Diffraction by an anisotropic dielectric half-plane: a uniformasymptotic PO solution

A uniform solution is proposed to, describe the diffraction by a penetrable anisotropic dielectric halfplane illuminated at normal incidence by an electromagnetic plane wave. Resorting to second-order boundary conditions on a sheet simulating a special type of anisotropic dielectric thin layer, a physical optics (PO) approximation for the induced electric and magnetic surface currents is derived. Then, a uniform asymptotic evaluation of the corresponding radiation integral provides the diffracted field in terms of the standard transition function relevant to the uniform theory of diffraction. The effectiveness of the solution is proved by many numerical tests     

Diffraction from a truncated grounded dielectric slab: acomparative full-wave/physical-optics analysis

The problem of diffraction at the edge of a semi-infinite grounded dielectric slab excited by a line source is investigated. This canonical problem may be used as a reference solution in the high-frequency regime for patch antennas radiating from a finite grounded slab. Both physical optics (PO) and integral equation (IE) approaches are used and compared. The PO formulation is cast in a convenient asymptotic form that neatly describes the diffraction processes associated with the various wave species. The IE, solved by the method of moments, is formulated by enforcing the continuity of the electric field on an infinite aperture orthogonal to the slab. This allows a drastic reduction of unknowns, provided that appropriate entire domain basis functions are used that are shaped to match the asymptotic behavior of the aperture field. Comparison between the PO and IE solutions is presented to determine the range of validity of PO     

ITD formulation for the currents on a plane angular sector

Approximate high-frequency expressions for the currents induced on a perfectly conducting plane angular sector are derived on the basis of the incremental theory of diffraction (ITD). These currents are represented in terms of those predicted by physical optics (PO) plus fringe contributions excited by singly and doubly diffracted (DD) rays at the two edges of the angular sector. For each of these two contributions, additional currents associated to vertex diffracted rays are introduced that provide continuity at the relevant shadow boundary lines. The transition region of DD rays is described by a transition function involving cylinder parabolic functions. The asymptotic solution presented is constructed in such a way to satisfy far from the vertex the expected edge singularities, which tend to be the same as those predicted by the exact solution of the half plane. Numerical results are compared with the exact solution of the same problem and with moments method results for scattering from polygonal plates     

Creeping waves on a perfectly conducting cone

The rigorously formulated scalar and vector Green's functions for a perfectly conducting semi-infinite cone are approximated asymptotically to furnish the high-frequency creeping wave contributions when the source and observation points are both located on the cone surface. The results are expressed in the ray-optical format of the geometrical theory of diffraction and thus provide another canonical solution for verification of the postulates of that theory. The analytical procedure for isolating the creeping waves from other high-frequency phenomena such as tip diffraction is motivated by the methodology for the simpler circular cylinder problem, to which the present solution reduces when the cone-to-cylinder transition is performed. The results are of interest for calculation of source-induced surface currents, and of mutual coupling between slot array elements, on conical surfaces.     

Coupled canonical grid/discrete dipole approach for computingscattering from objects above or below a rough interface

A numerical model for computing scattering from a three-dimensional (3D) dielectric object above or below a rough interface is described. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. To improve computational efficiency, the canonical grid method and the discrete dipole approach (DDA) are used to compute surface to surface and object to object point couplings, respectively, in O(N log N), where N is the number of surface or object sampling points. Two distinct iterative approaches and a preconditioning method for the resulting matrix equation are discussed, and the solution is verified through comparison with a Sommerfeld integral-based solution in the flat surface limit. Results are illustrated for a sample landmine detection problem and show that a slight surface roughness can modify object backscattering returns     

Physical optics analysis of beam waveguides using auxiliary planes

A physical optics (PO) method is presented which in two steps calculates the scattered field of a reflector or a lens in a beam waveguide (BWG). The first step involves a calculation of a set of currents on an auxiliary plane and the second step a field calculation from this current set. The method is named A-PO that refers to the calculation of PO currents on an Auxiliary plane. A-PO is less accurate than PO for sidelobe analysis, but useful for first-pass analysis of the main beam region in a BWG where it is significantly faster than standard PO. Two examples show that the co-polar as well as cross-polar radiation in a submillimeter BWG can be efficiently determined 40 dB below peak.     

