Scalar Wave Diffraction Research Articles

Diffraction of waves by inhomogeneous obstacles

The two dimensional problem of diffraction of scalar waves by a bounded inhomogeneity in an otherwise unbounded medium is studied both theoretically and numerically. Using singular operator properties, existence and uniqueness of the solution, and the convergence of the numerical method used are proved.

The effectiveness of dampers for the analysis of exterior scalar wave diffraction by cylinders and ellipsoids

AbstractThe technique of dampers is now widely used in the numerical analysis of unbounded problems. The dampers are used to absorb the outgoing waves. This paper will consider in detail the best formulations of damper methods. Examples will be given showing the effectiveness of three different dampers, in two dimensional and three dimensional models. The geometries considered are circular and elliptical cylinders, spheres and ellipsoids. The results indicate that dampers are indeed very effective, particularly those of higher order, which have recently been developed by Bayliss et al.1,2 and others.

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.

A Modal Theory Solution to Diffraction from a Grating with Semi-circular Grooves

A modal expansion formalism is presented to solve the scalar-wave diffraction problem for a perfectly conducting reflection grating whose grooves are semi-circular in cross-section. The theory is given for both of the fundamental polarizations, together with efficiency calculations for the first-order Littrow mounting. Similarity between the results and those of other profile shapes is observed and the groove radius which produces optimum blazing performance is determined. Resonance anomalies are observed in the efficiency spectra and are attributed to complex poles in the mode amplitudes. The positions of these poles are traced as a function of groove radius.

Coupled scalar wave diffraction theory

A simple but accurate coupled-wave theory describing diffraction from a volume grating is developed, which applies to planar diffraction geometries with the electric field polarized normal to the plane of incidence. Modulation of the dielectric and the absorption properties of the medium are considered, and the analysis is developed for gratings nonuniform with depth and for composite (multiplexed) gratings. The theory is based axiomatically on Maxwell's equations, and no approximations or simplifying assumptions other than those requisite to the scalar wave formulation of the theory enter into the analysis (except that for computational applications, only a finite number of diffracted orders may be retained in the analysis).

Diffraction by two parallel slits in a plane

The diffraction of scalar waves by two parallel slits in a plane screen is examined by a method which uses orthogonal functions and Fourier transformations. A solution is obtained in the case of a perfectly soft screen. Numerical results of the plane wave transmission coefficients for normal incidence are given for k=0.2∼4.0 and D=3∼10, where k is the wavenumber and D is the distance between slits.

Reexamination of Diffraction Problem of a Slit by a Method of Fourier-Orthogonal Functions Transformation

The diffraction of scalar waves by a slit is examined by a method which uses orthogonal functions and Fourier transformations. In the case of perfectly soft screen an exact solution and the far field are obtained. Numerical results of the plane wave transmission coefficients for normal incidence are given for k =0.2∼16, where k is the wave number.

Integral-Transform Formulation of Diffraction Theory*

An exact integral-transform formulation of the theory of the diffraction of monochromatic scalar waves from an infinite plane boundary with known boundary values is developed from first principles. The formulation is analogous to the Fourier-transform formulation of Fraunhofer diffraction, except that it is exact and is valid for both Fresnel and Fraunhofer diffraction. The known wavefunction on the boundary is expanded into a linear superposition of point-convergence patterns. The point-convergence pattern is defined as the pattern of the wavefunction that must exist on the boundary in order to produce a Dirac delta-function distribution of the wavefunction on a plane of observation that is parallel to the boundary. This pattern is described by a point-convergence function h determined by the position of the delta-function singularity on the plane of observation and the distance of that plane from the boundary. The point-convergence function is orthogonal to a function g called the point-divergence function. Together, g and h serve as kernels for a new integral transform called the diffraction transform. The pattern of the wavefunction on the plane of observation is the diffraction transform of the wavefunction on the boundary. We show that g represents the field of a dipole while h cannot be expressed by an ordinary function and must be defined as a functional. Successive diffraction transformations are discussed, and the transform formulation of Fraunhofer diffraction is obtained as a special case from the diffraction-transform theory.

Diffraction of a high-frequency plane electromagnetic wave by a perfectly conducting circular disc

AbstractA method already developed for the diffraction of scalar waves by a circular disc is generalized so as to be applicable to the diffraction of an electromagnetic wave. The generalization leads, in a straightforward manner, to an asymptotic development of the current density on the disc at high frequencies. The principal complication which arises is in solving three simultaneous linear equations for three constants which occur in the method of solution. Detailed calculations are given for a normally incident plane wave.

