Inverse scattering of Hz waves using local shape-function imaging: A T-matrix formulation

Inverse scattering algorithms for H_z polarized waves are scarce, due to the added difficulties of polarization charges. Nevertheless, the polarization charges cannot be ignored for 3D problems as well as for 2D H_z problems. This work aims to reconstruct arbitrary inhomogeneous dielectric objects from H_z scattering data using a new formulation that abandons the standard integral equation model for a T-matrix model. This new algorithm, called local shape-function (LSF) imaging, is modified for dielectric objects with H_z incident fields, where previously the LSF algorithm was applied to metallic objects with E_z incident fields. The advantage of the LSF algorithm is a more accurate modeling of the induced interfacial polarization charges. For comparison, the H_z distorted Born iterative method using integral equations is shown to be valid only for small contrasts, while the LSF algorithm converges for much larger dielectric contrasts.©1994 John Wiley & Sons Inc     

An iterative solution of the two-dimensional electromagnetic inverse scattering problem

A new method, based on an iterative procedure, for solving the two-dimensional inverse scattering problem is presented. This method employs an equivalent Neumann series solution in each iteration step. The purpose of the algorithm is to provide a general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations were calculated for several cases where the conditions for the first order Born approximation were not satisfied. The results show that in both high and low frequency cases, good reconstructed profiles and smoothed versions of the original profiles can be obtained for smoothly varying permittivity profiles (lossless) and discontinuous profiles (lossless), respectively. A limited number of measurements around the object at a single frequency with four to eight plane incident waves from different directions are used. The method proposed in this article could easily be applied to the three-dimensional inverse scattering problem, if computational resources are available.     

Time-domain finite methods for electromagnetic wave propagation and scattering

Time-domain finite methods are considered by many as good candidates for the powerful, versatile, and accurate numerical simulation of complex electromagnetic phenomena. However, some concerns still remain about the accuracy of these methods, and questions keep being raised about their modeling versatility. By reviewing the key characteristics of several of these finite methods, and considering the various sources of the associated discretization and numerical error, it is argued that their proper use permits the accurate modeling of electromagnetic scattering and propagation phenomena associated with structures of electrical size and complexity beyond the capabilities of present frequency-domain finite and integral equation methods.<>     

Signal-subspace method approach to the intensity-only electromagnetic inverse scattering problem

This paper investigates the signal-subspace method approach to solve the electromagnetic inverse scattering problem using intensity-only (phase-free) data. Due to the polarization of electromagnetic fields, the relationship between the rank of the multistatic matrix and the number of small scatterers is different from that associated with the scalar wave. Multiple scattering between scatterers is considered, and the inverse scattering problem of determining the polarization tensors is nonlinear, which, however, is solved by the proposed analytical approach where no associated forward problem is iteratively evaluated.     

A volume/surface potential formulation of the method of moments applied to electromagnetic scattering

A new integral method to compute the electromagnetic scattering by general inhomogeneous dielectric bodies is presented. The method is based on a volume/surface equivalence principle and it uses the electromagnetic potentials as primary unknowns. The main advantage of this method comes from the continuity of the potentials across interfaces separating different media so that very easy to handle nodal basis functions can be used to solve the integral equations with the method of moments.     

T-matrix computations of light scattering by red blood cells

The electromagnetic far field, as well as the near field, originating from light interaction with a red blood cell (RBC)volume-equivalent spheroid, was analyzed by utilizing theT-matrix theory. This method is a powerful tool thatmakes it possible to study the influence of cell shape on the angulardistribution of scattered light. General observations were that thethree-dimensional shape, as well as the optical thickness apparent tothe incident field, affects the forward scattering. Thebackscattering was influenced by the shape of the surface facing theincident beam. Furthermore sphering as well as elongation of anoblate RBC into a volume-equivalent sphere or a prolate spheroid, respectively, was theoretically modeled to imitate physiologicalphenomena caused, e.g., by heat or the increased shear stress offlowing blood. Both sphering and elongation were shown to decreasethe intensity of the forward-directed scattering, thus yielding lowerg factors. The sphering made the scattering patternindependent of azimuthal scattering angle phi(s), whereas the elongation induced more apparent phi(s)-dependent patterns. The lightscattering by a RBC volume-equivalent spheroid was thus found to behighly influenced by the shape of the scattering object. Anear-field radius r(nf) was evaluated as thedistance to which the maximum intensity of the total near field haddecreased to 2.5 times that of the incident field. It was estimatedto 2-24.5 times the maximum radius of the scattering spheroid, corresponding to 12-69 mum. Because the near-field radiuswas shown to be larger than a simple estimation of the distance betweenthe RBC's in whole blood, the assumption of independent scattering, frequently employed in optical measurements on whole blood, seemsinappropriate. This also indicates that one cannot extrapolate theresults obtained from diluted blood to whole blood by multiplying witha simple concentration factor.     

