On the role of the geometrical optics field in aperture diffraction

The asymptotic solution of a high-frequency electromagnetic field transmitted through a finite aperture is studied. In applying Keller's geometrical theory of diffraction (GTD), a basic yet unanswered question for an observation point in the lit region is: "Should the geometrical optics field on a direct incident ray be included in the total field solution?" By studying a test problem and utilizing the newly developed uniform asymptotic theory (UAT), we have deduced simple and explicit rules for the role of the geometrical optics field and the regions of validity for GTD in a general aperture diffraction. The rules reveal that the success of GTD in treating aperture problems in the literature depends critically on the assumption that both the source and the observation points are infinitely far away from the aperture. Had either point been a finite distance away, Keller's GTD, in general, would fail and UAT must be used. The paper also demonstrates a physical phenomenon: the diffusion of the incident field as the observation point moves away from the aperture.     

A uniform asymptotic theory of electromagnetic diffraction by a curved wedge

Diffraction of an arbitrary electromagnetic optical field by a conducting curved wedge is considered. The diffracted field according to Keller's geometrical theory of diffraction (GTD) can be expressed in a particularly simple form by making use of rotations of the incident and reflected fields about the edge. In this manner only a single scalar diffraction coefficient is involved. Near to shadow boundaries where the GTD solution is not valid, a uniform theory based on the Ansatz of Lewis, Boersma, and Ahluwalia is described. The dominant terms, to the order ofk^{-1/2}included, are used to compute the field exactly on the shadow boundaries. In contrast with the uniform theory of Kouyoumjian and Pathak, some extra terms occur: one depends on the edge curvature and wedge angle; another on the angular rate of change of the incident or reflected field at the point of observation.     

Slope diffraction and its application to horns

The first order geometrical theory of diffraction (GTD) predicts vanishing fields along the surface of a conducting wedge for the incident electric field polarized parallel to the diffracting edge. The slope diffraction coefficient is a valid correction term for incidence angles removed from the shadow boundary. A new slope diffraction function for the half plane is presented along with applications. This new form of slope diffraction coefficient for the half plane is valid through the shadow region. Reciprocity is invoked to find the far-fields for a source on the surface of the conducting wedge. In addition to applying the two-dimensional slope diffraction analysis to practical problems, the equivalent current concepts have been extended to include equivalent slope currents for the analysis of either finite or curved edges. This new form of the slope diffraction function has been successfully used to provide anH-plane horn pattern analysis that is considerably less tedious than previously possible with GTD. Both pure GTD solutions and hybrid solutions using conventional aperture integration for the main beam region and GTD for the far-out side and back lobes are compared with experimental results.     

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.     

Output coupling for closely confined Pb1-xSnxTe double-heterostructure lasers

The output coupling of an idealized, symmetric model of a double-heterostructure (DH) laser is analyzed theoretically using parameters suitable to Pb1-xSnxTe. For the TEOmode incident at the laser mirror and for thin optical guiding regions such that only the TEO, TE1, TMO, and TM1modes may propagate, an exact formulation of the coupling problem is obtained including mode coupling at the mirror into the continuum of unguided radiation modes. Using this formulation, the power reflection and transmission coefficients, the fraction of incident power coupled into the radiation modes, the mirror illumination, and the far-field pattern are calculated for typical parameters. Significant mode coupling can occur, limiting the maximum external efficiency of such lasers. This and other potentially undesirable characteristics resulting from close optical confinement, such as large output beam divergence, must be considered in design criteria for DH structures in this alloy system.     

On the GTD scattering by a polygonal cylinder

Using Keller's geometrical theory of diffraction (GTD) the field diffracted by a wedge is infinite at the shadow and reflection boundaries. In general, uniform diffraction coefficients must be used to provide continuous fields at these boundaries. In this communication it is shown that by properly adding the singular contributions from a pair of adjacent edges, Keller's diffraction coefficients yield a continuous far-zone field at the reflection boundaries of a polygonal cylinder illuminated by a plane wave. Furthermore the procedure is justified by noting that the uniform diffraction coefficients reduce to the Keller diffraction coefficients for this case.     

