A MATLAB-Based Virtual Tool for the Electromagnetic Wave Scattering from a Perfectly Reflecting Wedge

Physical optics uses geometrical optics to estimate the surface current. This current is then used in a radiation integral to find the scattered field. PO often works very well for electrically large and smooth bodies. However, in spite of its great success in many applications, the use of an approximate current can lead to inherent limitations of its accuracy. The physical theory of diffraction (PTD) is an important high‐frequency technique that addresses this problem. The PTD became a widely used technique for the analysis and design of antennas, radar cross‐section analysis, and stealth design. The PTD theory is first developed in 2D. Its use is demonstrated by calculating the radiation pattern of a reflector antenna. It is then be generalized to 3D and applied to the scattering by a circular disc. The PTD formulation is closely related to both geometrical theory of diffraction (GTD) and uniform theory of diffraction (UTD).

The physical theory of diffraction (PTD) has been expanded for the case of slope diffraction, when an incident wave is zero but its derivative is not zero in the direction of a perfectly conducting scattering edge. High frequency asymptotics are found both for elementary edge waves and for the total edge waves scattered by arbitrary curved edges. Great attention is given to fields created by the nonuniform (diffraction) component of edge currents. These fields are usually called ptd corrections to the Physical Optics approach. These corrections are found for diffraction fields in ray regions and in diffraction regions such as the vicinities of shadow boundaries, smooth caustics, and foci.

For the electromagnetic modeling of scattered fields from large and complex objects, a very efficient simulation tool based on the well-known Shooting-and-Bouncing-Rays (SBR) technique has been developed [1]. This algorithm uses field-based high-frequency approaches for finding the relevant propagation paths, i.e. rays are traced through the scenario according to the laws of Geometrical Optics (GO) and diffracted rays are generated according to the laws of the Uniform Theory of Diffraction (UTD). This GO/UTD part is combined with a source-based approach, where each ray generates an equivalent surface current at each interaction with the object. These currents are calculated using Physical Optics (PO) and Physical Theory of Diffraction (PTD), and the superposition of all these contributions leads to the total scattered field strengths. Further technical details about the ray tracing approach can be found in [1, 2, 4]. With this simulation tool, large and complex objects can be modeled, which are still too costly for numerically exact methods. Generally, both metallic and dielectric objects [2], and also combined metallic-dielectric objects, can be modeled.

The accurate prediction of the far field radiated or scattered by large structures, such as large reflector antennas, requires efficient techniques for representing the illuminating field. Complex Source Points (CSP) inherently contain information about the source directivity, hence they can be used as the basis function to expand a given, but arbitrary, radiating wave field [1-3], such as the field incident on an antenna or a more general complex structure. As a consequence, a CSP field representation, when combined with the analytic continuation in complex space of typical ray-techniques such as the Geometrical and the Uniform Geometrical Theory of Diffraction (GTD/UTD), may provide a very efficient tool to estimate the fields radiated by large objects [4]. In this framework, an extension of the Incremental Theory of Diffraction (ITD) formulation for the scattering by wedges illuminated by CSP has been introduced [5], which essentially overcomes the typical impairments of the GTD/UTD ray techniques associated with possible ray caustics and with the difficulties of ray tracing in complex space. On the other hand, when dealing with the description of the field radiated by large structures, many of the existing electromagnetic codes resort to a Physical Optics (PO) representation also with an arbitrary incident field. It is however well known that the PO approach does not always produce accurate field predictions [6]. A significative augmentation of the PO field estimate can be achieved by including along the structure's edges a line integration of an incremental fringe field, that acts as a correction term for the field estimate. Several techniques have been published to derive these elementary contributions, leading to Physical Theory of Diffraction (PTD), Elementary Edge Waves/Incremental Length Diffraction Coefficient (EEW/ILDC), and ITD. In this work we discuss some recent advances in the incremental formulation for the field diffracted by edges in perfect electric conductor (PEC) objects when illuminated by a CSP beam expansion, with application to the analysis of large reflector antennas. A fringe formulation of the field diffracted by wedges with PEC faces when illuminated by a single CSP has been recently presented [7]. At each point on the edge the incremental fringe correction term is deduced from tangential canonical problems as the difference between the local ITD diffracted field [5] and an appropriate incremental end-point PO field (IEPO) scattered by the half-lit plane tangent to the edge [8]. The total spurious effects due to the presence of the edge are corrected by adiabatically distributing and integrating the local incremental fringe field coefficients along the line of the edges. This formulation yields more accurate predictions of the radiated field. For configurations in which several metallic edges are present and for grazing aspects of incidence and observation, the correct interactions between the edges in the problem need to be properly accounted for. Hence we introduce correct incremental double-diffraction coefficients for CSP illumination in the first-order fringe formulation [9]. These incremental coefficients have been derived by a proper analytical continuation of their real counterparts [10]. The formulation provides an accurate first-order asymptotic description of the interaction between two edges, which is valid both for skewed separate wedges and for edges joined by a common PEC face. It also includes a double incremental slope diffraction augmentation, which provides the correct dominant high-frequency incremental contribution at grazing aspects of incidence and observation. The total doubly-diffracted field is obtained from a double spatial integration along each of the two edges on which consecutive diffractions occur. In the application to the analysis of large reflector antennas the first-order fringe correction to the PO scattered fields tends to fail in those directions parallel to the aperture plane. Here, the addition of the incremental double diffracted field provides the correct estimation of the radiated field.

