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

## K-REx Repository

 dc.contributor.author Ramm, Alexander G. dc.date.accessioned 2015-10-23T15:53:21Z dc.date.available 2015-10-23T15:53:21Z dc.identifier.uri http://hdl.handle.net/2097/20482 dc.description.abstract 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 a2−κ, where κ ∈ [0,1) is a parameter which can be chosen by an experimenter en_US as he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha−κ, where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a3, 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 ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the small impedance particles is N(∆) ∼ 1/a2−κ∆ N(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 ∆. 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. [http://dx.doi.org/10.1063/1.4929965] dc.language.iso en_US en_US dc.publisher American Institute of Physics (AIP) en_US dc.relation.uri http://www.aip.org/ en_US dc.rights http://www.sherpa.ac.uk/romeo/issn/0022-2488/ en_US dc.title Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies en_US dc.type Article (publisher version) en_US dc.date.published 2015 en_US dc.citation.doi http://dx.doi.org/10.1063/1.4929965 en_US dc.citation.eissn 1089-7658 en_US dc.citation.epage 21 en_US dc.citation.issn 0022-2488 en_US dc.citation.jtitle Journal of Mathematical Physics en_US dc.citation.spage 1 en_US dc.citation.volume 56 en_US dc.contributor.authoreid ramm en_US
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