The low frequency scalar diffraction by an elliptic disc

1967 ◽  
Vol 63 (4) ◽  
pp. 1273-1280 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Scattered Field ◽  
Low Frequency ◽  
Field Amplitude ◽  
Wave Number ◽  
Series Expansions ◽  
Far Field ◽  
Scalar Diffraction ◽  
Scattering Cross

SummaryThe problem of scalar Dirichlet diffraction of a plane wave by an elliptic disc is discussed. A scheme is given whereby the low frequency expansion of the scattered field may be readily obtained. Series expansions are obtained for the far-field amplitude up to and including the second order in the wave number. The first two terms of the scattering cross-section are also derived.

LOW-FREQUENCY ACOUSTIC SCATTERING BY AN INHOMOGENEOUS MEDIUM

2005 ◽  
Vol 15 (10) ◽  
pp. 1459-1468 ◽  
Author(s):  
GEORGE VENKOV
Keyword(s):  
Refractive Index ◽  
Plane Wave ◽  
Inhomogeneous Medium ◽  
Acoustic Waves ◽  
Spherical Wave ◽  
Low Frequency ◽  
Far Field ◽  
Scattering Medium ◽  
Wave Incidence ◽  
Plane Wave Incidence

This paper deals with the scattering of time-harmonic acoustic waves by inhomogeneous medium. We study the problem to recover the near and the far field using a priori information about the refractive index and the support of inhomogeneity. The incident spherical wave is modified in such a way as to recover the plane wave incidence when the source point approaches infinity. Applying the low-frequency expansions, the scattering medium problem is reduced to a sequence of potential problems for the approximation coefficients in the presence of a monopole singularity located at the source of incidence. Complete expansions for the integral representation formula in the near field as well as for the scattering amplitude in the far field are provided. The method is applied to the case of a spherical region of inhomogeneity and a radial dependent refractive index. As the point singularity tends to infinity, the relative results recover the scattering medium problem for plane wave incidence.

Modification of scattering of waves by central loading

1968 ◽  
Vol 46 (24) ◽  
pp. 2755-2763 ◽  
Author(s):  
Chin-Lin Chen
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Cross Sections ◽  
Normal Incidence ◽  
Physical Explanation ◽  
Lumped Element ◽  
Scattering Cross ◽  
Back Scattering ◽  
Conducting Wire ◽  
Scattering Cross Sections

The problem of the scattering of a plane wave by a long, thin, perfectly conducting wire is studied. The scatterer is loaded at its center by a lumped element. The effects of the loading on the scattering of waves are investigated. Numerical results are obtained for the case of normal incidence. The results show that for relatively short wires, the back-scattering cross sections may be modified effectively by central loading, while for longer wires, the modification is rather difficult to achieve. To nullify the back-scattering cross section completely, it is necessary to use active loading if kh > 3.6. A physical explanation is also presented.

SCALAR DIFFRACTION BY A PROLATE SPHEROID AT LOW FREQUENCIES

1960 ◽  
Vol 38 (12) ◽  
pp. 1632-1641 ◽  
Author(s):  
T. B. A. Senior
Keyword(s):  
Exact Solution ◽  
Plane Wave ◽  
Oblate Spheroid ◽  
Prolate Spheroid ◽  
Wave Number ◽  
Scalar Problem ◽  
Low Frequencies ◽  
Scalar Diffraction

For the scalar problem of the diffraction of a plane wave by a prolate spheroid the exact solution is known, and by expanding this in ascending powers of ka, where k is the wave number and 2a is the interfocal distance, the Rayleigh series for both the "soft" and "hard" bodies are obtained up to and including terms in (ka)6. The corresponding results for an oblate spheroid can be deduced by a trivial change of parameters. Some particular cases are examined.

SCATTERING BY A NARROW UNIDIRECTIONALLY CONDUCTING INFINITE STRIP

1960 ◽  
Vol 38 (12) ◽  
pp. 1623-1631 ◽  
Author(s):  
S. R. Seshadri
Keyword(s):  
Integral Equation ◽  
Electromagnetic Wave ◽  
Cross Section ◽  
Plane Electromagnetic Wave ◽  
Scattering Cross Section ◽  
Wave Number ◽  
Infinite Strip ◽  
Total Scattering ◽  
Scattering Cross ◽  
Total Scattering Cross Section

The scattering of a plane electromagnetic wave of wave number k by a uni-directionally conducting infinite strip of width 2a is investigated, The problem is formulated in terms of an integral equation whose solution is obtained by a well-known procedure in the form of a series in powers of ka. Expressions for the far-zone fields and the first two terms in the series for the total scattering cross section are obtained.

