Abstract
We derive the effective permeability and permittivity of a nanostructured metallicphotonic crystal by analysing the complex reflection and transmission coefficientsfor slabs of various thicknesses. These quantities were calculated using the transfermatrix method. Our results indicate that these structures could be used to realizea negative effective permeability, at least up to infrared frequencies. Theorigin of the negative permeability is a resonance due to the internalinductance and capacitance of the structure. We also present an analyticmodel for the effective permeability of the crystal. The model revealsthe importance of the inertial inductance due to the finite mass of theelectrons in the metal. We find that this contribution to the inductancehas implications for the design of metallic magnetic structures in theoptical region of the spectrum. We show that the magnetic activity in thestructure is accompanied by the concentration of the incident field energy intovery small volumes within the structure. This property will allow us toconsiderably enhance non-linear effects with minute quantities of material.
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