High Frequency Scattering by an Impenetrable Sphere

Sha, Wei E. I.; Chew, Weng Cho

doi:10.2528/pier09100102

Cited by 11 publications

(10 citation statements)

References 28 publications

(44 reference statements)

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“…The physical picture breaks down when q becomes 10 for the first intersection results. The reason of this failure can be determined if the geometrical relation between the incidence angle and the field angle, i.e., Equation (18), is plotted in Figure 16 for q values up to 10. For q = 10, the field angle starts from 180 • , monotonically increases to and crosses 360 • , then stops at 10.6 • .…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Geometrically Lit Region Analysis of the Single-Ray Debye Terms for the Transmission of a High Frequency Plane Wave Into a Double-Negative Cylinder by the Modified Watson Transformation and Debye Series Expansion

Sen¹

2013

PIER B

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Abstract-The Debye expansion integrals obtained by application of the Modified Watson Transformation and Debye series expansion to the Mie series for the high frequency plane wave transmitted into a double negative (DNG) cylinder are solved in the geometrically lit regions of the corresponding Debye series terms. The Debye series expansion is made up to the possible maximum term after which double ray field formation is first observed. Using the steepest descent method and the geometrical optics approximation, the role of the lower ray in the double-ray field formation is pointed out. For refractive indices satisfying |n| ≥ 10, it is shown that the maximum Debye series term index up to which simple single-ray tracing can be performed is bigger for a DNG cylinder than that for a DPS cylinder and the difference between the term indices increases as |n| increases.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Watson transform was first used in [15]. Some other applications can be found in the references from [16] to [18]. Debye series expansion was first used in [19].…”

Section: Introductionmentioning

confidence: 99%

Geometrically Lit Region Analysis of the Single-Ray Debye Terms for the Transmission of a High Frequency Plane Wave Into a Double-Negative Cylinder by the Modified Watson Transformation and Debye Series Expansion

Sen¹

2013

PIER B

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“…The j n ( ) and h (1) n (ρ) are spherical Bessel and Hankel functions of the first kind, respectively [18]. In Eq.…”

Section: Scattering Coefficientsmentioning

confidence: 99%

On the Scattering of Electromagnetic Waves by a Charged Sphere

Klačka¹,

Kocifaj²

2010

PIER

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Abstract-Scattering of electromagnetic radiation by a charged homogeneous spherical particle/body is treated. Theoretical solution represents a generalization of the Mie's scattering theory for electrically neutral sphere. It is shown that classical and quantum physics approaches may lead to different conclusions, as documented by numerical computations assuming various permeabilities, refractive indices, surface charges, temperatures, and other physical parameters of the spherical particles. Two discrete wavelengths (5 µm and 1 mm) of the incident radiation are considered. Optical properties of charged particles composed of absorbing and slightly absorbing materials can essentially differ. Especially, the resonance peaks typically occur when imaginary part of particle refractive index is low. The relative permeability of a material may differ from unity at large wavelengths, e.g., in microwave region. Basically, the relative permeability appears to be less important factor than the surface charge. However, the permeability can influence the scattering and extinction efficiencies, as well as the backscattering features of small particles, under some conditions.

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“…Above all, based on Equation (45) and Equation (50), we have the closed-form formula for I in Equation (14) on a triangular patch as follows:…”

Section: Highly Oscillatory Po Integral On the Triangular Patchmentioning

confidence: 99%

“…Some comprehensive numerical quadratures, such as Filon-type and Levintype methods, are developed by the aid of the asymptotic approximate expansion approach. The SDP or numerical SDP [37,45] techniques in the complex plane [1,17] is very efficient in computing highly oscillatory integrals by the steepest descent integral path deformation. Since less approximation is done compared with the traditional asymptotic expansion, the numerical SDP method opens up a hopeful way in computing PO integrals frequency independently and error controllably.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Method for Computing Highly Oscillatory Physical Optics Integral

Jiang

Chew

2012

PIER

Self Cite

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Abstract-In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes' phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are carefully studied by the numerical SDP method and complex analysis using contour deformation. Its result agrees very well with the leading terms of the traditional asymptotic expansion. Furthermore, the resonance points and vertex points contributions from the PO integral are also extracted. Compared with traditional approximate asymptotic expansion approach, our method has significantly improved the PO integral accuracy by one to two digits (10 −1 to 10 −2 ) for evaluating the PO integral. Moreover, the computation effort for the highly oscillatory integral is frequency independent. Numerical results for PO integral on the triangular patch are given to verify the proposed numerical SDP theory.

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High Frequency Scattering by an Impenetrable Sphere

Cited by 11 publications

References 28 publications

Geometrically Lit Region Analysis of the Single-Ray Debye Terms for the Transmission of a High Frequency Plane Wave Into a Double-Negative Cylinder by the Modified Watson Transformation and Debye Series Expansion

Geometrically Lit Region Analysis of the Single-Ray Debye Terms for the Transmission of a High Frequency Plane Wave Into a Double-Negative Cylinder by the Modified Watson Transformation and Debye Series Expansion

On the Scattering of Electromagnetic Waves by a Charged Sphere

An Efficient Method for Computing Highly Oscillatory Physical Optics Integral

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