A finite element free boundary formulation for the problem of multiphase heat conduction

The problem of heat conduction in a multiphase medium is a free boundary problem in which the free boundary is the phase transition line. The solution to this problem is highly irregular in that the temperature gradient is discontinuous at the free boundary. Two-dimensional, discontinuous, space–time finite elements are introduced to obtain a finite element, free boundary formulation for this problem. The jump in heat flux and position of the phase transition line become dependent variables in the finite element model. The resulting models give accurate results while allowing the calculation of free boundary problems with a fixed finite element mesh.     

Aperiodic Fourier modal method in contrast-field formulation for simulation of scattering from finite structures

This paper extends the area of application of the Fourier modal method (FMM) from periodic structures to aperiodic ones, in particular for plane-wave illumination at arbitrary angles. This is achieved by placing perfectly matched layers at the lateral sides of the computational domain and reformulating the governing equations in terms of a contrast field that does not contain the incoming field. As a result of the reformulation, the homogeneous system of second-order ordinary differential equations from the original FMM becomes non-homogeneous. Its solution is derived analytically and used in the established FMM framework. The technique is demonstrated on a simple problem of planar scattering of TE-polarized light by a single rectangular line.     

Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane

Scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane is rigorously solved. The scattered field is represented by a Fourier-integral representation. To analytically represent the fields in a general-shaped groove, the groove is divided into L number of layers. Fields are then expressed in each layer as summations of 2D spatial harmonic fields with unknown coefficients. Matching the boundary conditions between layers provides a linear set of equations connecting all the unknown harmonic coefficients. Judicious use of Fourier transform on the equations resulting from matching boundary conditions at the groove aperture provides a series representation of the scattered field in the spectral domain with unknown harmonic coefficients of the first layer in the groove. A stable solution is obtained by solving the complete system of equations with an adaptive choice for the number of modes in each layer.     

Coupling interactions in electromagnetic scattering from finite array of cavities with stratified dielectric coating

The coupling interactions in electromagnetic scattering from a finite array of two-dimensional identical cavities engraved in a perfectly electric conducting screen covered with stratified dielectric coating are presented using an algorithm based on the hybrid finite element-boundary integral method. The solution to the scattering from a finite array of cavities is approximated using the array factor method, which does not take into account the coupling between the cavities, and is compared to the recently developed finite element-boundary element method to demonstrate the importance of the inclusion of the coupling effect. Dependence of the coupling interactions between the cavities on various parameters such as separation periods, incident angle of the plane-wave excitation, and permittivity and thickness of the dielectric coating is demonstrated quantitatively through several numerical examples.     

Reducing computational costs using a multi-region finite element method for electromagnetic scattering

Electromagnetic scattering problems involving multiple scatterers can be solved by the finite element method using a single domain truncated with an absorbing boundary condition, but often it is more efficient to separate the single domain into several subdomains, separated by free-space, and to solve the set of subdomains iteratively. This multi-region method has been reported in the literature. Its relative computational cost is investigated and formulas for determining are provided when it is advantageous to use a multi-region against a single-region method.     

The application of scalable distributed memory computers to the finite element modeling of electromagnetic scattering

Large-scale parallel computation can be an enabling resource in many areas of engineering and science if the parallel simulation algorithm attains an appreciable fraction of the machine peak performance, and if undue cost in porting the code or in developing the code for the parallel machine is not incurred. The issue of code parallelization is especially significant when considering unstructured mesh simulations. The unstructured mesh models considered in this paper result from a finite element simulation of electromagnetic fields scattered from geometrically complex objects (either penetrable or impenetrable.) The unstructured mesh must be distributed among the processors, as must the resultant sparse system of linear equations. Since a distributed memory architecture does not allow direct access to the irregularly distributed unstructured mesh and sparse matrix data, partitioning algorithms not needed in the sequential software have traditionally been used to efficiently spread the data among the processors. This paper presents a new method for simulating electromagnetic fields scattered from complex objects; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms. © 1998 This paper was produced under the auspices of the U.S. Government and it is therfore not subject to copyright in the U.S.     

