Saturation effects in coherent anti-Stokes Raman scattering

Saturation effects in coherent anti-Stokes Raman scattering (CARS) spectroscopy are discussed. The discussion is limited to Raman-resonant CARS (l-s 21, where l,s are the frequencies of the pump fields with powers Pl,s, and 21 is the frequency of the Raman transition |1|2) with the possible addition of a one-photon resonance (l31 is the frequency of the electronic transition |1|3). For these cases we show that the CARS polarization pCARS is proportional to the off-diagonal density-matrix element 21. In order to determine 21, we use Laplace transforms to solve the Bloch equations for the effective two-level system |1 and |2 when l is far from resonance, or for the three-level system |1,|2, and |3, when l 31. The steady-state expression for pCARS in the former case gives pCARS PlPs12 at low powers and pCARS Pl0Ps-12 at high powers. In the three-level system, we show that when the pressure is low and at least one field is weak, the slow time dependence of 21 must be considered. When one field is strong and the other weak, the CARS spectrum is Stark split. When Pl is high, for example, pCARS Pl0Ps12 for s 32 and pCARS (PlPs)12 when s 32 V13 where V13 is the one-photon Rabi frequency for the |1|3 transition. The Wilcox-Lamb approximation is used to reduce the three-level Bloch equations to rate equations containing one- and two-photon terms. When the fields are so weak that both one- and two-photon terms are small compared to the decay terms, the usual expression for pCARS is reproduced. If only the direct two-photon processes are important, the effective-two-system results are reproduced. When both fields are intense and nearly resonant, the steady state is rapidly achieved. The results for the case where one field is much stronger than the other are essentially the same as those for one strong and one weak field. When the fields are of comparable strength, pCARS Pl12Ps0 for l 31 and s 32, and the CARS spectrum is split into five components.