A NEGATIVE INDEX META-MATERIAL FOR MAXWELL'S EQUATIONS

作者：Lamacz A^*; Schweizer B

来源：SIAM Journal on Mathematical Analysis, 2016, 48(6): 4155-4174.

DOI：10.1137/16M1064246

• Maxwell's equations
• negative index material
• homogenization

We derive the homogenization limit for time harmonic Maxwell's equations in a periodic geometry with periodicity length eta > 0. The considered meta-material has a singular substructure: the permittivity coefficient in the inclusions scales like eta(-2) and a part of the substructure (corresponding to wires in the related experiments) occupies only a volume fraction of order eta(2); the fact that the wires are connected across the periodicity cells leads to contributions in the effective system. In the limit eta -> 0, we obtain a standard Maxwell system with a frequency dependent effective permeability mu(eff) (omega) and a frequency independent effective permittivity epsilon(eff). Our formulas for these coefficients show that both coefficients can have a negative real part, and the meta-material can act like a negative index material. The magnetic activity mu(eff) not equal 1 is obtained through dielectric resonances as in previous publications. The wires are thin enough to be magnetically invisible, but, due to their connectedness property, they contribute to the effective permittivity. This contribution can be negative due to a negative permittivity in the wires.

• 出版日期2016