Diffraction Of Plane Research Articles

Low-energy electron current image diffraction (CID) of the basal plane of titanium

Abstract The basal plane of titanium has been studied by low-energy electron current image diffraction. Using a simple model, the average inner potential and surface interlayer distance were deduced from Bragg scattering features in the diffraction patterns which were obtained from a series of photographs of crystal surface images obtained at various primary beam energies. Computed geometric changes of Bragg scattering as a function of angle of incidence are presented for the energy range 0–200 eV. It is suggested that an energy monochromator incorporated in the electron gun would improve the pattern resolution and bring out energy sensitive lines which are not observed under the present conditions. Image enhancement methods would also increase the precision of the measurements.

Diffraction of plane polarized waves on a noncircular cavity

Diffraction of plane polarized waves on a noncircular cavity

On the asymptotic diffraction of scalar waves by a wedge

The diffraction of plane, cylindrical and spherical waves by a wedge is considered. Particular emphasis is placed on finding accurate and simple asymptotic field expansions which are valid in the transition regions as well as in the far field. The accuracy of previous diffraction coefficients for cylindrical and spherical waves is discussed and a more accurate derivation is presented. A new simple rational approximation of the resulting Fresnel integral is given and its special character is demonstrated.

Photoelastic investigation of stress wave diffraction about stationary crack-tips

Transient phenomena of reflection and diffraction of explosively-generated plane and cylindrical elastic waves at the tips of a finite crack buried at some depth below a free surface are investigated. Dynamic photoelasticity has been used as a means for visualizing the highly complex interaction process between stress waves and cracks. Primary and secondary diffraction are studied and sequences of isochromatic fringe patterns and their associated wave front reconstruction patterns are presented. Fracture mechanics aspects of dynamic crack initiation under stress wave loading are discussed.

Problem of constructing wide-band acoustooptic deflectors

A numerical calculation was made of the efficiency of the Bragg diffraction of plane and diverging light waves by a planar multielement equidistant piezoelectric-transducer array. A comparison was made of the characteristics of scanners with multielement arrays and with a single planar transducer. It was found that the acoustic wave intensity required to achieve efficient diffraction in a given frequency band is several times less for a sectioned transducer than for a single transducer.

Scattering and diffraction of plane P waves by circular cylindrical canyons with variable depth-to-width ratio

The scattering and diffraction of plane (P) waves by a circular canyon with variable width-to-depth ratio has been studied in this paper. Series of Bessel function expansions have been used to solve the problem. To illustrate the results, the surface displacement amplitudes and phases are presented. The following parameters are found to affect the results: 1. The angle of incidence, θα. 2. The ratio of the canyon depth to canyon width, h/a, 3. The dimensionless frequency of the incident P wave, η and 4. The Poisson's ratio, ν. The displacement amplitudes and phases on the ground surface show significant deviation from those of the uniform half-space motions, especially at high frequencies, when the wavelengths of the incident and scattered waves are small compared to the size of the canyon.

Numerical study of diffraction of plane elastic waves by a finite crack with application to location of a magma lens

abstractLocation, shape, and size of near-surface heterogeneities in the Earth may be determined by active or passive seismic diffraction experiments. An array of geophones would be set up to record near-field wave motion resulting from diffraction by the inhomogeneity. As an example of such inhomogeneities, we study the diffraction of plane P and S waves by a finite two-dimensional crack as a function of wavelength and direction of incident wave. We develop a method which can be used to solve for diffraction effects by empty and fluid-filled (zero viscosity) cracks. The magnitude of the effect of the fluid in the crack is governed by a parameter called the crack stiffness factor which is the ratio of bulk modulus of the fluid in the crack to the rigidity of the solid divided by the crack aspect ratio.The diffraction problem is solved using the finite difference scheme developed by Madariaga (1976) to study dynamic crack propagation problems. It is found that a crack has little effect on wave motion for incident wave with wavelengths greater than 10 times the crack length. For wavelengths less than 5 times the crack length there is a complicated diffraction pattern. The amplitude and phase of both components of motion are affected by the crack. We find that the diffraction effect decreases as the crack stiffness factor increases. For wavelengths less than 2 times the crack length there is a region of reduced amplitude (shadow zone) behind an empty crack. Relative phase of two components of particle motion varies rapidly with position inside the shadow zone.The results of the theoretical calculation are used to try to locate the edge of a magma lens in Kilauea Iki Crater, Hawaii. It is found that the ratio of vertical-to-horizontal displacement and the direction of rotation of initial particle motion measured by a seismic array located on the floor of the crater agree qualitatively with what the theory predicts. The edge of the magma found by this method shows excellent agreement with the one inferred from the distribution of seismic events originating in the crust of the lava lake (Aki et al., 1977).

