Geometrical Theory Of Diffraction Solution Research Articles

On Special Functions for Radiation From Sources Close to an Electrically Large Convex Surface

Several high frequency asymptotic methods in electromagnetics include Fock-type functions. Acoustic hard and soft Fock functions are used as special functions in asymptotic solutions for radiation from sources on an electrically large conducting convex surface. Formulations are available for accurate evaluation of these functions. Asymptotic solutions for radiation from sources close to an electrically large conducting convex surface include the derivatives of these Fock functions as well. However, the existing formulations for the functions do not yield accurate and continuous results for their derivatives. In this letter, the existing formulations are modified to adjust the boundaries between separate intervals for efficient and accurate evaluation of the Fock functions and their derivatives, and to assess continuity across the boundaries for different numbers of terms. The modified formulations are used in the extended uniform geometrical theory of diffraction solution to predict the radiation pattern of a quarter wavelength monopole antenna, which is validated in comparison with the results of the multilevel fast multipole method (MLFMM).

The spectral functions method for acoustic wave diffraction by a stress-free wedge: Theory and validation

Non Destructive Examination (NDE) of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, backwall …) of inspected blocks. For that purpose, the study of plane wave diffraction by a wedge is of great interest. The work presented here is preliminary research to model the case of an elastic wave diffracted by a wedge in the future, for which there exist various modeling approaches but the numerical aspects have only been developed for wedge angles lower than π. The spectral functions method has previously been introduced to solve the 2D diffraction problem of an immersed elastic wedge for angles lower than π. As a first step, the spectral functions method has been developed here for the diffraction on an acoustic wave by a stress-free wedge, in 2D and for any wedge angle, before studying the elastic wave diffraction from a wedge. In this method, the solution to the diffraction problem is expressed in terms of two unknown functions called the spectral functions. These functions are computed semi-analytically, meaning that they are the sum of two terms. One of them is determined exactly and the other is approached numerically, using a collocation method. A successful numerical validation of the method for all wedge angles is proposed, by comparison with the GTD (Geometrical Theory of Diffraction) solution derived from the exact Sommerfeld integral.

A Uniform Asymptotic Solution for Whispering Gallery Mode Radiation from a Cylindrically Curved Concave Conducting Surface

When a cylindrically curved concave conducting surface is terminated abruptly at the edge, the whispering gallery (WG) mode propagating toward the edge direction is radiated into the free space from the aperture plane at the edge. In this paper, by applying the new analysis method, we shall derive a uniform geometrical theory of diffraction solution (UTD) for the electric-type WG mode radiation field applicable in the transition region near the geometrical boundaries produced by the incident modal ray on the edge of the curved surface. The UTD is represented by the summation of the solution for the geometrical ray converted from the modal ray of the WG mode and the solution for the uniform edge diffracted ray scattered at the cylindrically curved edge. By comparing with the reference solution obtained numerically from the integral representation of the radiation field, we will confirm the validity and the utility of the UTD proposed in this paper.

Attenuation of waves behind a building

A physical-optics (PO) solution is proposed for the diffraction of waves around a model building. The model building is constructed of two rectangular diffracting screens with reflecting surfaces joining the edges of the two screens. The solution can be expressed in terms of the well known attenuation function for two infinitely wide diffracting screens, applied several times. A comparison is made with previous work on the same subject, and it is found that the PO solution agrees with a simpler PO solution if paraxial theory is used, but it agrees with a uniform version of the geometrical theory of diffraction solution if a wide-angle correction is applied. A contour plot of field amplitude at a constant height reveals an interference pattern between the wave arriving over the roof and the wave arriving around the walls.

