Bilinear reflection of a double-frequency laser beam from a superconductor

The bilinear current density induced in a superconducting metal by a laser beam with frequencies ω1 and ω2 has been calculated. The calculation is done within the framework of the BCS theory of superconductivity at temperature T=0 °K. It is shown that in the superconducting state of the metal the component of the induced current density, varying with the difference frequency Ω=ω1-ω2 and the wave vector Q=q1-q2, where q1 and q2 are the wave vectors of the fundamental fields in the metal, differs considerably from the corresponding component in the normal state of the metal when hΩ is of the order of the energy gap 2Δ. In this paper only that special case is considered where the wave vector Q is such that hQvf≪2Δ, vf being the Fermi velocity of the electrons. If the collision frequency ΩcS of the electrons in the superconducting state is small compared to Ω, there is a sharp peak at hΩ=2Δ in the energy flux of the light wave of frequency Ω reflected from the surface of the superconductor. For hΩ≫2Δ, the reflectivities are the same for both the normal and the superconducting states of the metal