Diffraction of an Electric Polarized Wave by a Dielectric Wedge

Berntsen, Svend

doi:10.1137/0143013

Cited by 33 publications

(20 citation statements)

References 9 publications

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“…To synthesize such beams, concentric ring arrays are assuming an increasing role [4], [6]. Owing the requirements in terms of desired gain/directivity, the use of electrically-large apertures is mandatory, but standard fully-populated layouts cannot be considered [2]- [4].…”

Section: Hybrid Bcs-deterministic Approach For Sparse Concentric Ringmentioning

confidence: 99%

“…Accordingly, the UAPO solutions should be not considered as "reference", but as "approximate, reliable and user-friendly solutions" that can be of interest for the electromagnetic engineering. Other available methodologies provide approximate analytical or heuristic solutions, or attempt to solve the problem in an exact sense by combining analytical and numerical techniques to evaluate integral equations (see [6]- [18] as interesting references). The aim of this work is to determine the UAPO solutions for the diffracted field originated by an acute-angled lossless dielectric wedge in both cases of -and -polarized incident plane waves.…”

Section: Introductionmentioning

confidence: 99%

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High-Frequency Evaluation of the Field Inside and Outside an Acute-Angled Dielectric Wedge

Gennarelli

Frongillo

Riccio

2015

IEEE Trans. Antennas Propagat.

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Explicit closed form solutions are presented for the high-frequency evaluation of the electromagnetic field produced inside and outside an acute-angled lossless penetrable wedge. Both cases of -and -polarized incident plane waves are addressed in the study. The problem is tackled and solved in the framework of the uniform theory of diffraction, so that the total field at the observation point is determined by adding the geometrical optics contributions and the diffraction one. This last is obtained by performing a uniform asymptotic evaluation of the radiation integrals arising from a physical optics approximation for the equivalent electric and magnetic surface currents lying on the infinite wedge boundaries. No limitation exists on the refractive index of the structure. The accuracy of the solution is assessed by comparisons with data produced by numerical tools. The physical optics approximation gives rise to inaccuracies when using the solution at grazing incidence and in correspondence of the dielectric interfaces.

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Section: Hybrid Bcs-deterministic Approach For Sparse Concentric Ringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-Frequency Evaluation of the Field Inside and Outside an Acute-Angled Dielectric Wedge

Gennarelli

Frongillo

Riccio

2015

IEEE Trans. Antennas Propagat.

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“…The available results relevant to diffraction by wedges mainly concern impenetrable objects (see [1][2][3][4][5][6] as quoted references). For penetrable wedges, the available methodologies provide approximate analytical or heuristic solutions, or attempt to solve the problem in an exact sense by combining analytical and numerical techniques to evaluate integral equations (see [7][8][9][10][11][12][13][14][15][16][17] as interesting bibliography). Note that only a few solutions account for the presence of penetrable materials with finite conductivity [10,11,13,17].…”

Section: Introductionmentioning

confidence: 99%

Diffraction by 90° penetrable wedges with finite conductivity

Gennarelli

Riccio

2013

J. Opt. Soc. Am. A

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This study concerns the diffraction problem relevant to a plane wave normally incident with respect to a 90° wedge. A penetrable material with finite conductivity forms the structure. A high-frequency solution is here obtained by adopting a physical optics approximation for the equivalent electric and magnetic surface currents involved in the radiation integrals used to represent the fields scattered in the inner region of the wedge and the surrounding space. Uniform asymptotic evaluations of such integrals lead to closed form expressions for the diffraction coefficient in terms of the transition function of the uniform theory of diffraction and the Fresnel coefficients for the reflection and transmission mechanisms. No limitation exists on the loss tangent of the medium. Comparisons with numerical tools assess the effectiveness of the proposed solutions for the field diffracted in the inner and outer regions.