Extended uniform geometrical theory of diffraction solution for the radiation by antennas located close to an arbitrary, smooth, perfectly conducting, convex surface

In this paper, the uniform geometrical theory of diffraction (UTD) based field expressions developed previously [Pathak et al., 1981] for predicting the radiation from antennas which are flush mounted directly on an arbitrary, smooth, perfectly conducting, convex surface are extended to allow the antennas to be raised slightly above the convex surface. This extension thus allows an efficient ray analysis of many practical antenna structures such as blade antennas or pod‐mounted antennas on convex surfaces or even antennas near convex cylindrical masts, etc. This extended UTD (EUTD) is developed such that it employs the same ray paths and retains the same simplicity and efficiency as the earlier UTD radiation solution [Pathak et al., 1981]. Furthermore, if the antenna is moved directly onto the surface, then the EUTD solution developed here automatically reduces to the earlier UTD solution. Numerical results based on EUTD are presented for antennas close to smooth, curved surfaces; in some of these cases, impressed sources of radiation are oriented so that they would produce no radiation if they were moved directly onto the surface.

Comparison of different order GTD solutions of double-edge diffraction problem

A second order diffraction coefficient for the uniform geometrical theory of diffraction (GTD) is obtained explicitly for two knife edges in terms of the usual complex transition function (a modified Fresnel integral). The results from conventional GTD (zero order), slope diffraction GTD (first order), and second order GTD are compared with those obtained from physical optics (PO), which uses the complex Fresnel double integral. The results from second order GTD are close to those from PO in most of the cases studied.

A generalized uniform geometrical theory of diffraction ray solution for the diffraction by a wedge with convex faces

An approximate asymptotic high‐frequency solution is obtained for the electromagnetic wave diffraction by a wedge with convex faces and a moderate wedge angle. The present solution properly includes the edge‐excited surface ray effect and can predict the transition between the space ray and the surface ray. This solution is uniform across the various ray shadow boundaries even when the transition regions associated with these ray shadow boundaries overlap and is expressed in the simple format of the geometrical theory of diffraction. The ansatz for the present solution is based on a uniform solution for the scattering from a curved screen obtained earlier by C.W. Chuang and M.C. Liang, used in conjunction with an asymptotic matching technique. Numerical results based on the present uniform geometrical theory of diffraction solution are found to be in excellent agreement with those based on an independent moment method solution of the exact integral equation.

Analysis of Electrically Small Hyperbolic Subreflectors Utilizing the Geometrical Theory of Diffraction

Cassegrain antennas have been utilized in applications where small size is critical. It has been observed that for antennas having subreflectors of the order of only several λ in diameter, near-in sidelobe levels rise beyond normally predicted values. E-plane sidelobes are often several dB higher than those in the H-plane. Disturbances in the illumination of the primary reflector due to diffraction limitations of the electrically small subreflector are a possible cause of the sidelobe phenomenon. In this work, the results for 3 to 8 λ -diameter hyperboloidal subreflectors, using the geometrical theory of diffraction (GTD) are presented and compared with the physical optics approach and other data. Degradation of the scatter patterns are observed as the subreflector size is decreased, and the differences in the E-and H-plane phase and amplitude patterns are observed in the GTD solution.

Plane Wave Diffraction by a Strip:Exact and Asymptotic Solutions*

High-frequency diffraction by a strip was previously analyzed approximately by the Geometrical Theory of Diffraction (GTD), but the GTD solution has an essential difficulty that it is valid only in the limited range of incidence and observation angles. To overcome this difficulty, in this paper, plane wave diffraction by a strip is reconsidered using the Wiener-Hopf technique and the complete high-frequency asymptotic solution is obtained, which is uniformly valid everywhere in space and has no restrictions on incidence and observation angles. Further asymptotic expansion is also carried out to derive the non-uniform asymptotic solution, which is compared with the previous GTD solution. As a result, some discrepancies are recognized.

