On the singularity of the field near a dielectric wedge

Bobrovnikov, M. S.; Zamaraeva, V. P.

doi:10.1007/bf00890884

Cited by 7 publications

(3 citation statements)

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“…In addition to the spectral methods analyzed in the article, it can be the boundary integral method, the finite-difference method, the finite-element method, and etc. The examples considered here have already been investigated previously in [8,9,14]. For completeness, we present the main results for simple cases, writing out the whole series of roots of the eigenvalues , Re( ) 0 k k τ τ ≥ , taking into consideration the degree of degeneracy, which is important for the correct writing of system (12).…”

Section: Discussionmentioning

confidence: 99%

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Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

Semenikhin

2021

Journal of Computational Physics

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Section: Discussionmentioning

confidence: 99%

“…In number of simple cases the value of 1 τ can be obtained analytically [8,9], in the rest it is necessary to solve the transcendental equation numerically. In general, 1…”

Section: Introductionmentioning

confidence: 99%

Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

Semenikhin

2021

Journal of Computational Physics

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“…It was first derived by Bobrovnikov and Zamaraeva [13] using an advanced mathematical technique, but it can also be derived elementarily following the general steps outlined in [11]. Since the latter derivation method is to solve a boundary value problem, Eq.…”

Section: Singularities Of a 3-wedge Assembly A General Considerationsmentioning

confidence: 99%

Field singularities at lossless metal–dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings

Li¹

2012

J. Opt. Soc. Am. A

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I extend a previous work [J. Opt. Soc. Am. A, 738 (2011)] on field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings to the case of arbitrary metallic wedge angles. Simple criteria are given that allow one knowing the lossless permittivities and the arbitrary wedge angles to determine if the electric field at the edges is nonsingular, can be regularly singular, or can be irregularly singular without calculating the singularity exponent. Furthermore, the knowledge of the singularity type enables one to predict immediately if a numerical method that uses Fourier expansions of the transverse electric field components at the edges will converge or not without making any numerical tests. All conclusions of the previous work about the general relationships between field singularities, Fourier representation of singular fields, and convergence of numerical methods for modeling lossless metal-dielectric gratings have been reconfirmed.

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Field Behaviour Near a Dielectric Edge

Andersen¹,

Solodukhov²

MTT-S International Microwave Symposium Digest

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On the singularity of the field near a dielectric wedge

Cited by 7 publications

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Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

Field singularities at lossless metal–dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings

Field Behaviour Near a Dielectric Edge

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