# Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies

## K-REx Repository

 dc.contributor.author Ramm, Alexander G. dc.date.accessioned 2016-04-06T15:03:24Z dc.date.available 2016-04-06T15:03:24Z dc.identifier.uri http://hdl.handle.net/2097/32340 dc.description Citation: Ramm, A. G. (2015). Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies. Journal of Mathematical Physics, 56(9), 21. doi:10.1063/1.4929965 dc.description A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a -> 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a(2-k), where k epsilon [0,1) is a parameter which can be chosen by an experimenter as he/she wants. The boundary impedance of a small particle is assumed to be of the form zeta = ha(-k), where h = const, Reh >= 0. The scattering amplitude for a small perfectly conducting particle is proportional to a(3), and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a << d << lambda, where d is the minimal distance between neighboring particles and lambda is the wavelength. The distribution law for the small impedance particles is N(Delta) similar to 1/a(2-k) integral N-Delta(x) dx as a -> 0. Here, N(x) >= 0 is an arbitrary continuous function that can be chosen by the experimenter and N(.) is the number of particles in an arbitrary sub-domain Delta. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a -> 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. (C) 2015 AIP Publishing LLC. dc.relation.uri https://doi.org/10.1063/1.4929965 dc.rights Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Ramm, A.G., Journal of Mathematical Physics, Vol. 56, 091901 (2015) and may be found at https://doi.org/10.1063/1.4929965. dc.rights.uri http://www.sherpa.ac.uk/romeo/issn/0022-2488/ dc.subject Physics dc.title Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies dc.type Article dc.date.published 2015 dc.citation.doi 10.1063/1.4929965 dc.citation.issn 0022-2488 dc.citation.issue 9 dc.citation.jtitle Journal of Mathematical Physics dc.citation.spage 21 dc.citation.volume 56 dc.contributor.authoreid ramm
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