Electromagnetic plane wave diffraction by a planar junction of two thin dielectric/ferrite half planes

A uniform geometrical theory of diffraction solution is developed for the two‐dimensional problem of high‐frequency plane wave diffraction by a planar junction of two thin dielectric/ferrite half planes. Each material half plane in this two‐part configuration is assumed to be electrically thin so that it can be replaced in the analysis by a generalized resistive boundary condition of 0(t), where t is the corresponding material slab thickness. The solution obtained is based on the Wiener‐Hopf technique, and it is shown that the present boundary value problem can be completely solved by imposing a junction condition at the junction of the two dielectric half planes in addition to the boundary and radiation conditions as well as the usual edge condition. This junction condition can be obtained if the field near the junction is modeled by a quasi‐static solution. The solution developed here can be further specialized to limiting cases for which either of the material half planes can become free space, perfectly conducting, or purely resistive, respectively. Several numerical examples are presented, and it is shown that the present solution reduces to known results and agrees very well with a moment method solution.

High-frequency electromagnetic scattering of plane waves from double wedges

The application of a high-frequency solution for the field doubly diffracted in the far zone from a pair of parallel wedges illuminated by a plane wave is described. It is shown how a spectral extension of the uniform geometrical theory of diffraction (GTD) is used to obtain closed-form expressions for the field that are valid at any incidence and observation aspects. These expressions exhibit the proper discontinuities and singularities so that they can be suitably combined with the other singly diffracted fields to provide a uniformly valid ray description of the scattering in the far zone by an obstacle which is illuminated by a plane wave. They smoothly reduce both to those derived by directly applying the uniform GTD solution for single diffraction augmented by slope diffraction and to those recently obtained for grazing illumination of the edges, in their respective regions of validity. The solutions to the scalar problems are then used to construct a dyadic diffraction coefficient for the doubly diffracted field in the ray-fixed coordinate system. Examples of triangular cylinders are considered, and numerical results are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A study of three techniques used in the diffraction analysis of shaped dual-reflector antennas

An examination is presented of three techniques used for the efficient computation of fields diffracted by a subreflector that has been shaped by geometrical optics synthesis. It is found that these techniques, which are based on the geometrical theory of diffraction (GTD), produce errors in the computed fields that are specific to shaped reflectors. These errors are examined for a reflector system shaped to produce maximum gain from a tapered feed illumination. The discrepancies are directly related to the caustic being located near an observation point of the GTD calculations. The errors found are localized, and they increase in magnitude as the caustic approaches the main reflector. In a general offset geometry, the location of the caustic may be located arbitrarily close to the main reflector given a prescribed output aperture distribution. For the specific case considered here-the common situation of shaping to produce maximum gain-the caustic is located near the edge of the main reflector and on the reflection shadow boundary. A local correction is derived which creates a uniform solution through the caustic and across the reflection shadow boundary. Away from this point the calculation recedes to the standard GTD solution. >

The backscattered field of a thin wire loop for H-polarization

For a thin wire loop illuminated by a plane electromagnetic wave, the backscattered field is determined when the incident magnetic vector is parallel to the plane of the loop. The complete second-order geometrical theory of diffraction (GTD) solution is obtained and found to be in excellent agreement with numerical data at angles close to normal incidence on the loop. At wide angles, however, the data exhibit a significant lobe that is not predicted by GTD. Analysis of the data shows that the lobe is due to currents circulating around the loop and the properties of these currents are deduced. Using a simple model for the current, the corresponding contribution to the backscattered field is determined. When this is added to the GTD solution, the resulting expression for the backscattered field is in good agreement with the numerical data for all angles of incidence and all loop diameters greater than a wavelength.

A uniform GTD solution for the far-field scattering by polygonal cylinders and strips

The results of our recent asymptotic treatment of the double diffraction by a pair of parallel perfectly conducting wedges are applied to polygonal cylinders and strips. The combination of the appropriate nonuniform expression for the doubly diffracted ray field with the nonuniform geometrical theory of diffraction (GTD) expressions for the singly diffracted fields yields a uniform, closed-form solution for the far scattered field valid throughout the overlapping transition regions. The advantage over the existing uniform GTD solution for a polygonal cylinder consists in the extension from strictly grazing to nearly grazing incidence. For a strip, the present solution improves upon the accuracy of the previous uniform high-frequency solutions.

