THz response of High T_c Layered Superconductors from a Microscopic Approach

We studied theoretically the optical properties of a high-T_c layered superconductor material joined by identical alternating Josephson junctions at the microscopic level. The layered high-T_c superconductor is modeled as a periodic photonic crystal with a Josephson junction in the unit cell. In this inherently anisotropic material, the Josephson effect introduces a characteristic dynamical frequency, typically in the terahertz (THz) range. To describe the electromagnetic response, we solved the Maxwell equations inside the crystal taking into account not only the supercurrents due to the Cooper pair tunneling, but also the quasiparticle currents flowing parallel and perpendicular to the superconducting layers. This approach provides the dispersion relation for electromagnetic waves in the system, as well as the components of its nonlocal effective permittivity tensor. A general homogenization method which is valid beyond the long wavelength limit is applied to calculate the components of such a tensor. The homogenization approach also allows us to calculate and analyze the THz reflectance and transmissivity of a layered superconductor slab without using additional boundary conditions.