  We develop an explicitly gauge-invariant semiclassical approach to
investigate nonlinear response of superconductors to monochromatic THz
radiation. We demonstrate that in clean superconductors charge conservation
forbids non-linear 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 incidence angle of the radiation. Our
predictions may be directly verified in experiments with quasi-two-dimensional
superconducting films.
