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

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.author | Ramm, Alexander G. | |

dc.contributor.authoreid | ramm | |

dc.date.accessioned | 2016-04-06T15:03:24Z | |

dc.date.available | 2016-04-06T15:03:24Z | |

dc.date.issued | 2015-09-08 | |

dc.date.published | 2015 | |

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.identifier.uri | http://hdl.handle.net/2097/32340 | |

dc.relation.uri | https://doi.org/10.1063/1.4929965 | |

dc.rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |

dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |

dc.subject | Physics | |

dc.title | Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies | |

dc.type | Article |

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