GTD solution with higher order terms to the diffraction by an edge: Towards a uniform solution

A UTD solution for an edge of a perfectly conducting wedge is presented which includes terms of order higher than the ordinary UTD. The problem is studied for three special cases: (i) plane and (ii) spherical wave incidence on a straight wedge with planar surfaces, and (iii) cylindrical wave incidence on a wedge with surfaces curved in the direction normal to the edge. This solution not only compensates the jump discontinuities in the GO field but also the discontinuities in the derivative. The solution found is exact for the special case of a plane wave incident on a halfplane. The solution with the higher order terms is found to be accurate when the large parameter is reduced by a factor of two as compared with the ordinary UTD solution

MUTUAL COUPLING EFFECTS OF FINITE RECTANGULAR PHASED-ARRAYS

A rigorous integral equation formulation for the analysis of a phased array of flangemounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of ihtegrd equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The blockToeplitr symmetry property for the uniformly spaced linear and rectangular grid arrays is utilized in the solution of the system of equations

Two alternative expressions for the spherical wave expansion of the time domain scalar free-space Green's function and an application: Scattering by a soft sphere

The importance of expanding Green's functions, particularly free-space Green's functions, in terms of orthogonal wave functions is practically self-evident when frequency domain scattering problems are of interest. With the relatively recent and widespread interest in time domain scattering problems, similar expansions of Green's functions are expected to be useful in the time domain. In this paper, two alternative expressions, expanded in terms of orthogonal spherical wave functions, for the free-space time domain scalar Green's functions are presented. Although the two expressions are equivalent, one of them is seen to be more convenient for the calculation of the scattered field for a known equivalent source density, whereas the second expression is more suitable for setting up an integral equation for the equivalent source density. Such an integral equation may be setup, for example, by the application of a time domain equivalent of the T-matrix (extended boundary condition) method. (C) 1997 Acoustical Society of America

AN EXTENSION OF THE PHYSICAL THEORY OF DIFFRACTION CONCEPT FOR APERTURE RADIATION PROBLEMS

A correction to the Kirchhoff-Huygens approximation in the format of a diffraction coefficient is derived for an aperture terminated by a half plane. As in the physical theory of diffraction (PTD), this is achieved by considering the end point contribution to the aperture integral. It is seen that when the aperture is taken as conformal with the surface of the half plane, the conventional PTD result is obtained

Near-field scanning in the time domain on a spherical surface - A formulation using the free-space Green's function

Two formulations for determining the characteristics of an unknown source of acoustic waves using the measurement of its field at its near zone are presented. The measurement in both cases is to be performed on a spherical scan surface which encapsulates the source. The first is for an ideal probe which measures the field at its location. The knowledge of the field is sufficient; its normal derivative is not required. In the second formulation a realistic probe is considered. This time it is required only that the probe has an axially symmetric receiving characteristic. With this formulation, the time functions which characterize the source are found using only the signal at the output of the probe. Both formulations are such that they are not specific to the scan surface radius. Furthermore, they are entirely in the time domain, requiring no inverse Fourier transformations left to be performed. (C) 2001 Acoustical Society of America

Spherical wave expansion of the time-domain free-space Dyadic Green's function

The importance of expanding Green's functions, particularly free-space Green's functions in terms of orthogonal wave functions is practically self-evident when frequency domain scattering problems are of interest. With the relatively recent and widespread interest in time-domain scattering problems, similar expansions of Green's functions are expected to be useful in the time-domain. In this paper, an expression, expanded in terms of orthogonal spherical vector wave functions, for the time-domain free-space dyadic Green's function is presented and scattering by a perfectly conducting sphere is studied as an application to check numerically the validity and to demonstrate the utility of this expression