Averaged field-enhancement

The total enhancement, 3, of the intensity of the Raman emission from the molecule is directly proportional to the total average field enhancement normal to the surface of the sphere and inversely proportional to the distance the molecule is away from the surface of the sphere. For a molecule adsorbed on the surface 3 is given by ... 

Figure 8.12 Averaged-field enhancements on the top half surface of a gold nanosphere as a function of the distance r from the surface of the nanosphere.

For very small electric fields ( <105 Vm"1), the linear term in E is positive and so the applied electric field enhances the escape of oppositely charged ions from each other. With small electric fields, where only the linear and quadratic terms need be considered, the influence of the electric field on the escape probability is small. Other analytical and numerical techniques have been discussed [327—331], There is little reason to anticipate any correlation of the orientation of an ion-pair when initially formed with the external electric field. Presuming that the distribution of ion-pair orientations is random with respect to the electric field, the escape probability of an ion-pair depends on r0 and E alone [332]. Averaged over 0 < 90 < 27t, eqn. (151) gives... 

Finally, Weber and Ford" estimate an upper limit of the field enhancement on the basis of conservation-of-energy considerations. They find for silver and a perfect coupler between the radiation and the metal excitations (a grating or a prism) that the maximum enhancement of the square of the field is approximately 300. This is probably the average quantity. For a rough surface they estimate an enhancement on the order of magnitude of unity ... 

The DCS is a rich source of information about atomic and molecular interactions as it allows one to unfold the partial wave averaging and analyze each /-contribution separately [43]. In addition, spin relaxation cross-sections are extremely sensitive to the atom-molecule interaction potential [19]. Therefore, we expect the spin relaxation DCS to be a sensitive probe of the anisofropic molecular interactions. As shown in Section 4.2, electric fields enhance the / / 1 transitions, and thus the sensitivity of the cross-sections to the anisotropic part of the interaction potential. Figure 4.20 illustrates that spin relaxation DCSs assume a specific 0 dependence near a shape resonance, which can be used for detection and assignment of shape resonances in cold collisions. 

The measurements done by Guo et al. [25] showed decay in the enhancement beyond approximately 80 nm. Their FDTD calculations instead showed a continued oscillation in the average field-squared at the position of the fluors out to at least 600 nm these oscillations correlate with Fabry-Perot resonances within the oxide, an observation which has been made previously by Andrewartha [59] for a similar type of structure (a "bottle grating interestingly calculations of the reflectivity from this related structure showed similar sharp oscillations [59]. The calculated oscillations originate from the interference between diffraction from the nanowire array and multiple reflections from the aluminum... 

This situation, despite the fact that reliability is increasing, is very undesirable. A considerable effort will be needed to revise the shape of the potential functions such that transferability is greatly enhanced and the number of atom types can be reduced. After all, there is only one type of carbon it has mass 12 and charge 6 and that is all that matters. What is obviously most needed is to incorporate essential many-body interactions in a proper way. In all present non-polarisable force fields many-body interactions are incorporated in an average way into pair-additive terms. In general, errors in one term are compensated by parameter adjustments in other terms, and the resulting force field is only valid for a limited range of environments. 

---