Magnetic activity at infrared frequencies in structured metallic photonic crystals

We derive the effective permeability and permittivity of a nanostructured metallic photonic crystal by analysing the complex reflection and transmission coefficients for slabs of various thicknesses. These quantities were calculated using the transfer matrix method. Our results indicate that these structures could be used to realize a negative effective permeability, at least up to infrared frequencies. The origin of the negative permeability is a resonance due to the internal inductance and capacitance of the structure. We also present an analytic model for the effective permeability of the crystal. The model reveals the importance of the inertial inductance due to the finite mass of the electrons in the metal. We find that this contribution to the inductance has implications for the design of metallic magnetic structures in the optical region of the spectrum. We show that the magnetic activity in the structure is accompanied by the concentration of the incident field energy into very small volumes within the structure. This property will allow us to considerably enhance non-linear effects with minute quantities of material.