This research involves finding new algorithms to solve the forward scattering and inverse scattering problems in electromagnetics. Symmetry concepts will be exploited to see if redundancies could be reduced in conventional methods of solving such problems. Of particular interest is how the translational symmetry and rotational symmetry of physical laws can be exploited to achieve this purpose. Moreover, nested principles and equivalence principles will be used to enhance the speed at which scattering and inverse scattering problems could be solved on computers.

This project studies the use of wavelets and fast multipole methods and their modifications to solve surface integral equations. The developed code will eventually be used to study the solution of multiple scattering from rough surfaces. Wavelet transforms can be used to generate a sparse matrix from a dense matrix. The resultant sparse matrix can be manipulated much more efficiently and inverted with less computer time. The fast multiple method can be used to expedite matrix-vector multiples in an iterative algorithm like the conjugate gradient method.

In this project, we study the use of the distorted Born iterative method and the local shape function method to study the inversion of well-logging tools. These new methods can invert a profile of much higher contrast than conventional technique where a linearization approximation is made. To expedite the inversion, the forward problem is solved with the CG-FFHT (conjugate gradient =M fast Fourier Hankel transform) method. Alternatively, a finite-element method with a frontal solver is also used to invert well-logging data.

In this project, we study the use of the CG-FFHT method to invert the induction logging tool. In particular, we study the effect of varying the number of coils in the induction tool for performance in the inversion. We will use Born inversion and the distorted Born iterative method (DBIM) to study the inversion of the well logs. The comparison of using the 6FF40 with other induction tools will be made. The robustness and the stability of the algorithm will be studied.

In this project, we use fast algorithms to study the multiple scattering of acoustic waves by random media. The effect of inclusions in the atmosphere on the effect of acoustic wave propagation will be studied using supercomputers. First, a small number of inclusions will be studied. Then the solution for N randomly distributed inclusions will be studied. The resultant computer program will be used as a computer simulation model for the propagation of low-frequency, high-energy acoustic waves through random inclusions or random media. The effect of the half-space and interface will be studied.

The goals of this multimillion dollar project are: (1) to substantially advance our knowledge in developing fast algorithms for solving integral equations of electromagnetic scattering with reduced computational complexity and memory requirements; (2) to enhance our ability to solve partial differential equations Magnetic scattering by reducing grid-dispersion error and modeling error; (3) hybridization with high-frequency methods to further expand the class of problems we can handle in addition to fast numerical methods; (4) parallelization of our algorithms on massively parallel machines and distributed systems to harness maximal throughput from present day computers; (5) development of computational engines as workhorses and application-specific modules for easy interfacing with real-world applications problems.

This project investigates efficient methods to solve the volume integral equation of scattering for inhomogeneous bodies in two and three dimensions. The forward solver is then used to solve inverse scattering problems involving many unknowns. The proposed forward scattering and inverse scattering solvers use iterative methods. In certain instances, recursive methods or nesting methods will be used.

This project proposes to build and design a multifrequency and broadband radar for nondestructive evaluation of the quality and condition of concrete. The system will consist of several transmitter antennas with many receiver antennas. It has the advantage of producing a superior image of voids and reinforcement bars in a concrete with a higher resolution. Such a system will be used for rapid nondestructive evaluation of constructed works.

In this project, we investigate (1) the linear and nonlinear gains of InGaAs quantum-well lasers using the realistic band structure and (2) the generation of ultrafast electrical pulses with femtosecond optical excitations. Our emphasis will be on the theoretical modeling of the gain spectra taking into account the valence band mixing effects and many-body interactions such as the band-gap renormalization. Differential absorption spectroscopy will also be used to characterize the quantum-well structures experimentally. Our study will provide quantitative information on the designs of novel high-speed quantum-well lasers and ultrafast optoelectronic devices.

Both the theoretical and experimental aspects of the ultrafast optoelectronic properties of semiconductor quantum-well devices will be researched. Theoretically, we will use our models for semiconductor quantum-well lasers to design high-performance quantum-well lasers for naval needs. We will also study the effects on the optical absorption spectrum due to optical pumping. Experimentally, differential absorption spectroscopy using both the electroabsorption and the optical pump-and-probe techniques will be used to study the fundamental properties of the InGaAs semiconductor quantum-well structures. The applications of our study to the design of high-speed quan- tum-well lasers and electrooptical modulators will be investigated.

