Sum-frequency generation echo and grating from interface

The work addresses spectroscopy of fourth-order Sum Frequency Generation Echo and Grating responses as an experimental tool to study structure and dynamics at interfaces. First, it addresses experimental geometry to extract background-free fourth-order Echo and Grating responses. Further, the article provides the analytical expressions of the response functions for these nonlinearities. The derived expressions are used to model the χ((4)) two-dimensional spectral responses of a hydrated methyl acetate, which resembles a hydrated carbonyl moiety at the polar outer side of a phospholipid membrane. Orientation, transition dipole moments, and Raman tensors are obtained from the results of classical and quantum calculations, respectively. The numerical studies for the nonlinear responses under different polarization schemes and timings suggest the possibility of securely factoring of spectral contributions of χ(YYYZX) and χ(YYYZY) macroscopic susceptibilities. As such, the nonlinearities provide an experimental perspective on orientation of a generic (low-symmetry) molecular system at interfaces. Besides, the spectral properties of the tensors may reflect correlations of the in-plane and out-of-plane field components specific to the interface. For the case of a phospholipid membrane, the experiment would address in-plane and out-of-plane anisotropy of hydrogen bonding and related dynamics.