A hybrid technique for analyzing wire antennas in the presence of a plane interface

A hybrid technique which combines the method of moments (MM) with ray methods is employed to analyze the radiation of wires in the presence of a plane interface. In this technique, which is an extension of that proposed for combining the MM with the uniform geometrical theory of diffraction (GTD), a piecewise sinusoid (PWS) Galerkin method formulation is used. In this paper the basic assumption is made that a PWS dipole can be replaced by three sources of transverse, spherical waves, so that their fields can be treated separately by standard ray methods. Via this procedure the MM matrix can be easily augmented to account for the wire-interface interactions. Calculations of the field both radiated in the antenna half-space and transmitted through a plane interface are found in very good agreement with those performed by using the rigorous Sommerfeld integral representation. These results show that this technique provides an accuracy which is widely acceptable in most engineering applications, even when the wire is placed very close to the interface. This approach, which employs ray methods to calculate reflected and transmitted field contributions, appears promising to treat the case of curved interfaces.     

Efficient calculation of the fields of a dipole radiating above an impedance surface

The classic problem of field computation for an infinitesimal dipole radiating above an impedance half-space is revisited. The expressions for the traditional solution consist of integrals of the Sommerfeld type that cannot be evaluated in closed form and due to their highly oscillatory nature are difficult to evaluate numerically. A method known as exact image theory, which has previously been applied to vertical electric and magnetic dipoles, is used to derive explicit expressions for dipoles of arbitrary orientation above impedance surfaces. Starting from the spectral representation of the field, the reflection coefficients are cast in the form of exact Laplace transforms and then by changing the order of integrations field expressions in terms of rapidly converging integrals are obtained. These expressions are exact, and valid for any arbitrary source alignment or observation position. It is shown that the formulation for a horizontal dipole contains an image in the conjugate complex plane resulting in a diverging exponential term not previously addressed in the literature. It is shown through further mathematical manipulations, that the diverging term is a contribution of the mirror image which can be extracted. Comparison of numerical results from exact image theory and the original Sommerfeld-type expressions shows good agreement as well as a speedup in computation time of many orders of magnitude, which depends on the distance between the transmitter and the receiver. This formulation can effectively replace the approximate asymptotic expressions used for predicting wave propagation over a smooth planar ground (having different regions of validity). The exact image formulation is also of practical use in evaluation of the Green's function for various applications in scattering problems where approximate solutions are not sufficient.     

Interaction of electromagnetic waves with general bianisotropicslabs

An efficient, elegant, and systematic formulation technique which, combining Fourier transform with matrix analysis methods, is suitable for problems related to radiation by dipole or other sources in the presence of an arbitrarily general stratified anisotropic medium has been recently developed. This technique is adapted further extended to allow the presence of general bianisotropic media described by four tensors with no limitations on their elements. Two specific applications pertaining to some canonical problems of fundamental importance are included to exemplify the method and demonstrate its usefulness: radiation by an arbitrarily oriented elementary electric dipole source located in the vicinity of a general bianisotropic slab, either grounded or ungrounded, leading to the expressions of the dyadic Green's function of the structure, and reflection and transmission of an arbitrarily polarized plane wave incident upon such a slab, leading to closed-form concise expressions for the reflection and transmission coefficient matrices     

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 alternative diffraction coefficient for the wedge

A geometrical theory of diffraction (GTD) interpretation of a uniform solution for the wedge given by Mohsen is given. The diffraction coefficients are equal to those given by Kouyoumjian and Pathak except that the Fresnel argument in the two solutions are different. This uniform geometrical theory of diffraction (UTD) result is compared with exact series expansions for a plane wave incident on a90degwedge.     

Analyzing electromagnetic pulse coupling by combining TLT, MoM, andGTD/UTD

An important problem in electromagnetic compatibility (EMC) analysis is to determine the coupling of an electromagnetic field into a shielded cable. Using the transmission line theory (TLT), the disturbance voltage induced inside the cable is easily calculated from the current distribution on its shield. This current distribution depends on the incident electromagnetic field and is efficiently determined by the method of moments (MoM). Extending the MoM with the geometrical and uniform theory of diffraction (GTD/UTD) makes it possible to solve scattering problems that are too large and too complex for the plain MoM. The combination of the three approaches-TLT, MoM, and GTD/UTD-allows calculation of the disturbance voltage inside a shielded cable, which is part of a complex scattering structure. The fundamentals of each method and the way of putting them together are shown in this paper. The application of the proposed method is demonstrated by an example: the pulse coupling between a monopole antenna and a shielded cable is analyzed, taking into account a large conducting structure in the vicinity     

