Nonlinear focusing of terahertz laser beam using a layered superconductor

We theoretically study the propagation of a terahertz (THz) Gaussian beam through a thin sample of layered superconductor. We consider the beam axis and the superconducting layers to be perpendicular to the sample interface, while the electric field in the beam is perpendicular to the layers. We show that, in such a geometry, the Josephson current between the superconducting layers supports lensing of the beam instead of divergence on the Rayleigh range. Moreover, due to the nonlinearity, the focal length and waist of the transmitted beam depend on the incident beam intensity. These dependencies demonstrate nontrivial hysteresis behavior that can be observed in experiments with THz lasers.