Intrinsic cascading contributions to the fifth- and seventh-order electronically off-resonant Raman spectroscopies

The cascading polarization contributing to the femtosecond fifth- and seventh-order coherent Raman scattering processes is obtained in terms of the third- and fifth-order Raman response functions. It is found that four cascading processes contribute to the fifth-order Raman scattering signal. In the case of the seventh-order Raman scattering, there are 34 possible cascading processes contributing to the seventh-order Raman scattering signal, and they are classified as χ⁽⁵⁾Xχ⁽³⁾- and χ⁽³⁾ Xχ⁽³⁾Xχ(3)-types depending on the involved low-order nonlinear optical processes. Due to the complicated interference among these polarization fields, it may not be possible to experimentally measure the pure seventh-order Raman scattering signal without contamination from the cascaded contributions.