Semi-infinite Array Research Articles

Amplification of bulk and surface plasmons in semiconductor superlattices

We study the amplification of bulk and surface plasmons in a type II semiconductor superlattice, which consists of a semi-infinite array of spatially separated electron and hole layers. Amplification is achieved by imposing an external drift velocity on the electrons. For drift velocities exceeding a threshold value, bulk plasmons can be amplified for an arbitrary plasmon wave vector parallel to the layers. Amplification of surface plasmons can occur only for finite wave vectors. Drift velocities required for these processes are calculated and are shown to be experimentally feasible.

Chemisorption on disordered binary alloys.

The problem of chemisorbing a hydrogen atom on a Cu-Ni or Au-Pt disordered binary alloy (DBA) is addressed. The DBA is modeled by a semi-infinite linear array of atomic sites each of which is randomly occupied by an atom of either component. The electronic properties of such a DBA are obtained via a Green's-function technique based on the coherent-potential (CP) approximation. The chemisorption process is described by the Anderson-Newns approach, which takes account of the intra-atomic electron interaction on the adatom. The chemisorption energy and the adatom charge transfer are then computed as a function of the alloy concentration. The calculations at the surface involve the solution of two coupled self-consistent equations, one being concerned with the CP on the surface atom and the other with the adatom occupancy. In the case of the Cu-Ni system, the effect of surface segregation is also investigated.

The Excitation of a Fluid-loaded Plate Stiffened by a Semi-infinite Array of Beams

The Excitation of a Fluid-loaded Plate Stiffened by a Semi-infinite Array of Beams

Electrostatic lattice sums for semi-infinite lattices

The techniques for the rapid computation of energies of three-dimensional neutral periodic assemblies of charged particles are extended to semi-infinite arrays and assemblies of ions in infinite filsm. The results will be useful for simulation of ionic movements in fast-ion conductors and dense colloidal dispersions.

Surface effects and the density of states of electrons in a semi-infinite array of identical potentials

The relationship between the surface effects and the boundary conditions of a semi-infinite array of identical potentials has been studied. It is found that the appearance of the surface states hinges on the appropriate consideration of the possible effects on atoms near the surface due to the presence of the surface. Criteria for the existence of the surface states for two specific models of the surface are obtained.

Nearfield beam patterns of exponentially shaded end-fire line arrays

A contour integration method of calculating nearfield beam patterns of continuous, exponentially shaded, end-fire line arrays is presented. Only semi-infinite arrays are considered; however, the method can be applied to arrays of finite length. Subject Classification: [43]30.85, [43]30.75; [43]25.35.

Addendum to "Mutual coupling effects in semi-infinite arrays"

Addendum to "Mutual coupling effects in semi-infinite arrays"

Mutual coupling effects in semi-infinite arrays

An analysis of mutual coupling in linear and planar uniformly spaced semi-infinite arrays is presented. The currents under arbitrary excitations at the array ports are obtained by solving an infinite order difference equation with the aid of an extension of the Wiener-Hopf factorization procedure to finite Fourier transforms. The solution for mutual coupling coefficients as well as for the active reflection coefficients in a phased semi-infinite array is expressed explicitly in terms of the active impedance in a phased infinite array. The analytical results are directly applicable to the evaluation of edge effects in large phased arrays. Numerical results for active reflection coefficients and element patterns are presented for a semi-infinite array of slots in a perfectly conducting ground plane and for a linear dipole array.

Improved Point-Matching Techniques Applied to Multi-Region Heat Transfer Problems

An analytical method is presented which extends the series solution of the Laplace and Poisson equations with irregular boundary conditions to multi-cell problems. The method employs a least-squares technique of satisfying the boundary conditions on the irregular boundaries and eliminates the use of a finite number of boundary points to satisfy these conditions. The technique is applied to the calculation of the fully developed temperature distribution of a constant-velocity fluid flowing parallel to a semi-infinite square array of circular nuclear fuel rods. The bounding wall of the array is located such that the flow area of the cell associated with the rod adjacent to the wall is different from the (equal) areas of all the other cells. The series solution is compared to a finite-difference solution for a sample case of two cells. The results for the semi-infinite array indicate that while the array temperature distribution is markedly affected by the difference in flow areas, the Nusselt numbers of the rods are relatively unaffected. Typical results are presented for a pitch-to-diameter of 1.2; the flow area of the first cell is 3.67 percent greater than the area of the other cells.

Mutual coupling effects in linear antenna arrays

The effects of mutual coupling among the array elements on the pattern and impedance characteristics of linear antenna arrays are examined. Based upon the assumption that the mutual impedance of two array elements depends only upon the separation of the elements, exact expressions are derived for the properties of infinite and semi-infinite arrays. Integral equations which describe finite arrays are derived and solved for special forms of the mutual impedance behavior and for large arrays.

