how to adequately correct for nonresonant interferences, it is very important to experimentally isolate the resonant contributions from any nonresonant interference, often done using the technique of nonresonant suppression. The resonating contribution is from the vibrational modes and shows changes in resonance. It can be expressed as a sum of a series of Lorentz oscillators where is the strength or amplitude, is the resonant frequency, is the damping or linewidth coefficient (FWHM), and each indexes the normal (resonant vibrational) mode. The amplitude is a product of , the induced dipole moment, and , the polarizability. Together, this indicates that the transition must be both IR and Raman active. The above equations can be combined to form which is used to model the SFG output over a range of wavenumbers. When the SFG system scans over a vibrational mode of the surface molecule, the output intensity is resonantly enhanced. In a graphical analysis of the output intensity versus wavenumber, this is represented by Lorentzian peaks. Depending on the system, inhomogeneous broadening and interference between peaks may occur. The Lorentz profile can be convoluted with a Gaussian intensity distribution to better fit the intensity distribution. Orientation information From the second order susceptibility, it is possible to ascertain information about the orientation of molecules at the surface. describes how the molecules at the interface respond to the input beam. A change in the net orientation of the polar molecules results in a change of sign of . As a rank 3 tensor, the individual elements provide information about the orientation. For a surface that has azimuthal symmetry, i.e. assuming rod symmetry, only seven of the twenty seven tensor elements are nonzero (with four being linearly independent), which are and The tensor elements can be determined by using two different polarizers, one for the electric field vector perpendicular to the plane of incidence, labeled S, and one for the electric field vector parallel to the plane of incidence, labeled P. Four combinations are sufficient: PPP, SSP, SPS, PSS, with the letters listed in decreasing frequency, so the first is for the sum frequency, the second is for the visible beam, and the last is for the infrared beam. The four combinations give rise to four different intensities given by and where index is of the interfacial -plane, and and are the linear and nonlinear Fresnel factors. By taking the tensor elements and applying the