Theoretical study on surface vibrational infrared-visible sum-frequency generation spectroscopy applied to adsorbed molecules

A comprehensive theory of sum-frequency generation (SFG) spectroscopies with infrared pump and infrared-visible probe is presented in a systematic way based on the Markovian master equation approach. A description of SFG as a five-wave mixing process is given by using a perturbation theory for both the stationary and time-resolved experiments. A criterion for the validity of the perturbation treatment is also presented in terms of the saturation parameter. Simple expressions are derived by introducing the rotating-wave approximation for a four-level model system of the adsorbed molecule. It is shown that the fourth-order induced nonlinear polarization at the SF can be expressed as a sum of three components which are induced by different field-molecule interactions. Numerical calculations for the recent experimental results of the SFG spectroscopy applied to C-H stretch modes on the hydrogen-terminated H/C(111) (1 x 1) surface are performed to show the applicability of our expressions as well.