Layered superconductors as nonlinear lenses for laser beams tunable by dc magnetic field

We develop a theory of focusing of a THz Gaussian laser beam by a layered superconducting slab of finite thickness in the presence of an external dc magnetic field in a nonlinear regime. We show that focusing abilities of the slab, which originate from the specific nonlinearity of the medium, can be flexibly tuned by the external magnetic field providing a way to control THz waves. We analytically study the main characteristics of the Gaussian beam transmitted through such a nonlinear lens, namely, a beam waist and a focusing distance, as functions of radiation frequency, beam intensity, and dc field magnitude. The results of analytic calculations are supported by the numerical simulation of the electromagnetic field distribution in the beam propagating through the superconducting slab.