novel elements: (i) the application of a mesh independent feed line to the modelling of feed lines of RTD devices, (ii) the coupling of the radiating system to a strongly non-linear component with negative differential resistance, and (iii) the verification of this model with circuit models where applicable and against the experimental observation of synchronisation when two RTDs are placed in close proximity. These three elements provide a methodology that create the capacity to model RTD sources and related technology.

Plasmon-enhanced lateral photovoltaic effect observed in Ag-ZnO core–shell nanoparticles

The lateral photovoltaic effect (LPE) is widely used in sensitive position detectors. Discovering comprehensive mechanisms and continuously improving their sensitivity are the ongoing goals in this field. However, the limited absorption and rapid recombination are two major challenges in the traditional LPE. Here, surface plasmon-based approaches have been used to boost the energy conversion efficiency, and the Ag-ZnO core–shell nanoparticles (NPs) with enhanced LPE are prepared on the Si substrate through atomic layer deposition. Owing to the enhanced light absorption, prolonged hot electron generation, and plasmon-induced charge separation, this system exhibits good LPE performance with a maximum sensitivity of 122.1 mV/mm at 980 nm, which is about seven times larger than that observed in conventional Ag/Si (5.03 mV/mm) and ZnO/Si (76.13 mV/mm). Besides, its sensitivity can increase up to 114.7% by using rapid thermal annealing to change the shape and size of active plasmon Ag NPs. Furthermore, the surface-enhanced Raman scattering spectra and finite-difference time-domain electric field simulation prove the occurrence of localized surfaced plasmon resonance excitation. This infrared sensitive shell-isolated structure has great potential for applications in high sensitivity and stability photoelectric devices.

Extracting Features of Transient Electric Fields With Fourier And Wavelet Transform–A Case Study Of Lightning Positive Return Stroke

Frequency domain information were extracted from the time domain electric fields pertinent to the lightning positive return strokes applying Fourier transform and Wavelet transform. The electric field radiated by positive ground flashes striking the sea were recorded at 10 ns resolution at a coastal station to minimize the propagation effects. The frequency spectrum of the electric field of positive return strokes were computed applying the Fourier transform technique in the range of 10 kHz to 20 MHz owing to the fact that this range of frequency is of very much interest to the researchers and design engineers. The amplitude of the energy spectral density decreases nearly as ƒ-1 from 10 kHz to about 0.1 MHz and drops nearly as ƒ-2 up to 8 MHz. Applying the wavelet transform technique, the same positive return strokes are found to radiate in the frequency range of 5.5 to 81 kHz with the average spread distribution of 13.6 kHz to about 30 kHz. From frequency spectrum obtained from the Fourier transform it is difficult to identify as which phase of the return stroke radiates in the higher frequency range and that in the lower frequency range, whereas, one can easily identify from the frequency spectrum obtained with the wavelet transform that ramp portion of the positive return stroke radiates in the larger spectral range as compared to that of initial peak of the return stroke. Also, from the spectral density map obtained from wavelet transform one can easily observe the contribution of each phase in a range of frequency, which is not possible from the Fourier transform technique. Clearly, the wavelet transform is much more powerful tool to extract the frequency domain information of a non-stationary signal as compared to that of Fourier transform.

Using Wavelet Transform To Extract Frequency Content In Electric Field Radiated By Unusual Lightning Activity

In this frequency spectrum electric fields radiated by the unusual lightning activities have been computed using the wavelet transform technique. The unusual lightning activities have very recently been identified activities and are very poorly understood among the lightning community. As the electric fields are very recently identified and are measured in time domain, to the best of our knowledge, their frequency content has not been studied as of today. To understand the physics of the discharge mechanism of such events, the frequency domain information plays a significant role. In order to extract frequency domain information from the time domain electric field signatures the wavelet transform technique has been employed. For the purpose, the electric field pertinent to the unusual activity, has been divided into two parts namely main activity and the preceding opposite polarity field change. From the computation, it is found that the opposite-polarity field change radiates energy in the spectral range of 2 kHz to 173 kHz whereas, the main activity predominantly radiates in the frequency range 2 kHz to 162 kHz. Such a wider spectral range that the unusual activities radiate have not been reported for the other known activities such as positive and negative return strokes. Evidently, the unusual events have some unique origin of discharge unlike the known activities. Further, as the unusual events were noticed in the temperate region (Uppsala, Sweden) and Sub-tropical climatic zone (Kathmandu, Nepal), it should have some common source of origin between two regions.

