Theory of sum-frequency generation spectroscopy of adsorbed molecules using thedensity matrix method—broadband vibrational sum-frequency generation andapplications

Abstract

A generalized theory of frequency- and time-resolved vibrational sum-frequency generation(SFG) spectroscopy of adsorbates at surfaces is presented using the density matrixformalism. Our theoretical treatment is specifically aimed at addressing issues thataccompany the relatively novel SFG approach using broadband infrared pulses. Theultrashort duration of these pulses makes them ideally suited for time-resolvedinvestigations, for which we present a complete theoretical treatment. A second keycharacteristic of these pulses is their large bandwidth and high intensity, which allow forhighly non-linear effects, including vibrational ladder climbing of surface vibrations. Wederive general expressions relating the density matrix to SFG spectra, and apply theseexpressions to specific experimental results by solving the coupled optical Blochequations of the density matrix elements. Thus, we can theoretically reproducerecent experimentally demonstrated hot band SFG spectra using femtosecondbroadband infrared excitation of carbon monoxide (CO) on a Ru(001) surface.