Diffraction of Spherical Scalar and Vector Waves at Axial Points of a Circular Aperture and Disk

The following work treats Kottler's saltus problem of diffraction of electromagnetic waves emitted by a Hertzian oscillator source and the analogous Kirchhoff's scalar problem of waves emitted by a point source. The medium is a homogeneous isotropic dielectric. In the vector case a new exact solution of the basic integrals is presented, at axial points only, (a) behind a circular aperture in a ``black'' screen, and (b) behind its complementary ``black'' disk. The relative time-averaged intensity of energy flow is plotted for the disk only. It is shown that the scalar theory predicts considerably larger values than the electromagnetic theory for identical geometrical dispositions.

Diffraction of scalar waves by a circular aperture. II

Communications on Pure and Applied MathematicsVolume 15, Issue 1 p. 1-33 Article Diffraction of scalar waves by a circular aperture. II J. Bazer, J. BazerSearch for more papers by this authorH. Hochstadt, H. HochstadtSearch for more papers by this author J. Bazer, J. BazerSearch for more papers by this authorH. Hochstadt, H. HochstadtSearch for more papers by this author First published: 1962 https://doi.org/10.1002/cpa.3160150101Citations: 12AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume15, Issue11962Pages 1-33 RelatedInformation

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Comments on "Diffraction of scalar waves by a circular aperture"

Some remarks on "Diffraction of scalar waves by a circular aperture"

Some remarks on "Diffraction of scalar waves by a circular aperture"

Transient Diffraction of Scalar Waves by a Fixed Sphere

Diffraction from a fixed sphere is treated as an initial value problem rather than as a boundary value problem. By requiring only boundedness of the diffracted wave potential rather than the stronger Sommerfeld radiation condition, it is shown via use of the Laplace transform and complete inversion integral that the diffracted wave potential consists of the usual steady-state term plus transient terms. The magnitude of the transient terms are governed by β = ka where a is the radius of the sphere and k is the wave number; however, the rate of decay is governed by the dimensionless decay parameter ωt. Both Dirichlet and Neumann boundary conditions are discussed in detail. Finally, the transient force on the sphere is computed in the Neumann case and the behavior examined for the long-wave (β≪1) and short-wave (β≫1) approximations.

Diffraction of scalar waves by a circular aperture

The problems of the diffraction of scalar waves by a circular aperture in a perfectly soft, and in a perfectly rigid, infinite, planar screen are treated. New integral representations of the solution are presented which have the virtue of automatically satisfying the time-reduced wave equation, the radiation condition and the boundary conditions. The unknown functions appearing in these representations are shown to satisfy Fredholm-type integral equations of the second kind which yield, after iteration, accurate, approximate solutions when ka (the product of the wave number and the aperture radius) is sufficiently small. These approximate solutions are in turn employed to calculate the aperture fields, the far fields, the transmission coefficients, and the edge behaviors. The results are in complete agreement with known results and for some of these quantities they are more accurate in that higher powers of ka are included. Finally, in the case of the rigid screen problem, for all values of ka , we determine the form of the edge behavior and give a simple proof of the unique existence of the solution.

Diffraction by a Wide Slit

The problem of diffraction of scalar waves by an infinite conducting plane with a slit is investigated. Approximate expressions for the near and far fields, taking into account the interaction between the edges, are derived in terms of the well-known solutions for the field produced when an isolated conducting half-plane is excited by (a) a plane wave, and (b) a line source. Results of numerical calculation are given for the case of a plane wave normally incident on the slit. Twelve values of slit width ranging from 0.96 to 2.5 wavelengths are considered. A comparison of transmission coefficients is given. It is found that the new approximate solution agrees well with the exact solution, and provides a significant correction to the noninteraction solution. The accuracy increases with the slit width, so that the result is useful in the range where interaction cannot well be neglected but where the exact solution converges so slowly that computation is impracticable.

Diffraction of Spherical Scalar Waves by an Infinite Half-Plane

A theoretical discussion of the problem of diffraction of spherical scalar waves incident upon a thin black infinite half-plane, which makes use of Maggi’s transformation, has previously appeared in the literature. However, previous treatments have been limited solely to the diffracted component. From the results of previous investigators a simple expression for the total energy distribution, which is suitable for computational purposes, is derived. The results are shown to reduce to Kirchhoff’s formulation of the same problem, for field points not far removed from the shadow-boundary-plane. A rapid approximation method, applicable to the cases of plane and cylindrical waves, is also given. Experimental results were obtained from a photometer employing a refrigerated multiplier phototube. It is shown that the theoretical and experimental intensity distributions agree only when the radius of the point source aperture becomes indefinitely small. Tests with metallic and nonmetallic screens indicate that the nature of the edge of the diffracting screen (for points far removed from the screen) is of minor importance. Possibly of somewhat greater significance, but yet minor, is the nature of the body of the diffracting screen, a metallic screen tending to displace the fringes toward the shadow-boundary-plane.