The Acoustical Impedance at the Junction of Non-Coaxial Cylindrical Ducts

1992 ◽  
Vol 11 (4) ◽  
pp. 114-123 ◽  
Author(s):  
Keith S. Peat
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Plane Waves ◽  
Low Frequency ◽  
Evanescent Waves ◽  
Wave Analysis ◽  
Cross Sectional ◽  
Low Frequencies ◽  
Duct Systems

At low frequencies, only plane waves can continuously propagate along uniform ducts, but evanescent, non-planar waves arise from discontinuities in the duct cross-section. The effect of these evanescent waves can be considered as an acoustical impedance to the propagation of plane waves. It is then possible to increase the accuracy of low frequency plane-wave analysis of duct systems with cross-sectional discontinuities, by inclusion of these impedance corrections. This paper considers the derivation of the acoustical impedance at the junction of non-coaxial circular ducts, a common feature within silencer systems.

SCATTERING OF DIRAC PARTICLES BY GRAVITATIONAL PLANE WAVES

1995 ◽  
Vol 04 (03) ◽  
pp. 291-304 ◽  
Author(s):  
DONATO BINI ◽  
VALERIA FERRARI
Keyword(s):  
Dirac Equation ◽  
Plane Wave ◽  
Cross Section ◽  
Plane Waves ◽  
Scattering Cross Section ◽  
Bogoliubov Transformation ◽  
Dirac Particles ◽  
Scattering Cross ◽  
Complete Set

We find a complete set of solutions of the Dirac equation in the background of a gravitational plane wave. The Bogoliubov transformation relating the in and the out modes and the scattering cross-section is also derived.

BACKSCATTERING FROM A CONDUCTING CYLINDER WITH A SURROUNDING SHELL

1960 ◽  
Vol 38 (12) ◽  
pp. 1665-1676 ◽  
Author(s):  
M. A. Plonus
Keyword(s):  
Cross Section ◽  
Propagation Constant ◽  
Scattering Cross Section ◽  
Graphical Form ◽  
Far Field ◽  
Scattering Cross ◽  
Conducting Cylinder ◽  
Incident Plane ◽  
Section Versus ◽  
Field Coefficient

Far-field backscattering from a perfectly conducting cylinder with a surrounding shell has been investigated. The spacing of the shell from the cylinder and thickness of the shell are arbitrary. The material in the shell is also arbitrary and is characterized by the propagation constant h. The incident plane wave is at right angles to the cylinder, and is either horizontally or perpendicularly polarized. When the shell is thin in units of wavelength a much simpler expression for the backscattered field coefficient is obtained. It was possible to express this coefficient in a form which resembles the coefficient from the conducting cylinder alone plus a perturbation term due to the shell. Another simplification resulted when the propagation constant h of the shell is much larger than the free-space propagation constant k.It was desirable to see what scattering properties a cylinder with a surrounding shell exhibits. The cylinder was chosen to be large with respect to wavelength and the shell spaced a resonant distance from the cylinder. The scattering cross section, for this particular combination of parameters was then given by a slowly converging series which proved too lengthy for hand-computation, and was then programmed for and computed by the IBM 704. The scattering cross section versus shell spacing is shown in graphical form.

Acoustic Diffraction of a Plane Wave by Two Coplanar Parallel Perfectly Soft or Rigid Strips

1972 ◽  
Vol 50 (9) ◽  
pp. 928-939 ◽  
Author(s):  
D. L. Jain ◽  
R. P. Kanwal
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Normal Derivative ◽  
Field Amplitude ◽  
Far Field ◽  
Soft Or ◽  
Transmission Coefficients ◽  
Incident Plane ◽  
Acoustic Diffraction ◽  
Conducting Screen

The problem of diffraction of a normally incident plane acoustic wave by two parallel and coplanar infinite strips is considered. The assumed boundary conditions on the strips are the vanishing of either the total wave function or its normal derivative. Expressions are obtained for the first few terms of the series for the far-field amplitude and the scattering cross section when the wavelength is much larger than the distance between the outer edges of the strips. The corresponding results for two parallel and coplanar infinite slits in a soft or a rigid screen follow by applying Babinet's principle. This analysis also gives the transmission coefficients for the case of two infinite parallel slits in a thin conducting screen when the electric or magnetic field vectors of the incident plane monochromatic waves are polarized parallel to the edges of the slits.

scholarly journals A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 315-342
Author(s):  
Masud Mansuripur
Keyword(s):  
Cross Section ◽  
Electromagnetic Scattering ◽  
Final Section ◽  
Scattering Amplitude ◽  
Plane Waves ◽  
Homogeneous Medium ◽  
Far Field ◽  
Scalar Diffraction ◽  
Optical Cross Section ◽  
Section Theorem

AbstractStarting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

Inverse Scattering Related to Cylindrical Bodies Buried in a Lossy Circular Cylinder with Resistive Boundary

Frequenz ◽  
2019 ◽  
Vol 73 (3-4) ◽  
pp. 1-9 ◽  
Author(s):  
Tanju Yelkenci
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Cross Section ◽  
Inverse Scattering ◽  
Scattered Field ◽  
Born Approximation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Measurements ◽  
Arbitrary Cross Section

Abstract An inverse scattering problem of cylindrical bodies of arbitrary cross section buried in a circular cylinder with resistive boundary is presented. The reconstruction is obtained from the scattered field measurements for a plane wave illumination under the Born approximation. Illustrative examples are presented in order to see the applicability of the method as well as to see the effects of some parameters on the solution.

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