The Fresnel equations are solution of Maxwell's equations subject to a boundary condition at an interface. Light can be transmitted or reflected at the interface. The coefficients of transmission and reflection for each polarization of incident light can be calculated based on the matching of fields on both sides of the boundary.
Attenuated total reflection is a special case of surface reflection described by the Fresnel equations. When light propagates in a medium of higher index of refraction than the substrate (i.e. the material outside) there is a critical angle, above which 100% of the light will be reflected. When light is totally internally reflected the component perpendicular to the surface is an attenuated (exponentially damped) wave. This geometry is quite useful for spectroscopy since it is still possible to detect molecular spectra in the region interrogated by the attenuated wave. In FTIR spectroscopy there is increasing use of Si, Ge and ZnSe materials for attenuated total reflection (ATR)-FTIR spectroscopy. In microscopy, there are many applications for total internal reflection (TIRF) microscopy for probing membranes and regions of cells near the membrane on a surface.
Plasmonic dispersion relations are a special case of attenuated total reflection in which the light propagates through a thin film of a conductor. The fact that the conducting material has a plasma frequency leads to to a dispersion curve, which descibes the relationship between the angle of the light and the frequency required to drive a plasmonic response. The plasmonic response is a total absorption of the radiation. The condition required for that absorption is a specific incident angle and frequency, which in turn is sensitive to the index of refraction in the substrate. Thus, plasmon dispersion relations have predictive power for the design of sensors based on the surface plasmon resonance (SPR) effect.
The surface selection rules are usually considered for conducting surfaces. In that case it is fair well understood that reflection of electromagnetic radiation by p- and s-polarized light depends in different ways on the image field in the conductor. For p-polarized light the perpendicular component induces a perpendicular component in the conductor that has the same orientation. Thus, the perpendendicular component of the electric vector of p-polarized light is enhanced by a factor of two relative to the incident radiation. However, the s-polarized component induces an image field in the conduct that has an opposite phase and therefore cancels the incident field. For this reason it is only possible to observe the absorption of light by transition dipoles that are perpendicular to a conducting surface. The selection rules become more complicated as the frequency of the indicent radiation approaches the plasma frequency. We consider this qualitatively here since there is some discussion still about how to treat the amplification in this case.
Most plasmonic applications have been studied using gold and silver as the conductor. However, gold and silver are limited in their wavelength range and are quite lossy in the infrared region of the electromagnetic spectrum. For this reason, there has been great interest in conducting metal oxides, which belong to the class of free electron conductors.
The field of near the surface of a conductor can be orders of magnitude larger than in vacuum. This field enhancment is particularly sensitive to the shape of the surface. One might liken the effect to an anteena, which captures traveling incident electromagnetic radiation and then focuses it near the curved regions of the surface.
Surface enhancement has both an electromagnetic and a chemical component. The chemical component may well be analogous to resonance Raman in metal complexes. For eample, pyridine on Ag metal is the classic surface-enhanced Raman system. However, if the pyridine is liganted to the Ag by binding of its lone pair to the metal then that chemical interaction may give rise to enhancement through charge transfer bands or any absorption band of the Ag that can couple to the vibrational modes of the pyridine. The needed ingredient for Raman spectroscopy is an excited state geometry change. Such a change will be induced by a change in the electron charge distribution in the excited state. It is not difficult to imagine that pyridine on Ag would experience a large change in the excited than free pyridine due to the mixing of the pyridine orbitals and the metal. It is also possible that electron transitions on Ag metal could give rise to these geometry changes. By looking at molecular complexes of pyridine we can test whether such a condition could be met in a an molecular complex. In this section we discuss the binding of pyridine to ferrous iron in a protein that contains a cavity under the heme iron. The protein is the H93G mutant of myoglobin. This mutant lacks the proximal hisitidine. Thus, non-native molecules can be introduced into the proximal pocket and will ligate to the heme iron. This is of interest since it makes it possible to prepare 5-coordinate complexes of ligands (such as pyridine). This would be impossible in solution. Free Fe heme would form a 6-coordinate adduct under these conditions. The trans effect makes it nearly impossible to form a 5-coordinate complex in free heme. However, in the H93G mutant of myoglobin the distal pocket is sterically congested, which prevents the binding of a sixth ligand. The point is that the 5-coordinate adduct can have mixing of Fe d-electrons with the ligand in precisely the same manner that we are proposing for Ag on a surface. The difference is that the molecular complex is a well-characterized species. The surface is difficult to characterize. For example, scientists have been arguing for 40 years about whether the pyridine is lying down on the side or is straight up when bound on the surface of Ag. There is no doubt how pyridine is boudn to Fe. The bottom line is that we observe enhancement of certain modes of pyridine when the molecule is bound to Fe. The estimated enhancement of these modes for the pyridine bound to Fe is ~2000. This is an important comparison for surface-enhanced Raman spectroscopy.