Physical optics (PO) and the physical theory of diffraction (PTD) are used to determine the backscatter cross sections of dihedral corner reflectors in the azimuthal plane for the vertical and horizontal polarizations. The analysis incorporates single, double, and triple reflections; single diffractions; and reflection-diffractions. Two techniques for analyzing these backscatter mechanisms are contrasted. In the first method, geometrical optics (GO) is used in place of physical optics at initial reflections to maintain the planar nature of the reflected wave and subsequently reduce the complexity of the analysis. The objective is to avoid any surface integrations which cannot be performed in closed form. This technique is popular because it is inherently simple and is readily amenable to computer solutions. In the second method, physical optics is used at nearly every reflection to maximize the accuracy of the PTD solution at the expense of a rapid increase in complexity. In this technique, many of the integrations cannot be easily performed, and numerical techniques must be utilized. However, this technique can yield significant improvements in accuracy. In this paper, the induced surface current densities and the resulting cross section patterns are illustrated for these two methods. Experimental measurements confirm the accuracy of the analytical calculations for dihedral corner reflectors with right, acute, and obtuse interior angles.

Due to simplicity, hybridization of geometrical optics (GO) and physical optics (PO) based on ray tracing has been widely used for fast scattering analyses. However, when targets of curved concavities are discretized by flat facets, the loss of divergence factor (DF) will degrade the simulation accuracy. To remedy this loss, a simple and efficient factor, entitled virtual divergence factor (VDF), is proposed to play the role of DF. To prove the validity of VDF and simulate the scattering of concave complex targets, a hybrid method of GO/PO and physical theory of diffraction (PTD) is elucidated. With VDF correction, several typical targets, including a S-shape cavity, are simulated by this hybrid method. In comparison to multilevel fast multipole algorithm (MLFMA) or measurements, the validaty of VDF is fully demonstrated by good agreements and the excellent performance relative to DF on canonical surfaces, where the great efficiency and flexibility of this hybrid method are also shown. Moreover, one interesting and important issue, the dependance of field convergence on the maximum number of ray reflections, is also investigated for the first time.

The physical optics (PO) and the physical theory of diffraction (PTD) are in extensive use in the antenna design and RCS calculation. The specific feature of these approximations is the phenomenon of polarization coupling. This phenomenon has been known since 1975, but its physical nature is still not explained in the literature. In the present communication, it is shown that this phenomenon is caused by the charges at the edge of a scattering structure, which are accumulated there due to the discontinuity of the PO current component normal to the edge.

The generalization1 of a solution obtained for wedge wave diffracted from the rib of impedance wedge for the case of Perfectly Electrically Conducting (PEC) wedge with cover is considered. The development of the Physical Theory of Diffraction (PTD) method for calculation of reflection coefficients from PEC wedge with cover is presented. The calculations were carried out according to strict formulas and assuming that impedance wedge conditions of Leontovich on the border «cover -- free space» are satisfied. Angular diagrams of wedge waves for different values of cover thickness are obtained. Radar Cross Section (RCS) diagrams of PEC cylinder with cover are presented.

