Finite-difference time-domain method

'Finite-difference time-domain' (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations). Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way. The FDTD method belongs in the general class of grid-based differential numerical modeling methods (finite difference methods). The time-dependent Maxwell's equations (in partial differential form) are discretized using central-difference approximations to the space and time partial derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field v

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Evaluation of Site Errors in LLS Magnetic Direction Finding Caused by Large Hills Using the 3D‐FDTD Technique

Hannes Kohlmann

Angle and amplitude estimation errors in magnetic direction finding, called site errors, are important sensor-specific errors in lightning location systems (LLS). They are known to be caused by nearby cables and overhead lines due to induced currents. Due to the reflection and diffraction of electromagnetic waves, hills and mountains are also expected to generate these effects. In this paper, numerical computations applying the finite-difference time-domain (FDTD) method are performed to analyze the impact of hills or mountains on the angle and amplitude estimation of LLS sensors for typical first and subsequent return strokes (RS). The influence of hill size, the distance of sensors to the hill, ground parameters, and sensor bandwidth, are evaluated. The results show that on top of low ridges of only 125 m elevation, up to ±10° angle site error and +50% amplitude site error occur. A key finding is that due to field attenuation caused by lossy ground and sensor bandwidth limitations, there is practically no difference in the angle site errors for first and subsequent RS. For two sensors, the average site errors obtained from real sensor measurements are compared to results from 3D-FDTD simulations, modeling the real terrain based on a digital elevation model. The simulation results are in good agreement with the observed, average angle site errors.

2021

The application of the finite-difference time-domain (FDTD) technique to lightning studies

Dongshuai Li, Marcos Rubinstein

We have seen in this chapter that the FDTD method for solving Maxwell's equations is accurate and versatile in a very wide variety of applications related to lightning. One can analyze the lightning electromagnetic field propagation over distances ranging from a few meters to hundreds of kilometers by just adjusting the smallest wavelength governed by the highest frequency of the band being simulated with the FDTD method. One can also take into account complex media in the EIWG by adding the media parameters through the simple discretization process. Moreover, a number of powerful software packages exist for FDTD modeling, including free, open-source packages and commercial program suites. One can also modify the basic codes to adapt them to any problem of interest. With the continued growth of computing resources, FDTD method will continue to serve as a helpful tool in research and engineering applications requiring lightning electromagnetic pulse (LEMP) simulations.

IET2022

PHz Electronic Device Design and Simulation for Waveguide-Integrated Carrier-Envelope Phase Detection

Yujia Yang

Carrier-envelope phase (CEP) detection of ultrashort optical pulses and low-energy waveform field sampling have recently been demonstrated using direct time-domain methods that exploit optical-field photoemission from plasmonic nanoantennas. These devices are compact and integratable solid-state detectors operating at optical frequencies under ambient conditions using low pulse energies (picojoule-level). Potential applications include frequency-comb stabilization, optical time-domain spectroscopy, compact tools for attosecond science and metrology, and petahertz-scale information processing. However, to date these devices have been driven by free-space optical waveforms and their implementation within integrated photonic platforms has yet to be demonstrated. In this work, we design and simulate fully-integrated plasmonic nanoantennas coupled to a Si3N4-core waveguide for CEP detection. We find that when coupled to realistic on-chip, few-cycle supercontinuum sources, these devices are suitable for direct time-domain CEP detection within integrated photonic platforms. We estimate a signal-to-noise ratio of 30 dB at 50 kHz resolution bandwidth, and address technical details, such as the tuning of the nanoantennas plasmonic resonance, CEP slippage in the waveguide, optical losses, and sensitivity to driving pulse characteristics such as energy and duration. Our results provide the basis for future design and fabrication of time-domain CEP detectors and allow for the development of fully-integrated attosecond science applications, frequency-comb stabilization and light-wave-based PHz electronics.

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