Spontaneous nonlinear Raman spectroscopy

Let us first briefly discuss spontaneous nonlinear Raman spectroscopy on an isolated single molecule. Generally the induced dipole moment p in a molecular system is written in the form... 

Applications of spontaneous nonlinear Raman spectroscopy (Hyper-Raman scattering)... 

The methods of nonlinear Raman spectroscopy, i. e. spontaneous hyper Raman scattering (based on the hyperpolarizability) and coherent nonlinear Raman scattering (based on the third-order-nonlinear susceptibilities) are discussed in detail in Sec. 3.6.1. In Sec. 3.6.2 the instrumentation needed for these types of nonlinear spectroscopy is described. In this section we present some selected, typical examples of hyper Raman scattering (Sec. 6.1.4.1), coherent anti-Stokes Raman. scattering (Sec. 6.1.4.2), stimulated Raman gain and inverse Raman spectroscopy (Sec. 6.1.4.3), photoacoustic Raman spectroscopy (Sec. 6.1.4.4) and ionization detected stimulated Raman spectroscopy (Sec. 6.1.4.5). 

As described at the end of section Al.6.1. in nonlinear spectroscopy a polarization is created in the material which depends in a nonlinear way on the strength of the electric field. As we shall now see, the microscopic description of this nonlinear polarization involves multiple interactions of the material with the electric field. The multiple interactions in principle contain infomiation on both the ground electronic state and excited electronic state dynamics, and for a molecule in the presence of solvent, infomiation on the molecule-solvent interactions. Excellent general introductions to nonlinear spectroscopy may be found in [35, 36 and 37]. Raman spectroscopy, described at the end of the previous section, is also a nonlinear spectroscopy, in the sense that it involves more than one interaction of light with the material, but it is a pathological example since the second interaction is tlirough spontaneous emission and therefore not proportional to a driving field... 

We will first discuss spontaneous Raman spectroscopy with lasers (linear Raman effect) and then briefly some investigations of the nonlinear Raman effect. 

The inelastic processes - spontaneous Raman scattering (usually simply called Raman scattering), nonlinear Raman processes, and fluorescence - permit determination of species densities as well as temperature, and also allow one, in principle, to determine the temperature for particular species whether or not in thermal equilibrium. In Table II, we categorize these inelastic processes by the type of the information that they yield, and indicate the types of combustion sources that can be probed as well as an estimate of the status of the method. The work that we concentrate upon here is that indicated in these first two categories, viz., temperature and major species densities determined from vibrational Raman scattering data. The other methods - fluorescence and nonlinear processes such as coherent anti-Stokes Raman spectroscopy - are discussed in detail elsewhere (5). 

Raman scattering (IRS), coherent anti-Stokes Raman spectroscopy (CARS), and coherent Stokes Raman spectroscopy (CSRS). Figure 3 shows Quanmm diagrams of the nonlinear Raman processes, with spontaneous Raman included as... 

In the previous sections, we derived general correlation function expressions for the nonlinear response function that allow us to calculate any 4WM process. The final results were recast as a product of Liouville space operators [Eqs. (49) and (53)], or in terms of the four-time correlation function of the dipole operator [Eq. (57)]. We then developed the factorization approximation [Eqs. (60) and (63)], which simplifies these expressions considerably. In this section, we shall consider the problem of spontaneous Raman and fluorescence spectroscopy. General formal expressions analogous to those obtained for 4WM will be derived. This will enable us to treat both experiments in a similar fashion and compare their information content. We shall start with the ordinary absorption lineshape. Consider our system interacting with a stationary monochromatic electromagnetic field with frequency w. The total initial density matrix is given by... 

---