The traditional finite-difference time-domain (FDTD) formulation is extended to include a discrete time-domain convolution, which is efficiently evaluated using recursion. The accuracy of the extension is demonstrated by computing the reflection coefficient at an air-water interface over a wide frequency band including the effects of the frequency-dependent permittivity of water. Extension to frequency-dependent permeability and to three dimensions is straightforward. The frequency dependent FDTD formulation allows computation of electromagnetic interaction with virtually any material and geometry (subject only to computer resource limitations) with pulse excitation. Materials that are highly dispersive, such as snow, ice, plasma, and radar-absorbing material, can be considered efficiently by using this formulation. >

A frequency-dependent finite-difference time-domain formulation for dispersive materials

The finite-difference time-domain (FD-TD) method is proposed as a means of accurately computing electromagnetic scattering by arbitrary-shaped extremely complex metal or dielectric objects excited by an external plane wave. In the proposed method, one first uses the FD-TD method to compute the near total fields within a rectangular volume which fully encloses the object. Then, an electromagnetic-field equivalence principle is invoked at a virtual surface of this rectangular volume to transform the tangential near scattered fields to the far field. To verify the feasibility of this method, the surface currents, near scattered fields, far scattered fields, and radar cross section of two canonical two-dimensional objects are presented. For these cases, it is shown that the FD-TD method provides magnitude of current and field predictions which are within ± 2.5 percent and further phase values within ± 30 of values predicted by the method of moments ( MOM) at virtually every point including in shadow regions.

A Novel Method to Analyze Electromagnetic Scattering of Complex Objects

The finite-difference time domain (FDTD) method for the solution of light scattering by nonspherical particles has been developed for small ice crystals of hexagonal shapes including solid and hollow columns, plates, and bullet rosettes commonly occurring in cirrus clouds. To account for absorption, we have introduced the effective permittivity and conductivity to circumvent the required complex calculations in the direct discretization of the basic Maxwell equations. In the construction of the finite-difference scheme for the time-marching iteration for the near field the mean values of dielectric constants are defined and evaluated by the Maxwell–Garnett rule. In computing the scattered field in the radiation zone (far field) and the absorption cross section, we have applied a new algorithm involving the integration of the electric field over the volume inside the scatterer on the basis of electromagnetic principles. This algorithm removes the high-angular-resolution requirement in integrating the scattered energy for the computation of the scattering cross section. The applicability and the accuracy of the FDTD technique in three-dimensional space are validated by comparison with Mie scattering results for a number of size parameters and wavelengths. We demonstrate that neither the conventional geometric optics method nor the Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20.

/pdf/finite-difference-time-domain-method-for-light-scattering-by-1auy0etqz4.pdf

Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing

Introduction to the Finite-Difference Time-Domain (Fdtd) Method for Electromagnetics

Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures

A numerical procedure is described that will simplify the analysis of the EMP response of structures with dielectric or poorly conducting segments.

On Implementing a Numeric Huygen's Source Scheme in a Finite Difference Program to Illuminate Scattering Bodies

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On Implementing a Numeric Huygen's Source Scheme in a Finite Difference Program to Illuminate Scattering Bodies