Scattering by a sphere

Senior, Thomas B. A.; Goodrich, Raymond F.

doi:10.1049/piee.1964.0145

Cited by 38 publications

(18 citation statements)

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“…It is found that the first term of the creeping wave varies as (ka) -•/a and it is expected, therefore, to be much smaller in amplitude than the first term of the specular return, which is independent of ka. This last statement draws much support from past experience on the study of creeping waves at high frequencies [see, e.g., Senior and Goodrich, 1964].…”

Section: Introductionsupporting

confidence: 67%

High‐Frequency Backscattering From a Perfectly Conducting Sphere Coated With a Radially Inhomogeneous Dielectric

Alexopoulos¹

1971

Radio Science

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In this paper, the backscattered electric field is derived when a plane electromagnetic wave is incident upon a perfectly conducting sphere coated with a radially inhomogeneous dielectric. The Mie series is obtained and then subjected to an asymptotic analysis that is valid for very short wave‐lengths. In particular, the first two terms for the reflected portion of the electric field are derived and the formulation for the creeping wave contribution is presented. Also, a numerical computation of the monostatic cross section is performed for various thicknesses of the coating by considering the reflected portion of the backscattered electric field. It is shown that this particular type of inhomogeneous sheath reduces considerably the monostatic cross section of the perfectly conducting sphere as its thickness increases.

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Section: Introductionsupporting

confidence: 67%

High‐Frequency Backscattering From a Perfectly Conducting Sphere Coated With a Radially Inhomogeneous Dielectric

Alexopoulos¹

1971

Radio Science

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“…(21) reduces to the asymptotic from of the exact (Mie series) solution obtained by Senior and Goodrich [8]. For a circular cylinder pg is constant and ptn becomes infinite, and Eq.…”

Section: Theorymentioning

confidence: 89%

Electromagnetic backscattering by spheroids for axial incidence

Hong

1996

Microw. Opt. Technol. Lett.

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“…This result is associated with rays incident on the sphere at a grazing angle, exciting surface waves that travel around the sphere any number of times without penetrating into the sphere, before leaving the sphere in the backward direction. Surface waves of this type are very similar to creeping waves associated with a perfectly conducting sphere [Senior and Goodrich, 1964].…”

Section: Poles For the Debye Expansionmentioning

confidence: 99%

“…However, the diffracted fields can be computed numerically to a certain degree of accuracy b.y employing Sch6be's formulas for the cylindrical functions [Sch6be, 1954]. Senior and Goodrich [1964] have investigated high-frequency scattering by a perfectly conducting sphere using a Watson transformation. The results have been shown to be in good agreement with the exact Mie results even for the resonance region ka _• 1 [Rheinstein, 1968].…”

Section: Introductionmentioning

confidence: 99%

Diffracted field computations by a series expansion

Inada¹

1975

Radio Science

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The possibility of a series expansion for the diffracted fields by a dielectric sphere or circular cylinder is considered by first expanding the Mie scattering coefficients into a geometric series (Debye expansion), and then applying a modified Watson transformation to each term of the series. The diffracted fields can then be obtained by finding poles of the D. ebye expansion, and evaluating the residues. The locations of the poles due to the Debye expansion as well as the Mie scattering coefficients themselves are discussed. Numerical values of the poles are tabulated. The diffracted field contributions associated with the first five terms of the Debye expansion are presented in the form of a radar scattering cross section. The geometrical optics contribution arising from each term of the Debye expansion is asymptotically evaluated. To compare the magnitude of a sum of the geometrical optics and diffracted field contributions, the radar scattering cross section of the total backscattered field, obtained from the exact Mie theory, is also plotted. 1. 1970]. The diffracted fields may be evaluated by a Copyright • 1975 by the American Geophysical Union. singularity expansion method. A direct application of a Watson transformation to the Mie solution results in geometrical optics and diffracted field contributions. The former can be evaluated by a saddlepoint method using a series expansion of the Mie scattering coefficients (Debye expansio.n), whereas the latter can be evaluated by the calculus of residues. The residue series thus obtained converges slowly because of the existence of many surface wave poles with a small imaginary part. The diffracted field contributions have been shown to be the dominant contributions to the total backscattered field [Inada and Plonus, 1970b]. An alternative approach is first to expand the Mie scattering coefficients into a geometric series (Debye expansion), and then apply a Watson transformation to each term of the series. Each term of the series then consists of geometrical optics and diffracted field contributions [Rubinow, 1961; Nussenzveig, 1969a, b]. Poles associated with the Debye expansion have a large imaginary part and move away from the real axis with increasing ka. This could lead to a rapidly convergent residue series. But no numerical results for the diffracted field contributions are available.In the present paper we shall investigate diffracted field contributions arising from each term of the Debye expansion in connection with the backscattering of an electromagnetic plane wave by a dielectric sphere. Numerical computations were performed for 205 206 HITOSHI INADA

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Scattering by a sphere

Cited by 38 publications

References 1 publication

High‐Frequency Backscattering From a Perfectly Conducting Sphere Coated With a Radially Inhomogeneous Dielectric

High‐Frequency Backscattering From a Perfectly Conducting Sphere Coated With a Radially Inhomogeneous Dielectric

Electromagnetic backscattering by spheroids for axial incidence

Diffracted field computations by a series expansion

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