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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 25, Issue 4


Born non-scattering electromagnetic media

Tilo Arens / John Sylvester
Published Online: 2016-09-30 | DOI: https://doi.org/10.1515/jiip-2016-0054


We consider the propagation of electromagnetic waves in an anisotropic medium. A local perturbation of the vacuum media that does not produce a detectable change in the far field is called non-scattering. Through testing by plane waves, we derive a variational equation characterizing non-scattering perturbations of permittivities and permeabilities to first order, i.e. in the Born approximation. We show that these perturbations can be characterized exactly by four functions. Three of these functions correspond to linearizations of known non-scattering media constructed by diffeomorphisms in transformation optics. The role of the fourth function is not yet understood, although some analytic properties can be derived.

Keywords: Maxwell equations; non-scattering media; Born approximation

MSC 2010: 35R30; 78A46


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About the article

Received: 2016-08-29

Accepted: 2016-09-14

Published Online: 2016-09-30

Published in Print: 2017-08-01

Funding Source: Deutscher Akademischer Austauschdienst

Award identifier / Grant number: D/08/11863

Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1309362

Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: CRC 1173

Initial work on this paper was supported by the German Academic Exchange Service (DAAD) under grant D/08/11863. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173. This research was partially supported by NFS grant DMS-1309362.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 25, Issue 4, Pages 469–481, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2016-0054.

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