text: 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 correct transformations, the orientation of the molecules on the surface can be found.