Magneto-optical response of a periodic metallic nano-structure

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When an applied magnetic field has an arbitrary direction with respect to the lattice axes of a periodically nano-structured metal-dielectric metamaterial, the macroscopic or bulk effective permittivity tensor becomes anisotropic and all its components can be nonzero. This effect can be especially strong and significant in the vicinity of surface plasmon and cyclotron resonances (the frequencies of which are also sensitive to the value and direction of the applied external magnetic field). A similar effect for the case of dc effective conductivity is already verified experimentally (since magneto-conductivity tensor can be measured directly). However, this prediction for the permittivity has not yet been tested experimentally (since the permittivity tensor cannot be measured directly). What can be measured directly is the Voigt rotation, for which general exact analytical expressions were not published previously. In this work we have studied analytically and numerically the rotation and ellipticity of polarization of the light propagating through a metamaterial film with periodic nanostructure for arbitrary direction of the applied static magnetic field, including both Voigt and Faraday configurations. In the Voigt configuration we found a strong dependence of the above mentioned effects on the direction of the applied magnetic field.