Electric quadrupole contribution to the nonresonant background of sum frequency generation at air/liquid interfaces

Abstract

We study an electric quadrupole contribution to sum frequency generation (SFG) at air/liquid interfaces in an electronically and vibrationally nonresonant condition. Heterodyne-detected electronic sum frequency generation spectroscopy of air/liquid interfaces reveals that nonresonant χ(2) (second-order nonlinear susceptibility) has a negative sign and nearly the same value for all eight liquids studied. This result is rationalized on the basis of the theoretical expressions of χ(2) with an electric quadrupole contribution taken into account. It is concluded that the nonresonant background of SFG is predominantly due to interfacial nonlinear polarization having a quadrupole contribution. Although this nonlinear polarization is localized at the interface, it depends on quadrupolar χ(2) in the bulk as well as that at the interface. It means that the sign of nonresonant χ(2) bears no relation to the "up" versus "down" alignment of interfacial molecules, because nonresonant χ(2) has a quadrupolar origin.