Laboratory measurements and T-matrix calculations of the scattering matrix of rutile particles in water

We present experimentally determined scattering matrix elements of birefringent rutile particles in water as a function of the scattering angle for a wavelength of 633 nm (in air). These elements are compared with the results of T-matrix calculations for prolate spheroids. For the diagonal matrix elements the results of the T-matrix calculations are in good agreement with those of the measurements. A good fit for the whole matrix, including the off-diagonal elements, is obtained when we compensate for the birefringence of the rutile particles by performing the computations for spheroids with a slightly larger length/width ratio than measured.     

On scattering and radiation problem for a cylinder in water of finite depth

Wave loadings due to scattering and radiation for a floating vertical circular cylinder in water of finite depth are derived. These are derived from the total velocity potential which can be decomposed as four velocity potentials; one due to scattering in the presence of an incident wave on fixed structure (diffraction problem), and the other three due to radiation respectively by surge, heave and pitch motion on calm water (radiation problem). For each case, the velocity potential is derived by considering two regions, namely, interior region and exterior region. The complex matrix equations can be solved numerically to determine the unknown coefficients to compute the wave loads. Numerical results can be obtained for different depth to radius and draft to radius ratios.     

Convergence of the finite element method as applied to electromagnetic scattering problems in the presence of inhomogeneous media

Approximate radiation boundary conditions (BCs) make partial-differential-equation-based methods attractive for the solution of electromagnetic scattering problems, especially for geometrically complex inhomogenous targets. These BCs allow for an exterior boundary value problem (BVP) to be approximated by an interior BVP. The use of the second-order Bayliss-Turkel BC for two-dimensional inhomogeneous targets is considered. In numerical experiments the rate of convergence with respect to mesh size previously predicted continues to hold.<>     

Approximation of the solution of inverse problem of scattering of electromagnetic waves on plane dielectrics

We propose a method for the determination of the material parameters of dielectric coatings according to the measured values of scattered electromagnetic fields which enables us to introduce an efficient procedure of processing of the data of measurements in the methods of nondestructive testing. As a specific feature of the proposed method for the solution of the formulated inverse problem, we can mention the possibility of reconstruction of piecewise continuous profiles of dielectric permittivity for laminated materials. The procedure of reconstruction is based on the method of integral equations. The solution of the problem is obtained approximately. The measured values of the coefficient of reflection of plane electromagnetic waves are extrapolated to the high-frequency region, which enables us to guarantee higher accuracy of reconstruction of the functions of dielectric permittivity for the analyzed structures.     

Initial value problem formulation of time domain boundary element method for electromagnetic microwave simulations

To aim to obtain more stable solutions and wider area applications for the Time Domain Boundary Element Method (TDBEM), initial value problem formulation of the TDBEM is newly introduced for microwave simulations. The initial value problem formulation of the TDBEM allows us to solve transient microwave phenomena as interior region problems, which gives us well matrix property and interior resonance free solutions. This paper concentrates on applying the initial value problem formulation of the TDBEM to wake field phenomena in particle accelerator cavities.     

Analysis of scattering from arbitrary configuration of elliptical obstacles using T-matrix representation

A new method of analysis of an arbitrary configuration of elliptical cylinders is presented. The treatment of such a problem is based on a combination of the cylindrical and elliptical coordinates systems. This approach is applied to the formulation of the scattered field at the surface of equivalent cylinder surrounding dielectric or metal elliptical object. To analyse the arbitrary set of elliptical cylinders, the iterative scattering procedure is used. A good agreement of the proposed method with the commercial FD simulator is achieved.     

Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane: comment

We show that the problem of scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane, which was recently studied by Basha et al. [J. Opt. Soc. Am. A24, 1647 (2007)], was solved 11 years ago using the same formulation. This method was further extended to deal with a finite number of grooves and also with complex apertures including several nonlossy and lossy dielectrics, as well as real metals.     

Mathematical formulation of the stefan problem

The Stefan problem describes the conduction of heat in a medium involving a solid-liquid phase change at a prescribed melting temperature. Considerations of physical, mathematical and numerical experiences with such problems all imply that enthalpy (not temperature) is the natural dependent variable to specify the solution. Our discussion centers on the physical interpretation of the multi-valued Heaviside “function” which arises in the mathematical formulation as the fraction of water. We show that this permits the consideration of (possibly large) regions of mush at the melting temperature and of problems with internally distributed sources of heat. Moreover, in order for such problems to be well-posed, this fraction of water must necessarily be specified initially in the part of the region at the melting temperature.