Scattering by a thick impedance half plane

In this paper we consider the scattering by a thick impedance half plane in the situation of a normally incident plane wave. The solution is based on the angular spectrum method in connection with the generalized scattering matrix formulation (GSMF) and as such it closely follows a parallel formulation applied recently in the diffraction analysis of the perfectly conducting thick half plane. Essentially, the angular spectrum method is first used to obtain the diffraction, coupling, reflection and radiation (or launching) coefficients relating to a pair of thin parallel impedance half planes which are then employed in the GSMF. The coefficients follow after an approximate solution of the resulting coupled dual integral equations which are derived in terms of the electric and magnetic current spectra. Several backscatter patterns are presented and compared with corresponding patterns based on the geometrical theory of diffraction (GTD) and a numerical model. It is found that a combination of the simple GTD solution and the present results give an acceptable solution for the diffraction by impedance half planes of almost any thickness.

High frequency scattering by a thin lossless dielectric slab

A high frequency solution for scattering from a thin dielectric slab is developed, based on a modification of the uniform geometrical theory of diffraction solution for a haft-plane, with the intention of developing a model for a windshield of a small private aircraft. Results of the theory are compared with experimental measurements and moment method calculations showing good agreement. Application of the solution is also addressed.

A uniform GTD solution for the radiation from sources on a convex surface

A compact approximate asymptotic solution is developed for the field radiated by an antenna on a perfectly conducting smooth convex surface. This high-frequency solution employs the ray coordinates of the geometrical theory of diffraction (GTD). In the shadow region the field radiated by the source propagates along Keller's surface diffracted ray path, whereas in the lit region the incident field propagates along the geometrical optics ray path directly from the source to the field point. These ray fields are expressed in terms of Fock functions which reduce to the geometrical optics field in the deep lit region and remain uniformly valid across the shadow boundary transition region into the deep shadow region. Surface ray torsion, which affects the radiated field in both the shadow and transition regions, appears explicitly in the solution as a torsion factor. The radiation patterns of slots and monopoles on cylinders, cones, and spheroids calculated from this solution agree very well with measured patterns and with patterns calculated from exact solutions.

A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface

The problem of the diffraction of an arbitrary ray optical electromagnetic field by a smooth perfectly conducting convex surface is investigated. A pure ray optical solution to this problem has been developed by Keller within the framework of his geometrical theory of diffraction (GTD). However, the original GTD solution fails in the transition region adjacent to the shadow boundary where the diffracted field plays a significant role. A uniform GTD solution is developed which remains valid within the shadow boundary transition region, and which reduces to the GTD solution outside this transition region where the latter solution is valid. The construction of this uniform solution is based on an asymptotic solution obtained previously for a simpler canonical problem. The present uniform GTD solution can be conveniently and efficiently applied to many practical problems. Numerical results based on this uniform GTD solution are shown to agree very well with experiments.

An asymptotic analysis of the scattering of plane waves by a smooth convex cylinder

An approximate asymptotic high‐frequency result which is convenient for engineering applications is obtained for the field exterior to a smooth perfectly conducting convex cylinder when it is illuminated by a plane wave. This result is uniform in the sense that it remains valid within the transition regions adjacent to the shadow boundaries where the pure ray optical solution based on the geometrical theory of diffraction (GTD) fails, and it automatically reduces to the GTD solution exterior to the transition regions where the latter solution becomes valid. Furthermore, this result is expressed in the simple format of the GTD, and it employs the same ray paths as in the GTD solution. This uniform result is not valid in the close neighborhood of the cylinder; hence a separate asymptotic result is presented for this special case in a form which is also convenient for applications. The asymptotic results presented here are useful for predicting the patterns of antennas radiating in the presence of convex conducting cylindrical structures.

Solution of electromagnetic scattering and radiation problems using a spectral domain appoach–a review

In this paper we present a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.