The Love wave scattering matrix for a continental margin (theoretical)

In this paper, we use the method of integral representation and Schwinger-Levine variational principle to describe, by means of a scattering matrix, the diffraction of plane, harmonic, monochromatic Love waves, incident normally (from either side) upon the plane of discontinuity in a structure consisting of a half-space with a surface step — an idealized model of a continental margin. Approximate expressions for the elements of the scattering matrix are obtained through the plane-wave approximation and their variational improvement is sought through the Schwinger—Levine variational principle. Complex reflection and transmission coefficients can be obtained through a transmission matrix related to the scattering matrix. We obtain the form of the transmission matrix (under both approximations) in some simple cases.

Diffraction of plane electromagnetic wave from arrays of conducting rectangular cylinders

The boundary value problem of diffraction of parallel and perpendicular polarised waves from gratings of conducting rectangular cylinders is solved by a rigorous mode-expansion formulation and numerical solution. Comparison of computed results with the limited theoretical and experimental results available in the literature demonstrates the accuracy of the numerical method. Further numerical results inducate the usefulness of these gratings for a variety of applications, and provide additional information on the physical phenomena which cause the unexpected transmission and reflection properties. Such results are also of considerable value in serving as standards to which various approximate solutions may be compared for accuracy and interpretation.

Diffraction by a grating of cylinders with an arbitrary cross-section

The diffraction of a monochromatic plane electromagnetic wave by a grating consisting of parallel, electrically perfectly conducting cylinders is investigated. Two separate two-dimensional scalar problems are dealt with viz. the case ofE-polarization and the case ofH-polarization. A new Green's function formulation of the problem is employed leading to integral equations for the unknown field distributions on an elementary scatterer of the grating. Numerical results are presented for a grating of cylinders with either square or circular cross-section.

Diffraction of a plane electromagnetic wave by arrays consisting of circular cylinders having a spiral slit

Diffraction of a plane electromagnetic wave by arrays consisting of circular cylinders having a spiral slit

Diffraction by a wide unidirectionally conducting strip

The diffraction of a plane electromagnetic wave by an infinitely long, unidirectionally conducting strip is formulated as a Wiener–Hopf integral equation and is solved asymptotically for a wide strip by transform techniques. In addition to the diffracted fields produced by a perfectly conducting strip, surface-wave excitation and scattering at the edges and interaction between the ends of the lines of conductivity appear in the solution. These effects are illustrated by numerical results of the scattering cross section at normal incidence for various directions of conductivity.

A Diffraction Problem and Crack Propagation

The exact solution to the problem of diffraction of plane harmonic polarized shear waves by a half-plane crack extending under antiplane strain is constructed. The solution is employed to study the nature of the stress field associated with an extending crack in an elastic medium excited by stress waves.

A method for computing<tex>E</tex>-plane patterns of horn antennas

This paper introduces a method for calculating the total antenna pattern in the E plane, including the backlobe region, of a horn by applying diffraction theory. Treatment of diffraction by a thick edge permits horns of various edge thicknesses to be treated. The diffraction concepts developed by Sommerfeld and Pauli, which treated plane wave diffraction by a wedge, are extended so that diffraction of plane and cylindrical waves by thin or thick edges may be treated. The diffracted fields are obtained by applying the relations developed by Pauli in conjunction with reciprocity. When the theory is applied to the horn, the significant radiation mechanisms are direct radiation from the source at the horn apex and diffracted radiation due to the edges. The computed E -plane patterns of a horn antenna agree with measured patterns.

Diffraction of a plane hydro-acoustic wave at a crack in an elastic plate

Diffraction of a plane hydro-acoustic wave at a crack in an elastic plate

Diffraction by a thick semi-infinite plate

The form of the exact solution for the diffraction of a two-dimensional plane harmonic wave by a semi-infinite plate of thickness d is found. The solution involves constants which satisfy an infinite set of equations, and these equations are solved when d is small compared with the wave-length. It is shown that, in the neighbourhood of the shadow, the field is that of a single semi-infinite plane occupying the nearer face of the plate, whatever d , if terms of O ( R -½ ) are neglected, R being the distance of the point of observation from the edge. It is further shown that, when d is less than wave-length/10, the plate behaves as a semi-infinite wave-guide whose sides project beyond the end of the plate by an amount 0.11 d together with, when the plane of polarization of the incident wave is perpendicular to the plate, a two-dimensional magnetic dipole at the end of the guide. When terms of O(kd) can be neglected, it appears from this result and Hanson’s (1930) work on a plate with a cycloidal end that the exact shape of the end of the plate is of no importance; the plate behaves as a semi-infinite wave-guide. The extension of the theory to the diffraction by a thick plate of finite length is briefly discussed. The theory is also extended to incident scalar waves whose direction of propagation does not lie in the plane perpendicular to the plate and, from this, the field due to an incident electromagnetic wave is deduced. It is found that, for all values of d , the diffracted electromagnetic wave at any point is effectively travelling along a cone of semi-angle Ɵ 0 and axis the nearer edge, where Ɵ 0 is the angle between the edge and the direction of propagation of the incident wave. When d is small compared with the wave-length the plate acts as two parallel planes together with a line of magnetic dipoles at the end of the planes.