Allen Taflove

Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations

A numerical method is described for the solution of the electromagnetic fields within an arbitrary dielectric scatterer of the order of one wavelength in diameter. The method treats the irradiation of the scatterer as an initial value problem. At t = 0, a plane-wave source of frequency f is assumed to be turned on. The diffraction of waves from this source is modeled by repeatedly solving a finite-difference analog of the time-dependent Maxwells equations. Time stepping is continued until sinusoidual steady-state field values are observed at all points within the scatterer. The envelope of the standing wave is taken as the steady-state scattered field. As an example of this method, the computed results for a dielectric cylinder scatterer are presented. An error of less than /spl plusmn/10 percent in locating and evaluating the standing-wave peaks within the cylinder is achieved for a program execution time of 1 min. The extension of this method to the solution of the fields within three-dimensional dielectric scatterers is outlined.

Correction to "Two-Dimensional FDTD Analysis Of A Pulsed Microwave Confocal System For Breast Cancer Detection: Fixed-Focus And Antenna-Array Sensors"

A novel focused active microwave system is investigated for detecting tumors in the breast. In contrast to X-ray and ultrasound modalities, the method reviewed here exploits the breast-tissue physical properties unique to the microwave spectrum, namely, the translucent nature of normal breast tissues and the high dielectric contrast between malignant tumors and surrounding lesion-free normal breast tissues. The system uses a pulsed confocal technique and time-gating to enhance the detection of tumors while suppressing the effects of tissue heterogeneity and absorption. Using published data for the dielectric properties of normal breast tissues and malignant tumors, the authors have conducted a two-dimensional (2-D) finite-difference time-domain (FDTD) computational electromagnetics analysis of the system. The FDTD simulations showed that tumors as small as 2 mm in diameter could be robustly detected in the presence of the background clutter generated by the heterogeneity of the surrounding normal tissue. Lateral spatial resolution of the tumor location was found to be about 0.5 cm.

FD-TD modeling of digital signal propagation in 3-D circuits with passive and active loads

Most existing computer-aided circuit design tools are limited when digital clock speeds exceed several hundred MHz. These tools may not deal effectively with the physics of UHF and microwave electromagnetic wave energy transport along metal surfaces such as ground planes or in the air away from metal paths that are common at or above this frequency range. In this paper, we discuss full-wave modeling of electronic circuits in three dimensions using the finite-difference time-domain (FD-TD) solution of Maxwells equations. Parameters such as stripline complex line impedance, propagation constant, capacitance per unit length and inductance per unit length can be easily computed as a function of frequency. We also discuss FD-TD Maxwells equations computational modeling of lumped-circuit loads and sources in 3-D, including resistors and resistive voltage sources, capacitors, inductors, diodes, and transistors. We believe that this approach will be useful in simulating the large-signal behavior of very high-speed nonlinear analog and digital devices in the context of the full-wave time-dependent electromagnetic field. >

A Novel Method to Analyze Electromagnetic Scattering of Complex Objects

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.

Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique

We report what we believe to be the first evidence of localized nanoscale photonic jets generated at the shadow-side surfaces of micronscale, circular dielectric cylinders illuminated by a plane wave. These photonic nanojets have waists smaller than the diffraction limit and propagate over several optical wavelengths without significant diffraction. We have found that such nanojets can enhance the backscattering of visible light by nanometer-scale dielectric particles located within the nanojets by several orders of magnitude. Not involving evanescent fields and not requiring mechanical scanning, photonic nanojets may provide a new means to detect and image nanoparticles of size well below the diffraction limit. This could yield a potential novel ultramicroscopy technique using visible light for detecting proteins, viral particles, and even single molecules; and monitoring molecular synthesis and aggregation processes of importance in many areas of biology, chemistry, material sciences, and tissue engineering.

Application of the Finite-Difference Time-Domain Method to Sinusoidal Steady-State Electromagnetic-Penetration Problems

A numerical method for predicting the sinusoidal steady-state electromagnetic fields penetrating an arbitrary dielectric or conducting body is described here. The method employs the finite-difference time-domain (FD-TD) solution of Maxwells curl equations implemented on a cubic-unit-cell space lattice. Small air-dielectric loss factors are introduced to improve the lattice truncation conditions and to accelerate convergence of cavity interior fields to the sinusoidal steady state. This method is evaluated with comparison to classical theory, method-of-moment frequency-domain numerical theory, and experimental results via application to a dielectric sphere and acylindrical metal cavity with an aperture. Results are also given for a missile-like cavity with two different types of apertures illuminated by an axial-incidence plane wave.

Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses

We report the initial results for femtosecond pulse propagation and scattering interactions for a Lorentz medium obtained by a direct time integration of Maxwells equations. The computational approach provides reflection coefficients accurate to better than 6 parts in 10,000 over the frequency range of dc to 3 × 1016 Hz for a single 0.2-fs Gaussian pulse incident upon a Lorentz-medium half-space. New results for Sommerfeld and Brillouin precursors are shown and compared with previous analyses. The present approach is robust and permits two-dimensional and three-dimensional electromagnetic pulse propagation directly from the full-vector Maxwells equations.

Finite-difference time-domain modeling of curved surfaces (EM scattering)

The finite-difference-time-domain (FDTD) method is generalized to include the accurate modeling of curved surfaces. This generalization, the contour path CP), method, accurately models the illumination of bodies with curved surfaces, yet retains the ability to model corners and edges. CP modeling of two-dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented. >

Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.

Three-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: design of an antenna-array element

We are investigating a new ultrawide-band (UWB) microwave radar technology to detect and image early-stage malignant breast tumors that are often invisible to X rays. We present the methodology and initial results of three-dimensional (3-D) finite-difference time-domain (FDTD) simulations. The discussion concentrates on the design of a single resistively loaded bowtie antenna element of a proposed confocal sensor array. We present the reflection, radiation, and scattering properties of the electromagnetic pulse radiated by the antenna element within a homogeneous, layered half-space model of the human breast and the polarization and frequency-response characteristics of generic tumor shapes. We conclude that the dynamic range of a sensor array comprised of such elements in conjunction with existing microwave equipment is adequate to detect small cancerous tumors usually missed by X-ray mammography.