Band structure calculations of low energy electron diffraction at crystal surfaces

The band structure formulation of the dynamical theory of Low Energy Electron Diffraction as proposed by Heine is considered from the point of view of actual calculations. This formulation is essentially based upon the continuous matching of the incident and reflected electron wavefunctions to the Bloch waves at the solid-vacuum interface. The equivalence to the multiple scattering formulation of McRae is illustrated by a calculation on a model crystal consisting in a semi-infinite cubic array of s-wave scatterers. The choice of this model crystal serves the two purposes of enabling quantitative comparison with the results of McRae and providing reasonable evidence that the method can be successfully applied to real situations. The multiple scattering effects and the surface wave resonance are shown to be accounted for by the formulation, in agreement with the theory of Boudreaux and Heine. In addition, the close correspondence between the band structure and the reflected intensity curves is pointed out. The application of the band structure formulation to real situations involving inelastic effects and pure surface effects is discussed.

Slow electron scattering from one-dimensional crystal models

Calculations have been made for low energy elastic scattering of electrons from several one-dimensional models of a crystal. Two forms of the surface potential have been used: the square barrier and the cutoff classical image potential. Interaction of the incident electron with the ion-cores of the “crystal” is introduced by δ-function potentials at “lattice” sites. Two models of the lattice are considered: (i) a semi-infinite array of identical δ potentials and (ii) a small finite number of δ-function of variable strength and spacing to represent limited penetration of low energy electrons. Reflection coefficients as a function of incident electron energy, i.e., ∼ 0–100 eV were calculated for all cases. The resulting curves exhibit considerable structure. Comparison is made with experimental data (i.e., slow electron reflection, electron diffraction, etc.) and other one-dimensional model calculations.

Radiation from an Infinite Array of Parallel-Plate Waveguides with Thick Walls

A semi-infinite array of parallel-plate waveguides with walls of finite thickness is excited by incident TEM modes in every waveguide identically. By proper application of the boundary conditions, two Wiener-Hopf equations are obtained which, however, cannot be solved by the standard techniques. A method originated by Jones is applied to recast these two equations so that the forms of the solutions are found. The solntions involve constants to be determined by an infinite set of linear simultaneous equations which converge absolutely. When the thickness of the walls b is small compared with the wavelength /spl lambda/, explicit solutions in the order of 0(b/ /spl lambda/) are found in very simple forms.

The long Yagi-Uda array

The King-Sandler array theory is used to analyze the excitation of a surface wave along a semi-infinite Yagi array, as well as the scattering of such a wave at the end of a semi-infinite array. A method for approximately analyzing the behavior of finite Yagi arrays is presented which involves the matching of two terminal-zone solutions for semi-infinite arrays. Before attempting to correlate the derived theory with the more rigorous array theory, an experimental study of a twenty-element Yagi array was undertaken, and all results are shown to be accurately predicted by the King-Sandler theory. An extensive set of numerical data is presented to compare wave theory with array theory, and once again the agreement is excellent. Finally, the new theory is shown to predict a certain critical point in the data at which the wave solution ceases to exist. This point is also observed to enter dramatically into the King-Sandler solution, thus providing a final contribution to the evidence which links the wave theory to the accepted King-Sandler theory.

Surface energy and configuration of inert gas crystals—I

An expression is derived for the average potential energy of a particle at any given distance above the plane face of a semi-infinite crystalline array of similar particles obeying an inverse power, pairwise additive potential function with spherical symmetry. This expression is then used with a Lennard-Jones potential function to discuss various models for the surface configuration of semi-finite crystals by comparing the minimum excess surface energy of the model with that of the undistorted half-crystal. The results indicate that the only likely distortion in the surface of the static lattice at0°K is a slight expansion normal to the surface as indicated by s huttleworth's calculations (1)

A Semi-Infinite Array of Parallel Metallic Plates of Finite Thickness for Microwave Systems

An array of parallel metallic plates of finite thickness are useful in microwave lenses. The effect of finite thickness in the idealized situation of a semi-infinite array of perfect conductivity, is treated theoretically and experimentally for normal incidence of a uniform plane wave on the plane interface separating the medium from free space. The theoretical discussion involves the approximate variational method and a procedure is given for estimating the order of magnitude of the error in the final result. It is shown that it can be advantageous to use plates of finite thickness since the reflection from the interface can be reduced from that existing for infinitely thin plates.

A general experimental method to determine the properties of artificial media at centimetre wavelengths, applied to an array of parallel metallic plates

This paper describes measurements at centimetre wavelengths (8.0–11.0cm) on a system representing a semi-infinite array of infinitely thin, perfectly conducting, metallic plates. The purpose is to illustrate a general experimental method of determining the properties of such artificial media. The parallel-plate system was chosen since, in addition to exhibiting the interface phenomena peculiar to artificial media, it is the only one for which a rigorous solution is known. The measurements were made using a parallel-strip transmission-line1 specially developed for the study of two-dimensional structures which are non-uniform transverse to the direction of propagation.