A novel space hybrid meshing technique combined with Laguerre polynomial to solve TD-EFIE

In this paper, we have developed a system of Time Domain Electric Field Integral Equation (TD-EFIE) for the resolution of a scattering electromagnetic problem by various shapes illuminated by an incident transient wave. The solvability of the TD-EFIE system is based on the Time Domain Method of Moments (TD-MoM) using Galerkin's method in space and time domains. In time domain, a linear combination of Laguerre functions is used as temporal basis functions. In order to approximate the unknown space variation of the transient current, we develop a novel space hybrid basis functions derived from the Rao-Wilton-Glisson function. The elaborated hybrid mesh technique using hexagonal and triangular mesh is applied for various analyzed structures: regular grid for planar structures and irregular grid for curved structures. The validity, the efficiency and the precision of developed meshing techniques are presented and discussed.

Oscillator Finite-Difference Time-Domain (O-FDTD) electric field propagation model: integrated photonics and networks

The recently developed Lorentz Oscillator Model-inspired Oscillator Finite-Difference Time-Domain (O-FDTD) is one of the simplest FDTD models ever proposed, using a single field equation for electric field propagation. We demonstrate its versatility on various scales and benchmark its simulation performance against theory, conventional FDTD simulations, and experimental observations. The model’s broad applicability is demonstrated for (but not limited to) three contrasting realms: integrated photonics components on the nano- and micrometer scale, city-wide propagating radiofrequency signals reaching into the hundreds of meters scale, and for the first time, in support of 3D optical waveguide design that may play a key role in neuromorphic photonic computational devices.

Damage characteristics of dual-band high reflectors affected by nodule defects in the femtosecond regime

The influence of nodule defects on the characteristics of femtosecond laser-induced damage has not been fully investigated. In this study, two types of 800 nm/1064 nm dual-band HfO2/SiO2 high-reflection films with different configurations were analyzed. Combined with finite-difference time-domain electric field simulation and focused ion beam analysis, the initial state and growth process of femtosecond laser damage of nodules were explored. In particular, the sequence of blister damage determined by the film design and the inner damage caused by nodules were clarified. The rule of the laser-induced damage threshold of different size nodules was obtained. The difference in the damage behavior of nodules in the two types of films was elucidated.

Stable and Accurate Marching-on-in-Time Solvers of Time Domain EFIE, MFIE, and CFIE Based on Quasi-Exact Integration Technique

The development of time-domain integral equation solvers with robust late-time stability properties has been a long-standing quest. Among the many methods that have been investigated, those leveraging quasi-exact integration techniques appear to be most successful. This article presents stable and accurate marching-on-in-time (MOT) solvers for time-domain electric, magnetic, and combined field integral equations (EFIE, MFIE, and CFIE) based on quasi-exact integration techniques. The novel MOT solvers exhibit excellent stability while yielding highly accurate results, as demonstrated by various numerical examples. In addition, the solvers' excellent stability and accuracy properties are used to examine spurious modes encountered when time-domain integral equations are applied to closed surfaces. It is demonstrated that MOT solutions to the time domain EFIE and MFIE often are polluted by spurious modes at the cavity's resonant frequencies whereas those of the CFIE solver are devoid of such contamination.

