Computer codes based on GTD, PTD, and on their hybridizations have been developed for prediction of high-frequency scattering from complex perfectly conducting objects. Relevant references can be found in (16), (18), and in special issues of Proc. IEEE (1989), IEEE Trans. Antennas Propag. (1989), and Annales des Telecommunications (1995), which are mentioned in the reading list. Note also the XPATCH code (based on the shooting-and-bouncing ray technique and PTD), which allows the calculation of backscattering from complex geometries. Information about this code is published in IEEE Trans. Anntennas Propagat. Magazine, 36 (1), pp. 65-69, 1994. Computer codes interfaced with graphical utilities of workstations can display three-dimensional chromatic views of scattering centers and magnitudes of their contributions to RCS. This is the end result of complicated computations. However, a part of this can be obtained without any computations. Nature can show us the location of all scattering centers if we bring a small metallized model of the scattering object into an anechoic optical chamber and illuminate the model by the light. Bright shining points (scattering centers) seen on a scattering object are exactly those from which the radar waves will be reflected toward the radar, if we look at the object from the light source direction. (The following text is taken from Ref. 16 and slightly modified.)

The locations of these points do not depend on the frequency of incident electromagnetic waves, and they are determined completely by the location of the light source (the radar), the observer, and the scattering object. These shining points obey the Fermat principle. This means that the path along the ray between the source, the reflecting point, and the observer is extremal (minimal or maximal) in comparison with similar paths corresponding to neighboring points on the object’s surface. A more detailed description of the Fermat principle is presented for example in Section 3.3.2 in Ref. 20.

Waves reflected from discrete shining points located on the smooth parts of the scattering object represent the

cos an 2a

cos cos —

n n

a P = n a2 |

1 |

2 |

When a = 0, the latter gives the RCS of a hemisphere, a = na2. The PTD backscattering RCS is determined by Eq. (19.12) in (14),

usual geometrical optics reflected rays. Waves reflected from discrete shining points located on edges, tips, and corners are diffracted rays. The farthest shining points on a smooth object, i. e., those located on the boundary between visible and invisible sides of the object, create surface diffracted rays.

As the orientation of the object is changed, the shining points move along the object. Some of them can merge with each other and create a brighter point. In this case our eyes (i. e., the radar) are located on a caustic is the envelope of merged rays.

We can also observe bright shining lines and bright shining spots on the object, which contain an infinite number of continuously distributed shining points. The important property is that the optical path through a shining point from the source to the observer is constant for all of these points. It is assumed here that the source and observer are far from the scattering object. All reflected waves from these points reach the observer with the same phase. From the mathematical point of view, each such point is a stationary point of the infinite order: the derivatives (of any higher order) of the wave phase along the shining line (or along the shining spots) are zero at these points.

Shining spots and lines located on smooth parts of the scattering surface generate powerful reflected beams (such as those radiated by reflector antennas) which represent the strongest contributors to RCS. Shining edge lines create edge- diffracted beams whose contributions can be comparable with those from ordinary reflected rays.

It is difficult to model in optics the electromagnetic properties of realistic scattering surfaces for the radar frequency band. But the optical modeling can be used to identify the scattering centers and to control them by an appropriate shaping of the scattering surface. As it is well known, one of the basic ideas of the current stealth technology is to use an appropriate body shaping and to shift all reflected beams and rays away from the directions to the radar. See, for example, Refs. 2, 16, and the radar cross-section handbooks mentioned in the reading list. Some interesting details about the development of stealth technology in the United States are presented in Refs. 26-28.

The second idea of stealth technology is traditional: to use radar absorbing materials (RAMs) and composite structures in order to reduce the intensity of reflected beams and rays. References 2, 16, 29, and radar handbooks (mentioned in the reading list) describe fundamental concepts used in the design and application of RAMs. We present here some details taken from Ref. 16. In order to use RAMs efficiently, it is necessary to place an electric (magnetic) RAM in the region where the average electric (magnetic) field is maximal. Location of these regions in the vicinity of real objects depends on many factors, such as the radar frequency, geometry, size, and electrical properties of the object, as well as properties of materials intended for absorption. Identification of such regions and optimization of the RAM parameters to minimize RCS is a very complex problem. Its solution is attainable only in some simple cases. Most of these relate to absorbing layers on an infinite metallic plane. From the physical point of view such absorbing layers can be considered as open resonators that can support eigen-oscillations. Frequencies of eigen-oscil — lations are complex quantities. Their imaginary part is responsible for the loss inside the resonator and radiation

from the resonator. It turns out that the minimal reflection from such resonators happens when the frequency of an incident wave is close to the real part of the resonator eigenfrequency.

Note that thin electric RAMs are not efficient when applied on metallic objects. This is due to the boundary condition: the tangential component of the electric field is very small on the metal surface. On the contrary, magnetic absorbing materials can be applied directly to the surface of a metallic object. This is an important advantage of magnetic materials over electric ones.

However, any RAMs (electric, magnetic, and hybrid) homogeneous in the direction parallel to the reflecting plate are not efficient for grazing incidence (в » 90°, in Fig. 5). In this case, the reflection coefficient tends to unity independently of the incident wave polarization when в ^ 90°. This is a fundamental limitation of ordinary RAMs. They do not work against grazing incident waves. That is why ordinary RAMs do not reduce forward scattering. Actually, the RAM terminology is justified only for incidence angles that are not too far from в = 0 and when the reflection coefficient is small enough.

Various geometrical and material inhomogeneities on the scattering surface can partially transform the incident wave into surface waves propagating along absorbing layers. This may be used to further reduce the RCS. However, this idea has two essential defects. First, any inhomogeneity creates an additional undesirable scattered field. Second, it is not a simple problem to design an absorbing layer that would allow the propagation of surface waves. To support surface waves with the electric vector parallel to the incidence plane, the surface impedance must be inductive. But the surface impedance must be capacitive to support surface waves with the electric vector perpendicular to the incidence plane. This means that the surface impedance, and therefore the absorbing layer, must depend on the radar polarization with respect to the incidence plane. But this plane is different at different points of the scattering surface and different at the same point when the scattering object changes its orientation with respect to radar. It is very difficult and probably impossible to design such an absorber, especially against radars with circular polarization. However, for some chosen orientations of the object and for an appropriate polarization of the incident wave, this might not be a hopeless problem.

Development of efficient hybrid techniques and computer codes to predict RCS of large complex objects with realistic materials and research efforts to overcome the above physical limitations in RCS reduction represent challenging problems for future stealth technology. One can expect that future advanced computer codes will contain as necessary constitutive components the known high-frequency techniques (such as GTD, PTD, and the Uniform Theory of Diffraction) extended for coated and composite objects. Diffraction coefficients used in these techniques can be determined by the numerical solution of appropriate canonical problems. Direct numerical methods should be used for calculation of scattering from those elements of the scattering object that cannot be treated by high-frequency methods. Diffraction interaction between the object’s elements handled by high-frequency techniques and by direct numerical methods can be described by the surface integral equations.