Scattering of Spherically and Hemispherically Stratified Lenses Fed by Any Real Source

An analytical method to compute the scattering of spherically and hemispherically stratified lens antennas is described. The expansion of any real source on spherical wave functions is detailed and validated by comparison to commercial software simulations and measurements at both 50 GHz and 77 GHz. A mode matching technique (MMT) based on spherical wave functions is first used to analyze the scattering by spherically stratified lens antennas. The far field patterns and directivity obtained are in excellent agreement with commercial software simulations and measurements for a six-shell Luneburg lens at 6 GHz. This MMT is then extended to hemispherically stratified lens antenna analysis. Its validation is also carried out by comparisons to both commercial software and measurements for a three-shell half Maxwell fish-eye lens fed by an open-ended waveguide at W-band. The expansion on spherical modes gives direct access to the field everywhere. To highlight the progressive focusing effect of inhomogeneous lens antennas, the electric field is mapped in terms of magnitude and phase in the neighborhood of the entire structure. One of the originalities of this work is the quantification of the reaction created by the scatterer on the feed. Narrowing the scatterer to a stratified lens does not affect the generality of the presented procedure. While providing controlled accuracy, the MMT tremendously reduces both computation time and memory load in comparison to commercial software.     

Near-to-far-field transformation by a time-domain spherical-multipole analysis

The contribution deals with a new time-domain near-to-far-field (NFF) transformation which is particularly suited for the finite-difference time-domain (FDTD) method. The far field is derived from the tangential field components on a surface enclosing the scatterer by employing a time-domain spherical-multipole representation. The necessary time-domain convolution is performed as "on the fly," in parallel with the FDTD time-stepping algorithm. The efficiency of the method is improved by incorporating a temporal linear interpolation of the near-field data. With the once obtained multipole amplitudes an analytic series representation of the time-domain far field is achieved, which allows a physical interpretability of the result. Moreover, this expansion serves as an ideal basis for a systematic and efficient post processing. The proposed technique may also be useful for other numerical and for asymptotic methods.     

Electromagnetic plane wave scattering by a system of two parallel conducting prolate spheroids

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, as exact solution is obtained for the scattering by two perfectly conducting prolate spheroids in parallel configuration, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Using the spheroidal translational addition theorems recently presented by the authors which are necessary for the two-body (or multibody) scattering solution, an efficient computational algorithm of the translational coefficients is given in terms of spherical translational coefficients. The field solution gives the column vector of the series coefficients of the scattered field in terms of the column vector of the series coefficients of the incident field by means of a matrix transformation in which the system matrix depends only on the scatterer ensemble. This eliminates the need for repeatedly solving a new set of simultaneous equations in order to obtain the scattered field for a new direction of incidence. Numerical results in the form of curves for the bistatic and monostatic radar cross sections are given for a variety of prolate spheroid pairs having resonant or near resonant lengths.     

Shadow boundary incremental length diffraction coefficients appliedto scattering from 3-D bodies

Shadow boundary incremental length diffraction coefficients (SBILDCs) are high-frequency fields designed to correct the physical optics (PO) field of a three-dimensional (3-D) perfectly electrically conducting scatterer. The SBILDCs are integrated along the shadow boundary of the 3-D object to approximate the field radiated by the nonuniform shadow boundary current (the difference between the exact and PO currents near the shadow boundary). This integral is added to the PO field to give an approximation to the exact scattered field that takes into account both PO and nonuniform shadow boundary currents on the scatterer. Like other incremental length diffraction coefficients, any SBILDC is based on the use of a 2-D canonical scatterer to locally approximate the surface of the 3-D scatterer to which it is applied. Circular cylinder SBILDCs are, to date, the only SBILDCs that have been obtained in closed form. In this paper, these closed-form expressions are validated by applying them for the first time to a 3-D scatterer with varying radius of curvature-the prolate spheroid. The results obtained clearly demonstrate that for bistatic scattering the combined PO-SBILDC approximation is considerably more accurate than the PO field approximation alone     

Conformal hybrid finite difference time domain and finite volumetime domain

A hybrid method that combines the finite difference time domain (FDTD) and the finite volume time domain (FVTD) methods is presented. The FVTD, based on a conformal and unstructured grid is used in the near vicinity of the surface of a scatterer, and the FDTD is used to model the fields in the surrounding area. The two are coupled together through interpolation. The vertex-based FVTD allows for more convenient and accurate interpolations than a conformal FDTD method. The hybrid method is validated through two examples-the scattering by a PEC cube and sphere-by comparison with the direct FDTD solution, and with an exact Mei series solution for the spherical case     

Accurate solution of square scatterer as benchmark for validationof electromagnetic modeling of plate structures

