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RECIPROCITY RELATIONS FOR A CONDUCTIVE SCATTERER WITH A CHIRAL CORE IN QUASI-STATIC FORM

Part of: Optics, electromagnetic theory - General Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  03 July 2018

C. E. ATHANASIADIS Open the ORCID record for C. E. ATHANASIADIS [Opens in a new window] ,
E. S. ATHANASIADOU Open the ORCID record for E. S. ATHANASIADOU [Opens in a new window]  and
S. DIMITROULA Open the ORCID record for S. DIMITROULA [Opens in a new window]
C. E. ATHANASIADIS*
Affiliation:
Department of Mathematics, Office 231, Panepistimiopolis 15784, Zografoy, Athens, Greece email cathan@math.uoa.gr, eathan@math.uoa.gr, sodimitr@math.uoa.gr
E. S. ATHANASIADOU
Affiliation:
Department of Mathematics, Office 231, Panepistimiopolis 15784, Zografoy, Athens, Greece email cathan@math.uoa.gr, eathan@math.uoa.gr, sodimitr@math.uoa.gr
S. DIMITROULA
Affiliation:
Department of Mathematics, Office 231, Panepistimiopolis 15784, Zografoy, Athens, Greece email cathan@math.uoa.gr, eathan@math.uoa.gr, sodimitr@math.uoa.gr
*
✉cathan@math.uoa.gr
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Abstract

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We analyse a scattering problem of electromagnetic waves by a bounded chiral conductive obstacle, which is surrounded by a dielectric, via the quasi-stationary approximation for the Maxwell equations. We prove the reciprocity relations for incident plane and spherical electric waves upon the scatterer. Mixed reciprocity relations have also been proved for a plane wave and a spherical wave. In the case of spherical waves, the point sources are located either inside or outside the scatterer. These relations are used to study the inverse scattering problems.

Keywords

conductive chiralspherical wavereciprocity relations

MSC classification

Primary: 35Q60: PDEs in connection with optics and electromagnetic theory
Secondary: 78A45: Diffraction, scattering
Type
Research Article
Information
The ANZIAM Journal , Volume 60 , Issue 1 , July 2018 , pp. 86 - 94
Copyright
© 2018 Australian Mathematical Society 

References

Angell, T. S. and Kirsch, A., “The conductive boundary condition for Maxwell’s equations”, SIAM J. Appl. Math. 52 (1992) 1597–1610; doi:10.1137/0152092.Google Scholar
Athanasiadis, C., Martin, P., Spyropoulos, A. and Stratis, I. G., “Scattering relations for point source: acoustic and electromagnetic waves”, J. Math. Phys. 43 (2002) 5683–5697; doi:10.1063/1.1509089.Google Scholar
Athanasiadis, C., Martin, P. and Stratis, I. G., “Electromagnetic scattering by a homogeneous chiral obstacle: scattering relations and the far-field operator”, Math. Methods Appl. Sci. 22 (1999) 1175–1188; doi:10.1002/(SICI)1099-1476(19990925)22:14 <1175::AID-MMA60 >3.0.CO;2-T .3.0.CO;2-T+.>Google Scholar
Athanasiadis, C. and Stratis, I. G., “The conductive transmission problem for a chiral scatterer”, Electromagn. Waves Electron. Syst. 2 (1997) 71–79.Google Scholar
Athanasiadis, C. and Tsitsas, N. L., “Radiation relations for electromagnetic excitation of a layered chiral medium by an interior dipole”, J. Math. Phys. 49 (2008); 013510-1; doi:10.1063/1.2834920.Google Scholar
Colton, D. and Kress, R., “Eigenvalues of the far field operator and inverse scattering theory”, SIAM J. Math. Anal. 26 (1995) 601–615; doi:10.1137/S0036141093249468.Google Scholar
Flapan, E., “When topology meets chemistry: a topological look at molecular chirality”, SIAM Rev. 43 (2001) 577–579; http://www.jstor.org/stable/3649818.Google Scholar
Hettlich, F., “Uniqueness of the inverse conductive scattering problem for time-harmonic electromagnetic waves”, SIAM J. Appl. Math. 56 (1996) 588–601;doi:10.1137/S003613999427382X.Google Scholar
Kirsch, A. and Kleefeld, A., “The factorization method for a conductive boundary condition”, J. Integral Equations Appl. 24 (2012) 575–601; doi:10.1216/JIE-2012-24-4-575.Google Scholar
Lakhtakia, A., Beltrami fields in chiral media (World Scientific, Singapore, 1994).Google Scholar
Liu, X., Zhang, B. and Hu, G., “Uniqueness in the inverse scattering problem in a piecewise homogeneous medium”, Inverse Problems 26 (2009) 015002; doi:10.1088/0266-5611/26/1/015002.Google Scholar
Potthast, R., “Point-sources and multipoles in inverse-scattering theory”, in: Research notes in mathematics series, Volume 427 (Chapman and Hall/CRC Press, Boca Raton, FL, 2001).Google Scholar
Tsitsas, N. L. and Athanasiadis, C. E., “On the interior acoustic and electromagnetic excitation of a layered scatterer with a resistive or conductive core”, Bull. Greek Math. Soc. 54 (2007) 127–141; http://bulletin.math.uoc.gr/vol/54/54-127-141.pdf.Google Scholar