Exact and approximate expressions for χ(3) in CARS diagnostics measurements

Coherent anti-Stokes Raman scattering (CARS) is a useful tool in combustion diagnostics. In such experiments, the measured spectrum is compared to the predicted one and information is obtained about species temperature and concentration. We examine conditions for the validity of approximate expressions for the nonlinear susceptibility
\chi^{(3)}
and indicate the importance of using the full expression in the general case, especially near one photon resonance, or under conditions of high pressure.