Used to drive ground state vibrations with optical pulses or cw fields. Two fields, with a frequency difference equal to a vibrational transition energy, are used to excite the vibration. The first field is the “pump” and the second is the “Stokes” field. A second interaction with the pump frequency lead to a signal that radiates at the anti-Stokes frequency: \(\omega_{sig}=2\omega_P-\omega_S\) and the signal is observed background-free next to the transmitted pump field: \(\bar k_{sig}=2\bar k_P-\bar k_S\). The experiment is described by R 1 to R 4 , and the polarization is \[\begin{aligned} R^{(3)} &=\bar \mu_{ev'} \bar \mu_{v'g} e^{-i\omega_{eg}\tau-\Gamma_{eg}\tau} \bar \mu_{gv} \bar \mu_{ve} +c.c. \\ &=\bar\alpha_{eg}e^{-i\omega_{eg}\tau-\Gamma_{eg}\tau}\bar\alpha_{ge}+c.c. \end{aligned} \nonumber\] The CARS experiment is similar to a linear experiment in which the lineshape is determined by the Fourier transform of \(C(\tau)=\langle\bar\alpha(\tau)\bar\alpha(0)\rangle\). The same processes contribute to Optical Kerr Effect Experiments and Impulsive Stimulated Raman Scattering.