Cascaded 3 " -order Raman signal

Since the direct and cascaded responses satisfy the same phase matching condition, the total nonresonant fifth-order Raman signal will contain both contributions. Using Equations (11), (14), and (28), the ratio between the absolute values of the direct and cascaded contributions is... 

Golonzka, O., Demirdoven, N., Khalil, M., Tokmakoff, A. (2000). Separation of cascaded and direct fifth-order Raman signals using phase-sensitive intrinsic heterodyne detection. J. Chem. Phys. 113 9893-9896. 

Fig. 1.15 The energy level diagrams corresponding to the two different cascaded signal contributions in the fifth-order Raman experiment. Sa is the first sequential cascade step, Sb the second sequential cascade step, Pa the first parallel cascade step, and Pb the second parallel cascade step. Each step is on a different chromophore...

Now that the signal had been established as measurable and uncontaminated with cascades, the next step was to fully characterize the response. Several papers had been pubUshed examining the merits of various polarization tensor elements and the potentially unique information they might contribute. Tokmakoff et al. had pubhshed a set of two papers examining the third-order [82] and fifth-order [83] tensor elements for the nonresonant Raman case and the dipole resonant case. The result was seven nonzero tensor elements that could be measured for the fifth-order Raman response iiimii, f ii22ii 111122 ... 

The major problem in the comparison of 2D fifth-order Raman spectra to theory is that the theoretical calculations do not include all the contributions to the experiment in their calculated response functions such that there is tendency to selectively isolate certain regions of the spectrum in which one finds coincidences. An additional means of verifying the purity and origin of the fifth-order signal was necessary. One of the most important contributions to the field was the discovery of a mixed-polarization tensor element by Jansen, Snidjers, and Duppen that leads to a factor of 10 increase in contrast against cascaded nuclear contributions (vide infra) [50]. The proposed response... 

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