Finite-difference Time-domain Framework Research Articles

A unified 3-D simulating framework for Debye-type dispersive media and PML technique based on recursive integral method

A novel implementation of the Debye dispersive model with the recursive integration (RI) approach is proposed for the finite-difference time-domain (FDTD) method simulation. The RI method also demonstrates good compatibility with the traditional FDTD framework, particularly for efficiently constructing the perfect matched layer (PML) technique. Therefore, a crucial feature of the proposed simulation framwork is its unified formulation for constrcuting the lossy Debye dispersive media and the PML technique. Meanwhile, the von Neuman method combined with the Routh-Hurwitz criterion is employed to analyze the stability of the introduced method, which provides a systematic analysis method for determining the CFL limitation of the FDTD method in solving the dispersive model. The numerical results further confirm the accuracy and efficiency of the RI method for simultaneously simulating Debye dispersive media and setting RI-PML.

Symmetric Positive Semi-Definite FDTD Subgridding Algorithms in Both Space and Time for Accurate Analysis of Inhomogeneous Problems

In this article, we develop a systematic approach to derive symmetric positive semi-definite (SPD) finite-difference time-domain (FDTD) subgridding operators in both space and time for analyzing general inhomogeneous problems in an accurate fashion. The operators are SPD by construction and independent of the grid ratio. The resultant explicit time marching is guaranteed to be stable because such subgridding operators have only nonnegative real eigenvalues. Furthermore, the use of a time step local to the base grid and the subgrid is permitted without sacrificing stability and accuracy. Moreover, the algorithm takes the subgrid information into account to accurately analyze inhomogeneous problems. In addition, we provide an interpretation of the proposed subgridding operators and show how to implement them in the original difference equation-based FDTD framework. Extensive numerical experiments involving both 2- and 3-D subgrids with various grid ratios and inhomogeneities have demonstrated the stability, accuracy, and efficiency of the proposed new SPD subgridding algorithms.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell’s equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell’s equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Capturing Plasmon–Molecule Dynamics in Dye Monolayers on Metal Nanoparticles Using Classical Electrodynamics with Quantum Embedding

A multiscale hybrid quantum/classical approach using classical electrodynamics and a collection of discrete three-level quantum systems is used to simulate the coupled dynamics and spectra of a malachite green monolayer adsorbed to the surface of a spherical gold nanoparticle (NP). This method utilizes finite difference time domain (FDTD) to describe the plasmonic response of the NP within the main FDTD framework and a three-level quantum description for the molecule via a Maxwell/Liouville framework. To avoid spurious self-excitation, each quantum molecule has its own auxiliary FDTD subregion embedded within the main FDTD grid. The molecular parameters are determined by fitting the experimental extinction spectrum to Lorentzians, yielding the energies, transition dipole moments, and the dephasing lifetimes. This approach can be potentially applied to modeling thousands of molecules on the surface of a plasmonic NP. In this paper, however, we first present results for two molecules with scaled oscillator ...

Electron Energy-Loss Spectroscopy Calculation in Finite-Difference Time-Domain Package

Electron energy-loss spectroscopy (EELS) is a unique tool that is extensively used to investigate the plasmonic response of metallic nanostructures. We present here a novel approach for EELS calculations using the finite-difference time-domain (FDTD) method (EELS-FDTD). We benchmark our approach by direct comparison with results from the well-established boundary element method (BEM) and published experimental results. In particular, we compute EELS spectra for spherical nanoparticles, nanoparticle dimers, nanodisks supported by various substrates, and a gold bowtie antenna on a silicon nitride substrate. Our EELS-FDTD method can be easily extended to more complex geometries and configurations. This implementation can also be directly exported beyond the FDTD framework and implemented in other Maxwell’s equation solvers.

GPU-Based Acceleration for FDTD Method of Acoustic Field Analysis

The finite difference time domain (FDTD) method is a numerical technique used in time-domain acoustic simulation. However, the huge computing capacity has been an important limiting factor for its applications. In this paper, we will present a graphics processing units (GPU) - based parallel FDTD framework and its successful application to the estimation of time-series sound pressure data. Compared with the computer, the runtime of acoustic field FDTD simulation on GPU is dramatically decreased. The acceleration in runtime has made such study possible, and will pave the way for other studies of large-scale computational acoustic problems which were previously impractical.

