Total-field/scattered-field Research Articles

Analytic Field Propagation TFSF Boundary for FDTD Problems Involving Planar Interfaces: PECs, TE, and TM

A total-field scattered-field (TFSF) boundary can be used to introduce incident plane waves into finite-difference time-domain (FDTD) simulations. For fields which are traveling obliquely to the grid axes, there is no simple way to account fully for the effects of the inherent numerical artifacts associated with plane-wave propagation in the FDTD grid. Failure to account for these artifacts causes erroneous fields to leak across the TFSF boundary. Recent publications have proposed ways to use the dispersion relation to describe precisely plane-wave propagation in the FDTD grid thus permitting the realization of a nearly perfect TFSF boundary. However, these publications did not cover certain implementations details (such as the type of Fourier transform which is needed) or their scope was so broad as to mask the relative simplicity with which the approach can be applied to problems involving planar interfaces. This work considers the Fourier transforms needed in order for the implementation to be exact. Reflection and transmission coefficients for a planar interface are derived. Implementation for planar perfect electric conductors is also presented

Analytic Field Propagation TFSF Boundary for FDTD Problems Involving Planar Interfaces: Lossy Material and Evanescent Fields

Recently, total-field scattered-field (TFSF) boundaries have been developed for the finite-difference time-domain (FDTD) method which are essentially perfect. The implementation requires an analytic description of the incident field and hence is termed the analytic field propagation (AFP) TFSF method. Previous papers described the implementation for problems involving homogeneous as well as layered media. In this work we provide the details for problems involving lossy media. Additionally, the case of fields incident beyond the critical angle are considered (i.e., when, for lossless material, there is total reflection of the incoming wave and the fields in the second medium are evanescent)

Numerical artifacts in finite-difference time- domain algorithms analyzed by means of principal components

Finite-difference time-domain (FDTD) algorithms are affected by numerical artifacts and noise. In order to obtain better results we propose the use of the principal component analysis based on multivariate statistical techniques. It allows a straightforward discrimination between the numerical noise and the actual electromagnetic field distributions, and the quantitative estimation of their respective contributions. Besides, the FDTD results can be filtered to clean the effect of the noise. The method has been applied successfully to two dimensional simulations: propagation of a pulse in vacuum using total field-scattered field techniques, and mode computation in a two-dimensional photonic crystal. In this last case, PCA has revealed hidden electromagnetic structures related to actual modes of the photonic crystal.

Plane Waves in FDTD Simulations and a Nearly Perfect Total-Field/Scattered-Field Boundary

The total-field/scattered-field (TFSF) boundary has been successfully used for a number of years to introduce energy into finite-difference time-domain (FDTD) grids. If the propagation of the incident field is grid-aligned, a TFSF implementation can be realized by using an auxiliary one-dimensional FDTD simulation which models propagation of the incident field. Here perfect implies the incident field propagation exactly matches the way in which the field propagates in the FDTD grid. However, for propagation which is not grid-aligned, no similarly implementation has previously been presented. This work provides a framework for a TFSF boundary for pulsed plane waves which do not propagate in a grid-aligned fashion. To achieve this, homogeneous plane-wave propagation is rigorously quantified. Using this knowledge and a specification of the desired incident field, the dispersion relation is used to ascertain the incident field at any point in the grid. It is required to account for, unlike in the continuous world, the electric field, the magnetic field, and the wavenumber vector not forming a mutually orthogonal set. Group velocity is also considered because of its relevance to the implementation.

Perfect Plane-Wave Injection into a Finite FDTD Domain throughTeleportation of Fields

A new method is proposed for injecting plane waves (although not constrained solely to plane waves) into the computational domain of a finite-difference time domain (FDTD). Fields from a background FDTD space that can support perfect plane waves traveling at an arbitrary angle of incidence are used to calculate the equivalent currents on a rectangular boundary such that the currents so defined satisfy the discrete curl operator of FDTD. When these equivalent currents are copied onto another FDTD domain, the rectangular boundary acts as a perfect teleportation window, inside of which the plane wave exists and outside of which no fields are produced. Thus a scatterer within the window is illuminated with a perfect plane wave and its scattered fields exit transparently through the window. Thus a total field-scattered field FDTD formulation is attained automatically. This method correctly accounts for the nonlinear grid dispersion created by the discretization of the Yee grid. The only error in the plane wave injection is numerical round off of the CPU and is of the order of −300dB for double precision (−150 dB single precision).