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     

Efficient method of moments formulation for large PEC scatteringproblems using asymptotic phasefront extraction (APE)

A method is introduced for reducing the exorbitant dependence on computer storage and solution time in the method of moments (MoM) for electrically large electromagnetic (EM) scattering problems. The unknown surface currents on large, smooth parts of a perfect electrical conductor (PEC) scatterer are expressed by an efficient set of linearly phased surface current basis functions. The phasefront characteristics of the surface currents are numerically extracted from known current samples obtained from a lower-frequency solution of the same configuration. The use of such basis functions for efficiently representing the surface currents that are constructed in terms of linearly phased currents at higher frequencies is justified by considering the form of the surface currents predicted by high-frequency asymptotic ray methods. The procedure for extracting the current phasefronts is purely numerical, obviating computationally expensive and nonrobust operations such as ray-tracing, and thus, is amenable to general purpose scattering codes. The new MoM with linearly phased basis functions is shown to greatly relieve the storage and solution time of the conventional MoM while accurately reproducing the induced surface currents and scattered fields of some chosen targets     

Wire antennas in the presence of a dielectric/ferrite inhomogeneity

A moment method solution for treating thin-wire antennas in the presence of an arbitrary dielectric and/or ferrite inhomogeneity is presented. The wire is modeled by an equivalent surface current density, and the dielectric/ferrite inhomogeneity is modeled by equivalent volume polarization currents. The conduction currents on the wire and the polarization currents in the dielectric/ferrite inhomogeneity are treated as independent unknowns and determined in the moment method solution. The method is applied to the problem of a loop antenna loaded with dielectric or ferrite. Numerical results are presented, and are in good agreement with measurements and previous calculations.     

High-frequency Green's function for a semi-infinite array ofelectric dipoles on a grounded slab .I. formulation

A uniform, high-frequency solution is presented for the electromagnetic field radiated at finite distance by a semi-infinite array of elementary electric dipoles placed on an infinite grounded dielectric slab. This solution is useful for the efficient analysis of printed arrays. The field is represented in terms of a series encompassing propagating and evanescent truncated Floquet waves together with their corresponding diffracted rays, which arise from the edge of the array. The high-frequency formulation also includes surface and leaky wave contributions excited at the array edge. The diffracted waves contain discontinuities which compensate the disappearance of surface, leaky and truncated Floquet waves at their pertinent shadow boundaries     

Equivalent edge currents for arbitrary aspects of observation

Explicit expressions for equivalent edge currents are derived for an arbitrary local wedge angle and arbitrary directions of illumination and observation. Thereby the method of equivalent currents (MEC) is completed as a practically applicable theory of the electromagnetic high-frequency diffraction by edges. The derivation is based on an asymptotic relationship between the surface radiation integral of the physical theory of diffraction (PTD) and the line radiation integral of MEC, and the resulting expressions are deduced from the exact solutions of the canonical wedge problem.     

A uniform ray approximation of the scattering by polyhedralstructures including higher order terms

A uniform ray representation of the far field scattered by flat plate structures is investigated by postulating an approximation of the surface current on each face of the object, which is subsequently integrated either in closed form or asymptotically in terms of the well-tabulated edge transition function. Specifically, the current on each plate is approximated, in addition to the usual physical optics (PO) component, by a primary nonuniform current, obtained from the canonical solution to the wedge problem and truncated at edges of the plate, as well as a secondary nonuniform current induced by doubly diffracted fields and expressed in terms of an equivalent edge source. The superimposed effect of the rays resulting from the primary and secondary nonuniform current integration improves the agreement of the calculated pattern as compared with method of moments computations     

Electromagnetic Scattering From Arbitrarily Shaped Dielectric Bodies Using Paired Pulse Vector Basis Functions and Method of Moments

A pair of orthogonal pulse vector basis functions is demonstrated for the calculation of electromagnetic scattering from arbitrarily-shaped material bodies. The basis functions are intended for use with triangular surface patch modeling applied to a method of moments (MoM) solution. For modeling the behavior of dielectric materials, several authors have used the same set of basis functions to represent equivalent electric and magnetic surface currents. This practice can result in zero-valued or very small diagonal terms in the moment matrix and an unstable numerical solution. To provide a more stable solution, we have developed orthogonally placed, pulse basis vectors: one for the electric surface current and one for the magnetic surface current. This combination ensures strongly diagonal moment matrices. The basis functions are suitable for electric field integral equation (EFIE), magnetic field integral equation (HFIE), and combined field formulations. In this work, we describe the implementations for EFIE and HFIE formulations and show example results for canonical figures.      