Dipole radiation over an inhomogeneous thin sheet

A general Sommerfeld integral formulation is given for the electromagnetic (EM) fields of an oscillating vertical magnetic or electric dipole over an electrically inhomogeneous thin sheet. The electrical properties of the sheet are characterized by a conductance function that is an arbitrary function of spatial coordinates. When the conductance function has axial symmetry relative to the source dipole, the general solution form simplifies to a Fredholm integral equation of the third kind. The general solution is shown to reduce to the special case of an infinite sheet having uniform conductance. When the sheet conductance is either uniform or varies linearly, the field expressions show an algebraic dependence on the conductance. For a general inhomogeneous conductance distribution, the field dependence is not algebraic     

A hybrid asymptotic solution for the scattering by a pair ofparallel perfectly conducting wedges

The overlapping transition regions of the double diffraction by a pair of parallel wedge edges are considered for the hybrid case where the gap between the edges is small compared to the distances from the source and the observation point (plane-wave-far-field limit) and the scatterer as a whole is large (or infinite). A closed-form asymptotic solution for the scattered field continuous at all angles of incidence and scattering is constructed for this case. The peculiar feature of this solution is a hybrid representation of the field singly diffracted by the first wedge: a part of it is described by a nonuniform, geometrical theory of diffraction (GTD) expression, while the other part is described in terms of the uniform theory of diffraction (UTD). The rest of the diffracted ray fields are described by nonuniform expressions, with singularities mutually canceling on summation. This solution is applied to the scattering by a perfectly conducting rectangular cylinder with appropriate geometrical parameters, and agreement with moment method calculation is demonstrated     

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.     

High frequency fields in the presence of a curved dielectric interface

A high-frequency line source in a dielectric medium that is separated by a concave cylindrical boundary from an exterior medium with lower dielectric constant generates a variety of wave phenomena which have been explored extensively. This problem is reexamined here with a view toward clarifying relevant reflection and transmission characteristics within the framework of ray optics, with emphasis on the more complicated transmitted field. The exterior domain is divided into illuminated and shadow regions separated by the transmitted tangent ray launched by a ray incident at the critical angle. Conventional ray optics is valid far from the tangent ray shadow boundary on the illuminated side. The shadow boundary is surrounded by transition regions wherein Fock type integrals and Weber functions yielding local lateral waves provide alternative representations. On the shadow side, not too far from the shadow boundary, the field can be interpreted via "tunneling" and subsequent radiation along a ray from a virtual caustic to the observer. The tunneling is associated with the initial evanescent decay of the transmitted field excited by a totally reflected incident ray. However, deeper inside the shadow, this mechanism is inapplicable, and the field is expressed either in terms of the Fock integrals or a creeping wave-type residue series. The results are presented in a format that permits insertion into a geometrical theory of diffraction (GTD) user's manual.     

A study of three techniques used in the diffraction analysis ofshaped 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     

Radiation properties of a flanged parallel-plate waveguide loadedwith an ε-μ general anisotropic slab

In this analysis, the excitation is taken to be either (1) the lowest-order transverse electric (TE) or the lowest-order transverse magnetic (TM) (i.e. transverse electromagnetic) waves, or (2) a uniform, E- or H-polarized, incident plane wave. As a result of the anisotropy, cross-polarization effects are observed. The formulation of the boundary-value problem is carried out in the Fourier transform domain. Considerable contraction results by using previously developed matrix analysis techniques. In this way, a fruitful integral representation of the tangential components of the magnetic field is first derived in terms of the tangential components of the electric field at the excitation aperture. Next, and after imposing the boundary conditions at the aperture boundary surface, this representation is used as the starting point for a solution on the basis of a moment method (MM) approach using the eigenmodes as basis and weighting functions. Numerical results related to the reflection and coupling coefficients as well as the directive diagrams of the structure are presented in graphical form for various cases     

Electromagnetic waves in a suddenly created magnetized Lorentzmedium (transverse propagation)

The interaction of electromagnetic waves in a suddenly created Lorentz medium with impressed steady uniform magnetic field is considered. It was shown that for the case of the incident electric field normal to the static magnetic field, the source wave splits into six new extraordinary waves whose frequencies are different from the incident waves. Three of those six new waves are transmitted waves, and the other three are reflected waves. The dispersion relation, power transmission, and reflection coefficients are derived and discussed