Theory of sum-frequency generation spectroscopy of adsorbed molecules using the density matrix method - broadband vibrational sum-frequency generation and applications

A generalized theory of frequency- and time-resolved vibrational sum-frequency generation (SFG) spectroscopy of adsorbates at surfaces is presented using the density matrix formalism. Our theoretical treatment is specifically aimed at addressing issues that accompany the relatively novel SFG approach using broadband infrared pulses. The ultrashort duration of these pulses makes them ideally suited for time-resolved investigations, for which we present a complete theoretical treatment. A second key characteristic of these pulses is their large bandwidth and high intensity, which allow for highly non-linear effects, including vibrational ladder climbing of surface vibrations. We derive general expressions relating the density matrix to SFG spectra, and apply these expressions to specific experimental results by solving the coupled optical Bloch equations of the density matrix elements. Thus, we can theoretically reproduce recent experimentally demonstrated hot band SFG spectra using fetmosecond broadband infrared excitation of carbon monoxide (CO) on a Ru(001) surface.