In two-dimensional problems, the physical theory of diffraction (PTD) is valid for both electromagnetic and acoustic waves. This chapter presents the theoretical fundamentals for acoustic and electromagnetic waves. To complete formulation of the diffraction problem and ensure the uniqueness of its solution, the wave equation and boundary conditions are supplemented by the Sommerfeld radiation condition for the scattered field. The high-frequency physical optics (PO) approach is widely used in acoustic and electromagnetic diffraction problems. Among the properties of the shadow radiation, the most significant are the shadow contour theorem and the total power of shadow radiation, which are verified for acoustic and electromagnetic waves, in the chapter. Taking into account the diffraction and nonuniform components of surface fields, PTD overcomes the PO shortcomings and provides more accurate asymptotic results for high-frequency scattered fields.

In this paper the 3-D mathematical formulation and study for the simulation of the radio-propagation mechanisms in urban cellular environments are presented. The proposed methods and techniques are applicable to the 3-D radiocoverage prediction model, currently being developed by the authors' research group. In the far field area, the proposed analysis is based on the well-known deterministic methods of Physical Optics (PO) and Physical Theory of Diffraction (PTD). In the near field and Fresnel zone, a novel and time-efficient technique for the computation of the scattered and diffracted field is applied. Emphasis is also given to the time efficiency of the proposed approach since the high simulation time is one of the most important drawbacks of such radio-propagation prediction codes.

The paper presents various methods for the calculation of the field reflected from a subreflector in a dual reflector antenna system. It is demonstrated that the physical-optics (PO) solution agrees well with the geometrical theory of diffraction (GTD) for the copolar component. Significant discrepancies may appear for the crosspolar component, and it is necessary to introduce additional fringe currents in the PO solution. If the subreflector is located in the near field of the feed, special precautions must be taken. One can either subdivide the feed aperture into a number of smaller subapertures for each of which standard GTD can be applied or an alternative and more efficient method is to use complex ray analysis (CRA), where the directive feed is represented by a point source located in the complex co-ordinate space. Both methods are compared with PO solutions taking the near-field effects into account. The theoretical results are verified experimentally for a near-field illuminated offset hyperboloidal subreflector.

At radar frequencies, asymptotic techniques such as physical optics and the physical diffraction theory can be used for radar cross section prediction of the scattering from a material coated body of arbitrary shape. A physical optics formulation for a wide class of shapes is presented for use with the impedance surface model for lossy materials. Appropriate polarization dependence is incorporated. Both the monostatic and bistatic cases are considered through a uniform treatment of the radiation integrals. >

Based on the conventional split-step Fourier transform(SSFT),the recursive two-way parabolic equation(TWPE) modeling is presented for the problems of former algorithms' deficiencies and computational error.The traditional algorithms forecast only forward-propagating waves and neglect the backward-propagating waves,which causes greater error in the presence of irregular terrain boundary environment.The new algorithm enhances the computation accuracy and remedies the insufficiencies by the recursive two-way split-step method.Compared to traditional wide-angle parabolic equation(WAPE) and geometrical theory of diffraction(GTD),the correctness and applicability of the model are verified by simulation results in the complex environment including single knife-edge,double knife-edges and real terrain.

In this article, we compare deterministic methodologies for characterizing channel behavior in heterogeneous and composite scenarios. These techniques include one that combines a 3D ray launching (RL) approach based on geometrical optics (GO), a second based on GO and the uniform theory of diffraction (UTD), and another that includes a diffusion equation (DE) method based on the equation of transfer. A new methodology based on the GO and DE is presented and shown to achieve accurate results when compared with real measurements. The proposed technique provides a computational time reduction of up to 90% compared to the conventional approach using GO with the UTD and DE.

A design method for an offset-fed, dual reflector antenna (Cassegrain type or Gregorian type) system with an axisymmetric main reflector is presented. Geometrical optics (GO) and the geometrical theory of diffraction (GTD) are used to find the surface-current density on the main reflector. A modified Jacobi-Bessel series (JBS) method is used to find the far-field pattern for the physical optics (PO) integral. In the defocused mode of operation, a new technique is developed to find the reflection point on the subreflector corresponding to the defocused feed and a general field point on the main reflector. Two sample systems are designed.