Fifth-order coherent light scattering: Extension of the Kramers-Heisenberg expression for light scattering and two-dimensional measurement of vibrational dynamics

A theoretical description of the fifth-order coherent light scattering is presented. By calculating the corresponding radiative transition rate, it is found that the intensity of the fifth-order scattering light is proportional to the squares of the number density as well as to the thickness of the optical sample. The fifth-order coherent light scattering expression is a two-dimensional extension of the Kramers-Heisenberg expression for light scattering. The intensity of each peak in the two-dimensional spectrum is determined by the product of three Raman transition matrix elements. A detailed discussion on the relative intensities of the diagonal and off-diagonal peaks is presented.