Homogenization near resonances and artificial magnetism from dielectrics

Abstract

The homogenization of periodic dielectric structures in harmonic regime usually leads to an effective permittivity tensor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mi>ɛ</mml:mi> <mml:mi mathvariant="normal">eff</mml:mi> </mml:msup> </mml:math> . It has been observed by Bouchitté and Felbacq [Waves Random Media 7 (1997) 245–256], that in the high contrast case (high conductivity fibers), this tensor depends on the angular frequency ω . In this Note, we enlight a new effect induced by microscopic resonances which leads in parallel to a possibly negative effective permeability <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mi>μ</mml:mi> <mml:mi mathvariant="normal">eff</mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> (although the original medium is assumed to be nonmagnetic i.e. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>μ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> ).