  The Higgs mode in superconductors is a scalar mode without electric or
magnetic dipole moment. Thus, it is commonly believed that its excitation is
restricted to a nonlinear two-photon Raman process. However, recent efforts
have shown that a linear excitation in the presence of a supercurrent is
possible, resulting in a new resonant enhancement at $\Omega=2\Delta$ with the
driving light frequency $\Omega$ and the energy of the Higgs mode $2\Delta$.
This is in contrast to the usual $2\Omega = 2\Delta$ resonance condition found
in nonlinear third-harmonic generation experiments. In this communication, we
show that such a linear excitation can still be described as an effective Raman
two-photon process, with one photon at $\omega=2\Delta$ and one virtual photon
at $\omega=0$ which represents the dc supercurrent. At the same time we
demonstrate that a straightforward infrared activation with a single photon
excitation is negligible. Moreover, we give a general context to our theory,
providing an explanation for how the excitation of the Higgs mode in both THz
quench and drive experiments can be understood within a conventional
difference-frequency generation or sum-frequency generation process,
respectively. In such a picture, the observed new resonance condition $\Omega =
2\Delta$ is just a special case. With the same approach, we further discuss
another recent experiment, where we find a suppression of odd order higher
harmonics in the presence of a dc supercurrent.
