Manipulating one- and two-dimensional stimulated-x-ray resonant-Raman signals in molecules by pulse polarizations

The simulation of spontaneous (RIXS) and stimulated x-ray Raman scattering (SXRS) signals in isotropic samples requires rotational averaging of a fourth-rank tensor product of two polarizabilities. Attosecond stimulated x-ray Raman spectroscopy excites multiple valence transitions covered by the pulse bandwidths. These excitations depend on the orientation of the molecule with respect to the pulse polarizations in the laboratory frame, making the response a high-rank tensor operator. Many contributions to the response coming from different tensor components complicate the analysis and interpretation of these measurements. By using the magic angle between the excitation and detection fields these signals may be expressed as correlation functions of the scalar isotropic polarizabilities, which greatly simplifies their interpretation. We show that a similar simplification of three-pulse two-dimensional stimulated x-ray Raman scattering (2D-SXRS), which depends on a rotationally averaged sixth-rank tensor, is possible by a super magic angle (SMA) combination of two measurements with specific pulse polarization configurations. Calculated SMA 2D-SXRS signals for trans-N-methylacetamide (NMA) at the nitrogen K edge reveal different features compared with the all-parallel polarization configuration.