Robert W. Scharstein

Mutual coupling in a slotted phased array, infinite in E-plane and finite in H-plane

The mutual admittance matrix is computed for a planar phased array of thin slots with assumed single-mode cosinusoidal aperture electric field. The array is of infinite extent in the E-plane and of finite extent in the H-plane. The H-plane excitation is arbitrary and the array is phase scanned in the E-plane. Resultant active row-port admittances and H-plane aperture distribution are in agreement with large strictly finite array calculations and with a Floquet mode infinite array model, for the example case of uniform H-plane excitation. >

The complete extension of the Biot–Tolstoy solution to the density contrast wedge with sample calculations

The Biot–Tolstoy exact time-domain solution for the three-dimensional impulse response of an impenetrable wedge is extended to accommodate the isovelocity or density-contrast wedge. Fourier transformation of the time and axial variables, along with a Kantorovich–Lebedev transform applied to the cylindrical radial coordinate, leads to a solution in terms of residue series. When the wedge angle is a rational fraction of π, the residue series can be reduced to a finite sum which is evaluated for some special cases. The total pressure field consists of geometrical acoustics contributions, as predicted by Snell’s laws, plus a modified version of the Biot–Tolstoy diffraction field.

Near-Field and Plane-Wave Electromagnetic Coupling into a Slotted Circular Cylinder: Hard or TE Polarization

An analytically tractable model is proposed in this initial study of the electromagnetic phenomena that control our ability to synthesize, by using a near-field source, the effect of plane-wave coupling through an aperture into the interior of a vehicle under test. An integral equation for the tangential electric field in the slot aperture of a perfectly conducting, infinitesimally thin-walled circular cylinder is solved using a basis set of Chebyshev polynomials that are properly weighted according to the static edge condition. The resulting matrix elements from a Galerkin procedure are computed to high precision upon extracting the logarithmic singularity of the kernel of the integral operator. Exact expressions for the matrix elements, in the form of rapidly convergent series of elementary terms, are constructed by isolating another logarithmic function of the aperture width. A minimization of the mean-square error between the true plane-wave response and that due to a near-field line-source establishes the optimal complex source strength of the near-field source

Mellin transform solution for the static line-source excitation of a dielectric wedge

An integral transform analysis of the static scattering of the two-dimensional potential radiated by a line source in the vicinity of a penetrable wedge is presented. The Mellin transform is used to derive the exact static solution to Laplaces equation for the dielectric wedge, in the form of a modal series. The important dielectric edge condition behavior is explicitly contained in this analytic solution. >

Matched asymptotic expansion for the low-frequency scattering by a semi-circular trough in a ground plane

Plane wave scattering by an electrically small circular trough cut in an infinite ground plane is solved analytically for both the TM and TE polarizations. A quasi-static solution for the inner field based upon a transformation to bipolar coordinates exploits the failure of the narrow trough to react to the detailed wave nature of the incident field and forms the starting point for the method of matched asymptotic expansions. The distant behavior of the inner field must agree with the near behavior of the outer field, which is a radiative solution of the Helmholtz equation. In addition to yielding several analytic terms of the solution in low-order powers and the logarithm of the trough wave size k/spl alpha/ the matching process provides an account of the interplay between all of the physical parameters.

Acoustic scattering from two parallel soft cylinders

The scattered field due to two parallel circular cylinders illuminated by a plane wave is formulated in terms of outgoing cylindrical waves emanating from each cylinder. Dirichlet boundary conditions are enforced on each cylindrical surface. Grafs addition theorem for cylindrical harmonics makes possible the closed-form evaluation of the coefficients in two infinite, coupled sets of linear equations for the unknown modal coefficients. Resultant far scattered fields in the frequency domain are graphed for several geometries and plane wave incidence angles. The effects of coupling between cylinders are studied via a comparison between far-field scatter computed by this accurate method and a noninteracting sum of the isolated cylinder responses.<<ETX>>

Electrostatic Excitation of a Conducting Toroid: Exact Solution and Thin-Wire Approximation

Abstract Laplaces equation is solved via separation of variables in toroidal coordinates for the electrostatic potential external to a conducting torus placed in a uniform electric field and excited by an arbitrarily located point charge. The accuracy of the static thin-wire kernel approximation in an integral equation applied to the circular loop is verified using the exact results in the limit as the toroid shrinks to a ring. An equivalent lineal charge density from the exact solution agrees remarkably well with the integral equation solution for the conducting ring. Since the singularity in the Helmholtz Greens function for the electrodynamic problem is the static singularity considered herein, the results confirm the applicability of the thin-wire kernel to the scattering and radiation problems of the circular loop.

Transient electromagnetic plane wave reflection from a dielectric slab

Reflection of a transient plane wave normally incident upon a lossless dielectric slab is analyzed via the Fourier transform. The exact expression for the time-harmonic field is used in the inverse Fourier transform to obtain the transient response to a class of exponential exciting functions. Cauchys integral theorem and the Poisson sum formula yield closed-form expressions for the unit step and impulse response functions. >

Green's function for the harmonic potential of the three-dimensional wedge transmission problem

The point-source static potential in a wedge geometry consisting of two homogeneous media is solved via the Kontorovich-Lebedev and Fourier transforms. Inverse transforms enable the solution of Laplaces equation to be expressed in terms of image contributions plus residue sums (Fourier series) of toroidal functions. As in previous wave equation solutions for isovelocity wedges, explicit expressions for the poles that are the site of the residues are exploited when the wedge angle is a rational multiple of /spl pi/.

Helmholtz decomposition of surface electric current in electromagnetic scattering problems

In view of the Helmholtz theorem of vector calculus, the surface electric current induced on a conducting body is decomposed into lamellar and solenoidal parts. The solenoidal component is derivable from the normally directed surface curl of the current, and the lamellar component is derivable from the surface divergence (or surface charge) of the current. This representation is an alternative to specifying directly the two scalar components of the surface current. The physical interpretation of the surface curl of the surface current is examined. Examples of scatterers with induced surface currents that are purely lamellar, purely solenoidal, or a combination of both components are cited. A physical feel for the nature of the surface current induced on scatterers is developed, and computational simplifications offered by the Helmholtz decomposition are examined.<<ETX>>