Nonlinear microwave response of clean superconducting films

We develop an explicitly gauge-invariant semiclassical approach to investigate the nonlinear response of superconductors to monochromatic terahertz radiation. We demonstrate that in clean superconductors charge conservation forbids nonlinear response to a uniform field. We apply our approach to quasi-two-dimensional films and obtain an explicit expression for the photoinduced current. We find that the photoinduced current exhibits a strong dependence on polarization and the incidence angle of the radiation. Our predictions may be directly verified in experiments with quasi-two-dimensional superconducting films.