An infinitesimally thin-square scatterer, of size λ×λ, excited normally by an incident plane wave, which is polarized along a scatterer edge, is analyzed. The accurate solution of its current distribution is found in the form of a double series of basis functions, which automatically satisfy the continuity equation at the plate edges and include the edge effect. The coefficients that multiply basis functions are determined starting from the electric field integral equation by using the Galerkin method. The solution obtained for the order of approximation n=8 is adopted as a benchmark. The corresponding coefficients are tabulated and graphs of such obtained current distribution are given. The solution adopted as a benchmark is applied for comparison of rooftop basis functions and polynomial entire-domain basis functions. The relative error of the mean absolute value of current deviation is used as an error metric     

Moment method with isoparametric elements for three-dimensionalanisotropic scatterers

A new method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatterers is presented. The method is based on a general volume integro-differential formulation of the scattering problem, and consists of the numerical solution of the coupled integral equations by the moment method and point matching. A particularly powerful feature of this method is that the numerical model of the scatterer is obtained by parametric volume elements and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented here to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples     

Construction of heuristic diffraction coefficients in the analytical solutions to the problems in which wave fields of different physical nature are scattered by polygonal flat plates with complex boundary conditions

The heuristic diffraction coefficients of the problem in which the wave field of an arbitrary physical nature is scattered by a polygonal flat plate with complex boundary conditions are determined. Diffraction coefficients are constructed with the help of the geometric optics coefficients of wave field reflection from an infinite plane surface by analogy with the known solution to the electrodynamic problem of diffraction by a perfectly conducting scatterer. It is established that the new approach makes it possible to derive simple formulas for diffraction coefficients. Their accuracy exceeds that of the formulas of the known heuristic analytical methods and tends to the accuracy of rigorous solutions. It is demonstrated that the derived results can be used in both electrodynamics and the other areas of physics, e.g., in calculations of the seismic wave diffraction.     

A phase matrix for a dense discrete random medium: evaluation ofvolume scattering coefficient

In the derivation of the conventional scattering phase matrix of a discrete random medium, the far-field approximation is usually assumed. In this paper, the phase matrix of a dense discrete random medium is developed by relaxing the far-field approximation and accounting for the effect of volume fraction and randomness properties characterized by the variance and correlation function of scatterer positions within the medium. The final expression for the phase matrix differs from the conventional one in two major aspects: there is an amplitude and a phase correction. The concept used in the derivation is analogous to the antenna array theory. The phase matrix for a collection of scatterers is found to be the Stokes matrix of the single scatterer multiplied by a dense medium phase correction factor. The close spacing amplitude correction appears inside the Stokes matrix. When the scatterers are uncorrelated, the phase correction factor approaches unity. The phase matrix is used to calculate the volume scattering coefficients for a unit volume of spherical scatterers, and the results are compared with calculations from other theories, numerical simulations, and laboratory measurements. Results indicate that there should be a distinction between physically dense medium and electrically dense medium     

Feasibility of compact ranges for near-zone measurements

The purpose of this paper is to demonstrate the feasibility of using compact range reflector systems to make near-zone radiation or scattering measurements. This can be achieved by designing the compact range to provide a uniform spherical wave incident upon the antenna or scatterer under test. The basic design technique is demonstrated using the Scientific Atlanta reflector system which has been modified by adding an elliptic rolled edge to improve the uniformity of the incident wave. The near-zone range design is validated (from around 50 ft range to the far zone) by probing the field in the measurement volume and by comparing measured backscattering patterns from a circular cylinder with those calculated by the geometrical theory of diffraction (GTD). All the advantages of a conventional far-zone compact range are now made available by our demonstrated variable-zone (adjustable continuously from 50 ft to infinity) compact range.     

Electromagnetic scattering for oblique incidence on impedancebodies of revolution

Combined field integral equations for the surface currents induced by an obliquely incident wave on a rotationally symmetric body are considered. The relative surface impedance is independent of the azimuthal angle but may vary along the profile of the scatterer in any plane containing the axis of symmetry; the currents are conveniently expressed in terms of Fourier series of uncoupled terms in the azimuthal angle. Simple integral expressions for the far field are given and a computer code is described and tested on a variety of scatterers. Geometry of scatterer, surface impedance and Fourier harmonics of induced currents are described by splines. The results are in agreement with physical interpretation     

A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section

A new method is introduced for formulating the scattering problem in which the scattered fields (and the interior fields in the case of a dielectric scatterer) are represented in an expansion in terms of free-space modal wave functions in cylindrical coordinates, the coefficients of which are the unknowns. The boundary conditions are satisfied using either an analytic continuation procedure, in which the far-field pattern (in Fourier series form) is continued into the near field and the boundary conditions are applied at the surface of the scatterer; or the completeness of the modal wave functions, to approximately represent the fields in the interior and exterior regions of the scatterer directly. The methods were applied to the scattering of two-dimensional cylindrical scatterers of arbitrary cross section and only the TM polarization of the excitation is considered. The solution for the coefficients of the modal wave functions are obtained by inversion of a matrix which depends only on the shape and material of the scatterer. The methods are illustrated using perfectly conducting square and elliptic cylinders and elliptic dielectric cylinders. A solution to the problem of multiple scattering by two conducting scatterers is also obtained using only the matrices characterizing each of the single scatterers. As an example, the method is illustrated by application to a two-body configuration.     

