  In superconductors the Anderson-Higgs mechanism allows for the existence of a
collective amplitude (Higgs) mode which can couple to eV-light mainly in a
non-linear Raman-like process. The experimental non-equilibrium results on
isotropic superconductors have been explained going beyond the BCS theory
including the Higgs mode. Furthermore, in anisotropic d-wave superconductors
strong interaction effects with other modes are expected. Here we calculate the
Raman contribution of the Higgs mode from a new perspective, including
many-body Higgs oscillations effects and their consequences in conventional,
spontaneous Raman spectroscopy. Our results suggest a significant contribution
to the intensity of the A1g symmetry Raman spectrum in d-wave superconductors.
In order to test our theory, we predict the presence of measurable
characteristic oscillations in THz quench-optical probe time-dependent
reflectivity experiments.