Effects of surface waves on the currents of truncated periodic arrays

The behavior of surface waves in truncated periodic arrays is examined through analysis of the currents. The surface waves to be studied are guided by the perfectly conducting elements of the array itself and are to be distinguished from the dielectric slab-guided surface waves encountered elsewhere in the literature. The conditions under which surface waves may arise are given. The surface wave currents are extracted from the method of moments solution for the finite by an infinite array using a least squares algorithm. Surface wave excitation and reflection coefficients are then be determined from the data and compared with the semi-infinite array solution.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Computation of TM and TE modes in waveguides based on a surfaceintegral formulation

The surface integral formulation is used for the computation of TM and TE modes propagating in dielectric loaded waveguides. This formulation makes use of the surface equivalence principle whereby the field at any point internal or external to the waveguide can be expressed in terms of equivalent surface currents. This procedure reduces the original problem into a set of integro-differential equations which is then reduced to a matrix equation using the method of moments. The solution of this matrix equation provides the propagation characteristics of the waveguide and the equivalent surface currents existing on the waveguide walls. The equivalent surface currents can be used to compute the fields at all points, both inside and outside the waveguide. The surface integral method has been used to compute the propagation characteristics of waves propagating in dielectric loaded waveguides. The computed results agree very well with analytical and published data. A method that can be used to remove spurious modes is illustrated     

复杂目标宽带电磁散射特性幅相分离插值方法

本文针对目标散射体表面感应电流的特性,提出了一种新的插值方法—幅相分离法,该方法将最佳一致逼近和相位提取结合起来,通过求解给定频带内的切比雪夫节点和节点处的表面电流,结合相位提取得到整个频带内的感应电流,从而快速有效地计算了复杂目标的宽带雷达散射截面。数值结果证明了方法的有效性和准确性。     

High-frequency fields excited by a line source located on a concave cylindrical impedance surface

A previous study of high-frequency currents induced by a line source on a perfectly conducting concave cylindrical surface is extended to the case of nonvanishing surface impedanceZ_{s}. Alternative field representations are formulated and evaluated asymptotically as combinations of ray-optical, whispering gallery (WG) mode, surface wave, continuous spectrum, and canonical integral contributions. Numerical calculations provide an insight into the accuracy and utility of the various formulations. Sufficiently far from the source point, a combination of ray optical fields and tightly bound WG modes was previously found to be a most appealing form whenZ_{s} = 0. As the surface impedance becomes more dissipative, the WG modes axe weakened by attenuation and eventually render the ray optical fields adequate by themselves. A representation in terms of rays and a canonical integral is found to be useful for all parameter ranges. The canonical integral has been evaluated numerically and tabulated.     

Analytic Analysis of Transient Scattering From a Finite Second-Order Surface Illuminated by an Incident Plane Wave

A closed-form analytic solution based on a time-domain (TD) physical optics (PO) approximation is developed for the scattering from a finite second-order surface when illuminated by a transient impulsive plane wave. This TD-PO solution can be applied via a convolution to derive the early time transient fields scattered from the same scatterer that is illuminated by a realistic astigmatic finite-energy pulse. The closed form TD-PO solution is obtained by inverting the corresponding frequency-domain PO solution into TD. This solution can be expressed in terms of reflection and diffraction components of the scattering mechanisms as in other conventional high-frequency asymptotic solutions. Numerical examples are presented to demonstrate its physical phenomenon of the scattering mechanisms.     

A radar cross-section model for power lines at millimeter-wave frequencies

The knowledge of radar backscatter characteristics of high-voltage power lines is of great importance in the development of a millimeter-wave wire detection system. In this paper, a very high-frequency technique based on an iterative physical optics approach is developed for predicting polarimetric radar backscattering behavior of power lines of arbitrary strand arrangement. In the proposed scattering model the induced surface current is obtained using the tangent plane approximation in an iterative manner where the first-order current, obtained from the incident wave, is used as the source for the second-order current and so on. The approximation is valid for frequencies where the cable strand diameter is on the order of or larger than the wavelength. It is shown that the copolarized backscatter is dominated by the contribution from the first-order PO currents, whereas the cross-polarized backscatter is generated by the second- and higher order PO currents. Using this model, the effects of radar antenna footprint, surface irregularities, and cable sag (when suspended between towers) on radar backscatter are studied. To verify the validity of the proposed model, theoretical results are compared at 94 GHz with experimental results and are found to be in good agreement.