Extrapolation of Electromagnetic Response from Linear Antennas in Time Domain without Late-Time Instabilities in Numerical Solution of EFI Equation

The paper presents a new hybrid method relied upon to solve integral equations of the electric field in time domain and to model linear antennas with pulse excitation. The method consists in a mixed, numerical-analytical description of the process that helps maintain the stability of calculations during the late time phase. As described in the analytical part, the modified spherical Bessel function of the first kind allows for extrapolation with a high degree of accuracy and loworder expressions. The modified spherical Bessel functions of the first kind are of the oscillating character, and their combination with the exponential factor makes them convenient for extrapolation of the answer of the antenna with pulse excitation. New functions are introduced to computational practice.

A comparison of three temporal basis functions for the time-domain method of moments (TD-MoM)

Three techniques are applied for the resolution of the time-domain electric field integral equation (TD-EFIE) for a thin wire antenna based on the well-known time-domain method of moments. Three temporal bases are used to approximate the unknown temporal variation. The first is derived from Dirac functions, the second from B-spline functions, and the third from Laguerre functions. Piecewise triangular functions are used for the spatial expansion and testing function for the wire structure using Galerkin’s method. The aim is to compare these three techniques in terms of their formulation, complexity, and accuracy. Numerical results are presented to identify which time technique is best suited to solve such transient electromagnetic problems.

Large Time Step and DC Stable TD-EFIE Discretized With Implicit Runge–Kutta Methods

The Time Domain-Electric Field Integral Equation (TD-EFIE) and its differentiated version are widely used to simulate the transient scattering of a time dependent electromagnetic field by a Perfect Electrical Conductor (PEC). The time discretization of the TD-EFIE can be achieved by a space-time Galerkin approach or, as it is considered in this contribution, by a convolution quadrature using Implicit Runge-Kutta methods. The solution is then computed using the Marching-On-in-Time (MOT) algorithm. The differentiated TD-EFIE has two problems: (i) the system matrix suffers from ill-conditioning when the time step increases (low frequency breakdown) and (ii) it suffers from the DC instability, i.e. the formulation allows for the existence of spurious solenoidal currents that grow slowly in the solution. In this work, we show that (i) and (ii) can be alleviated by leveraging quasi-Helmholtz projectors to separate the Helmholtz components of the induced current and rescale them independently. The efficacy of the approach is demonstrated by numerical examples including benchmarks and real life applications.

Influence of delay stage positioning error on signal-to-noise ratio, dynamic range, and bandwidth of terahertz time-domain spectroscopy

Terahertz time-domain spectroscopy (THz-TDS) employs a mechanical stage to introduce the time delay between pump and probe optical pulses during the sampling process of the time-domain electric field of a terahertz pulse. The positioning error and limited resolution of a mechanical delay stage cause an inaccurate sampling of a terahertz pulse. In this study, we numerically and experimentally investigated the influence of delay stage positioning error on the major characteristics of THz-TDS, such as bandwidth and dynamic range of the system, along with the signal-to-noise ratio (SNR) of the intensity spectra. We demonstrate that the positioning error in the delay stage not only reduces bandwidth and dynamic range of the measurement system but also decreases the SNR of the intensity spectra.

Speed-up of scattered field formulation of FDTD method combining with time-domain EFIE by using spherical harmonic expansion of Green’s function

This paper proposes a scattered field formulation of the finite-difference time domain method (S-FDTD) combining with a time-domain electric field integral equation (TD-EFIE) based on surface equivalence theorem. The scattered field formulation enables us to reduce computation cost effectively for the case that scatterers are located at a far distance from field sources of electromagnetic wave since we need to calculate the scattered field component only on the region in the vicinity of the scatterers. Then it is required for the use of the scattered field formulation that the field source for the incident field component has to be expressed by any analytical solutions such as a point dipole source, plane wave, and so on. In this work, the scattered field formulation of the FDTD method is applied to cases that there are no analytical expressions of the field sources, in which the field source contains conductors such as antennas, combining with the TD-EFIE on a virtual surface which encloses the field sources. Then, it is known that calculation of the TD-EFIE itself is time consuming. This paper considers speed-up of the S-FDTD simulation based on the TD-EFIE using a spherical harmonic expansion of Green’s function of Helmholtz equation, additionally.