Off-resonant coherent hyper-Raman scattering spectroscopy

A theoretical description of the off-resonant coherent hyper-Raman scattering spectroscopy is presented. By considering two pump fields whose frequencies and corresponding wave vectors are ω₁, ω₂(= 2ω₁), k₁, and k₂, respectively, the effective Hamiltonian is derived to show that the spatial transient grating can be created by the third-order interaction with the pump fields. A delayed probe field with frequency of ω₁ and wave vector of k₁ is scattered by the spatial transient grating to produce the macroscopic polarization with wave vector 4k₁ - k₂. The expressions for the measured signals by homodyne and heterodyne method are derived and compared with that of the spontaneous hyper-Raman scattering signal.