Energy based Markov Chain Monte Carlo algorithms for Bayesian model selection

Markov Chain Monte Carlo (MCMC) algorithms for Bayesian model selection have been increasingly applied to acoustics applications. One of challenging tasks required in Bayesian model selection is the exploration of high-dimensional multi-variate spaces such that a key quantity, termed the Bayesian evidence, can be estimated in order to rank a set of competing models. This work presents a class of energy-based MCMC algorithms specifically designed to estimate the Bayesian evidence. As illustrative examples, the energy-based MCMC algorithms are applied to the problem of filter design as used in human head-related transfer functions and in acoustic impedance boundaries within the finite-difference time-domain framework for room-acoustics simulations.

An extension of the lumped-network FDTD method to linear two-port lumped circuits

The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional finite-difference time-domain (FDTD) method that allows the systematic incorporation of linear one-port lumped networks (LNs) into a single FDTD cell. This paper presents an extension of the LN-FDTD technique, which allows linear two-port (TP)-LNs to be incorporated into the FDTD framework. The method basically consists of describing a TP-LN by means of its admittance matrix in the Laplace domain. By applying the Mobius transformation technique, we then obtain the admittance matrix of the TP-LN in the Z-transform domain. Finally, appropriate digital signal-processing methodologies are used to derive a set of difference equations that models the TP-LN behavior in the discrete-time domain. These equations are solved in combination with the Maxwell-Ampere's equation. To show the validity of the TP-LN-FDTD technique introduced here, we have considered the equivalent circuit of a chip capacitor and a linear circuit model of a generic metal-semiconductor field-effect transistor. These LNs have been placed on a microstrip gap and the scattering parameters of the resulting hybrid circuit have been computed. The results are compared with those obtained by using the electromagnetic simulator Agilent HFSS in combination with the circuital simulator ADS, and with those calculated by ADS alone. For the chip capacitor, experimental measurements have also been carried out. The agreement among all the simulated results is good. Generally speaking, the measured results agree with the simulated ones. The differences observed are mainly due to the influence of the subminiature A connectors and some mismatching at the ports.

A simple multigrid approach for calculating time-harmonic fields with FDTD

A coarse-to-fine multigrid algorithm for the finite-difference time-domain (FDTD) method is proposed and applied to calculate the time-harmonic electromagnetic field in the presence of a resonant structure. The obtained results and the related efficiency are compared to those ones achieved with a conventional merely fine-grid FDTD run. The method is easy to implement into an existing FDTD framework, and most efficient if the steady-state electromagnetic field at a given frequency has to be computed within the entire solution domain.

A study on the stability of bipolar-junction-transistor formulation in finite-difference time-domain framework

Recently, a new stability result has been put forward for three-dimensional finite-difference time-domain (FDTD) framework by deriving a discrete energy relation similar to the Poynting Theorem in electromagnetism. In this paper, the result is used to show how stability analysis of an FDTD model containing three-terminal nonlinear components can be performed. Here the bipolar junction transistor (BJT) is used to illustrate the idea. It is shown that instability can be due to the BJT contributing numerical energy to the system during simulation, thus causing the E- and H-field components to blow up. This paper also shows how we can prevent instability by identifying the operating region of the device where it is contributing numerical energy. By preventing the device from contributing numerical energy to the system, dynamical stability can be maintained. Formulation, which can source and sink numerical energy, is called conditionally proper. The BJT formulation in FDTD is such an example.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI—applications to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The program has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering.

Modeling of Bipolar Junction Transistor in Fdtd Simulation of Printed Circuit Board - Abstract

A simple and efficient approximate method to incorporate nonlinear bipolar junction transistor (BJT) into Finite-Difference Time-Domain (FDTD) framework is presented. This method applies Taylor expansion on the nonlinear transport equations of the BJT based on Gummel-Poon model [5]. The results are two coupled one-step explicit finite difference schemes for the electromagnetic fields in the vicinity of the BJT, which can be solved easily. A simulation example is carried out for a power amplifier and the result compares well with the measurement. A two-step simulation scheme is introduced to hasten the process of reaching transient steady state. Finally, brief comments on treating the FDTD framework as a dynamical system is included. This perspective is useful for analyzing the stability of FDTD framework with nonlinear lumped elements.