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“…Typeset by AVT&X formulation, while rendering integral equations developed [2][3][4][5][18][19][20][21][22]28,59] for finite bodies inefficient and effectively nonapplicable.…”

Section: 26 143mentioning

confidence: 99%

“…The radiation condition is invoked in both regions, ensuring uniqueness of the integral equation solution. The unboundedness of the penetrable scatterer is thusly the very feature of the physical problem that permits this 93 11 26 143Typeset by AVT&X formulation, while rendering integral equations developed [2][3][4][5][18][19][20][21][22]28,59] for finite bodies inefficient and effectively nonapplicable.To extract the physical solution from this exciting and mathematically sound formulation of the boundary value problem, we are concentrating on a creative and physicallymotivated approach to these issues:(1) Choice of a suitable basis in which to expand the surface distribution. Convergence of the solution, as well as physical interpretation and utility, is greatly enhanced through an expansion that anticipates the actual physical behavior.…”

mentioning

confidence: 99%

Penetrable Wedge Analysis

Scharstein¹,

Davis²

1993

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We can now confidently state that the pair of coupled difference equations, that arose [61] in the Kontorovich-Lebedev analysis of the actual Leontovich-boundary-condition wedge, are a more complicated and therefore inferior version of William's [7] formulae. Although the literature has concentrated on the formulation of .Maliuzhinets [6], an asymptotic evaluation of the Williams result to extract high frequency diffraction mechanisms would ultimately duplicate the work of Tiberio, et al [10], since the Williams and Maliuzhinets results are necessarily equivalent. Therefore, we will not be pursuing the physical impedance boundary wedge anymore during the remainder of this grant. INHOMOGENEOUS OR LINEARLY-VARYING IMPEDANCE BOUNDARYFelsen's 1959 (!) paper [661 presents a rather complete analysis and discussion of this curious problem that I re-discovered in 1992 [61]. A thorough dissection and understanding of Felsen's work is required before any meaningful extensions or extrapolations can be made. This has not been done to date, owing to our attention to the: as III. GENERAL PENETRABLE WEDGE 'Since our previous quarterly report of 3 August 1993, and motivated partly by the findings above for both cases of impedance boundaries, we have returned (again!) to the truly penetrable wedge scatterer. A fresh, and in retrospect, logical approach starting with a fundamental application of Green's theorem, has yielded a surface integral equation for a single unknown surface distribution. The kernel is specific to the wedge geometry; the free-space Green's function is not used. The radiation condition is invoked in both regions, ensuring uniqueness of the integral equation solution. The unboundedness of the penetrable scatterer is thusly the very feature of the physical problem that permits this 93 11 26 143Typeset by AVT&X formulation, while rendering integral equations developed [2][3][4][5][18][19][20][21][22]28,59] for finite bodies inefficient and effectively nonapplicable.To extract the physical solution from this exciting and mathematically sound formulation of the boundary value problem, we are concentrating on a creative and physicallymotivated approach to these issues:(1) Choice of a suitable basis in which to expand the surface distribution. Convergence of the solution, as well as physical interpretation and utility, is greatly enhanced through an expansion that anticipates the actual physical behavior. In this problem of a semi-infinite domain, the expected far (r --+ oo) behavior on the wedge surface should be that of the (2) Line-source excitation of the Sommerfeld half-space problem. All wave mechanisms that we can asymptotically pull out of this simpler geometry and account for in the wedge problem are valuable both computationally and conceptually. Abstract (Maximum 200 words).The continuation of this wedge scattering research is proceeding as proposed, with several significant accomplishments and findings to date. The nature of this rigorous mathematical approach to scattering problems is such that origin...

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Diffraction of an Electric Polarized Wave by a Dielectric Wedge

Cited by 33 publications

References 9 publications

High-Frequency Evaluation of the Field Inside and Outside an Acute-Angled Dielectric Wedge

High-Frequency Evaluation of the Field Inside and Outside an Acute-Angled Dielectric Wedge

Diffraction by 90° penetrable wedges with finite conductivity

Penetrable Wedge Analysis

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