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Intensity as a function of analysis polarizer for a surface with dipole response.
Intensity as a function of analysis polarizer for a surface with dipole and quadrupole response.

As those who use polarized sunglasses know, light becomes polarized when it bounces off a surface. The degree of polarization depends on the angle between the light beam and the surface as well as the index of refraction of the surface a measure of the electron density and mobility. In nonlinear spectroscopy, both light beams hitting the surface are usually polarized. So the polarization of the generated sum frequency is influenced by the incoming polarization. In addition the polarization depends on the index of refraction plus the configuration of molecules at the surface. A very effective methodology for probing the molecular configuration is to polarize the incoming infrared radiation vertically and to rotate the visible between vertical and horizontal. If the surface molecules do not affect the polarization, called a surface independent polarization, the sum frequency polarization is determined by the choice of visible input polarization and the substrate index of refraction. Interaction with the surface molecules rotates the sum frequency polarization away from this surface independent direction.

The most sensitive method for determining the polarization direction is to put a polarizer in the sum frequency beam and rotate it until no sum frequency is detected called the polarization angle null. The null angle is perpendicular to the light polarization direction.

The polarization angle null methodology is capable of revealing even more information about the surface. If the interaction between light and the surface is a dipole-dipole interaction, the generated sum frequency will be plane polarized. However, if the molecules of the surface have a significant quadrupole or higher moment, the generated sum frequency polarization will be more complex. This more complex behavior is revealed by analyzing the full 360 polarization of the sum frequency. Using this methodology we have discovered a significant quadrupolar component in the ice surface. The dipole plus quadrupolar components provide a rich picture for the configuration of water molecules in the ice surface.

The detailed picture revealed by PAN and SFG forms a basis for determining interaction of a wide variety of molecules with ice and water including those that form clathrates.

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