The recent observation of a transmitted Thz pulse oscillating at three times
the frequency of the incident light paves the way to a new protocol to access
resonant excitations in a superconductor. Here we show that this non-linear
optical process is dominated by light-induced excitation of Cooper pairs, in
analogy with a standard Raman experiment. The collective amplitude (Higgs)
fluctuations of the superconducting order parameter give in general a smaller
contribution, unless one designs the experiment by combining properly the light
polarization with the lattice symmetry.Comment: Slightly revised introduction, to appear on Phys. Rev. B. as Rapid
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