We propose to develop optical fiber Bragg grating sensors for measuring strain and temperature with applications to smart structure systems. The optical wavelength shift for fiber Bragg grating sensors will be calibrated using fiber lasers and light-emitting diodes as sources for the designs of fiber optical sensor systems. Tunable fiber lasers will also be developed to enhance the signal-to-noise ratio. Potential applications to railroad safety systems will be explored.

Fundamental linear and nonlinear gains and their polarization dependencies in strained semiconductor quantum wells will be investigated theoretically and experimentally. We will design strained quantum wells such that the gain of the TE (parallel to the quantum-well planes) polarization is dominant, the gain of the TM (perpendicular to the planes) polarization is dominant, and the gains of both polarizations have nearly the same magnitude using InGaAs/InGaAlAs and InGaAs/InGaAsP material systems. Strained quantum wells have important technological applications in optoelectronic devices. With our comprehensive study, polarization-insensitive semiconductor optical amplifiers using strained quantum wells will be designed using both InGaAlAs and InGaAsP systems.

This research is to develop a numerical simulation tool for the investigation of the interactions between high- power electromagnetic fields and complex electronic systems deployed in a large complex platform. A clear understanding of such interactions is instrumental in developing electronic systems capable of functioning normally in a high-intensity ambient electromagnetic environment.

The interaction of electromagnetic fields with biological objects such as a human body is an important issue in MRI and microwave hyperthermia applications. Better understanding of such interactions cannot only provide vital safety information, but can also enable engineers to design better and new devices. In this project, we develop highly accurate and efficient three-dimensional computational methods for simulation of the interaction of electromagnetic fields with biological objects.

The goal of this project is to develop a finite-element method using vector elements for electromagnetic analysis of electronic devices, circuits, antennas, and radar scattering. Special emphasis is on the method's accuracy, efficiency, and versatility. Both frequency and time-domain methods will be investigated and their performance will be evaluated. Specific applications will be demonstrated.

In this project, we develop hybrid numerical methods to compute electromagnetic scattering from realistic three-dimensional targets. These hybrid methods combine the high-frequency techniques, such as the shooting-and-bouncing-ray technique, and the low-frequency technique, such as the finite-element method and integral equation methods, to take the advantages and eliminate the disadvantages of both. As a result, they are accurate and efficient and can be applied to large complex targets.

This project is to develop new and innovative schemes for calculating the electromagnetic scattering from complex objects. Special emphasis is in the area of scattering from large cavities, such as the jet engine inlets. General-purpose computer codes based on the shooting and bouncing ray technique are being developed.

The goal of this project is to develop a high-frequency computational tool for analyzing the radar signature of a realistic complex target. The target itself is described by a CAD package (e.g., BRL-CAD or Geomod). The scattered field computation is done with physical theory of diffraction and ray techniques.

For the identification of realistic air and ground targets, a large library of range profiles is needed. The present project is to study computational methods for the range profile computation. Two areas of research are conducted. The first is to develop visualization, editing, and interfacing tools for CAD files that include flat facet file, IGES files, and CSG files from various CAD programs. The second area is to research effective and efficient techniques for calculating the scattering filed from realistic targets such as airplanes and tanks.

A four-arm sinuous zigzag planar antenna can provide simultaneous reception/transmission of two polarizations, e.g., two orthogonal linear or right and left circular, over a very wide band of frequencies. Despite the usefulness of this antenna, very little analysis has been published. Sole dependence upon experimental development has sometimes resulted in unexplained anomalous performance. In this project the moment method is used in the supercomputer solution for the currents on the arms of sinuous antennas. A link has been established between variations in pattern beamwidth and antenna geometric parameters.

A demonstrated successful way of achieving very wide band performance from a log-periodic array of monopoles is to alternate driven and parasitic elements. These arrays contain so many elements that theoretical solution of systems involving several such arrays taxes even supercomputers. By using the computer to characterize the coupling between the feeder and a single parasitic monopole in terms of an equivalent circuit, the number of unknowns can be greatly decreased. This materially reduces the computer resources needed to analyze systems with many such arrays.