The SNFGTD method and its accuracy

The spherical near-field geometrical theory of diffraction (SNFGTD) method is an extended aperture method by which the near field from an antenna is computed on a spherical surface enclosing the antenna using the geometrical theory of diffraction. The far field is subsequently found by means of a spherical near-field to far-field transformation based on a spherical wave expansion of the near field. Due to the properties of the SNF-transformation, the total far field may be obtained as a sum of transformed contributions which facilitates analysis of collimated beams. It is demonstrated that the method possesses some advantages Over traditional methods of pattern prediction, but also that the accuracy of the method is determined by the quasioptical methods used to calculate the near field.     

“Blind” shape reconstruction from experimental data

A method for reconstructing the shape of a bounded impenetrable object from measured scattered field data is presented. The reconstruction algorithm is, in principle, the same as that used before for reconstructing the conductivity of a penetrable object and uses the fact that for high conductivity the skin depth of the scatterer is small, in which case the only meaningful information produced by the algorithm is the boundary of the scatterer. A striking increase in efficiency is achieved by incorporating into the algorithm the fact that for large conductivity, the contrast is dominated by a large positive imaginary part. This fact together with the knowledge that the scatterer is constrained in some test domain constitute the only a priori information about the scatterer that is used. There are no other implicit assumptions about the location, connectivity, convexity, or boundary conditions. The method is shown to successfully reconstruct the shape of an object from experimental scattered field data in a “blind” test     

Electromagnetic scattering by buried objects of low contrast

The Born approximation is used to derive the plane-wave scattering matrix for objects of low dielectric contrast. For general shapes a numerical integration over the volume of the scatterer is required, but analytical expressions are derived for a sphere, a circular cylinder and a rectangular box (parallelepiped). The plane-wave scattering-matrix theory is used to account for the air-Earth interface. Numerical results are presented for the scattered field and far field for plane-wave excitation. The scattered field are weak for low-contrast objects, but the near-field results have application to electromagnetic detection of buried objects     

Missile Circumferential Current Density for Plane Wave Electromagnetic Field Illumination

The asymmetry in current density along the periphery of cylindrical scattering obstacles of both finite and infinite length illuminated by a plane wave electromagnetic field is discussed. In the Appendix the same problem for a spherical scatterer is considered.     

Comparison of a class of subdomain and entire domain basisfunctions automatically satisfying KCL

Accuracy, number of unknowns, and CPU time are compared for piecewise linear subdomain basis functions and polynomial entire domain basis functions. Both types of functions automatically satisfy a continuity equation at wire ends and junctions, according to Kirchoff's current law (KCL). The relative root mean square (RMS) current deviation is chosen as the error metric. An electrically short scatterer, a crossed wire scatterer and an electrically long scatterer are used for comparison. Currents are obtained by solving the electric field integral equation (EFIE), by means of the Galerkin method. It was shown that in most cases, for the same accuracy required, the entire domain approximation uses three to five times less numbers of unknowns and 10-100 times less CPU time than the subdomain approximation. Generally, such efficiency is achieved by using entire domain expansions the order of which is up to n=5 and cannot be significantly improved by using higher order expansions     

Theory and measurement of the field of a pyramidal horn

Edge-wave diffraction theory is used in an unconventional way to predict the field in the immediate vicinity of the aperture plane of a pyramidal microwave horn. The far field may then be inferred by Fourier transformation. The theoretical predictions for the near field are compared with measurements almost in the aperture plane and inside a horn made by the modulated scatterer method. The directivity on axis, which is our primary concern, is mainly determined by the curvature of the wavefront at the aperture. When computed as a function of frequency, it shows oscillations similar to those observed. They arise because edge waves, multiply reflected inside the horn, mimic the effect of a wave reflected back from the throat; this interferes with the main wave to change the curvature of the emerging wavefront, and hence, the directivity     

Reduction of the number of unknowns in large stacked planarstructures by a fringe aperture formulation

For scattering problems comprising a combination of planar structures, the total number of unknowns may be significantly reduced if an aperture formulation is employed rather than a patch formulation. The rationale behind using the aperture formulation is based on the recognition that the decay rate of the scattered aperture field is independent of the size of the scatterer. Therefore, any scatterer may be surrounded by an aperture of fixed width over which an integral equation is formulated. The area of this aperture is proportional to the perimeter of the scatterer rather than its area, and it becomes much smaller compared with the entire scatterer area as the size of the scatterer increases, hence the reduction in the number of independent unknowns. A truncation criterion for the finite aperture is determined via a numerical study of the aperture field behavior for various angles of incidence. In addition, the a priori knowledge of the physical optics component is also taken into account, reducing the unknown function to an aperture field component that is the outcome of the remaining fringe current only. The total current distribution can be subsequently derived from this field by adding the known physical optics field and invoking the inverse of the Green's function in the spectral domain. This analysis of isolated planar scatterers results in a spectral scattering matrix representation that is subsequently used for cascading of stacked structures