Second-order surface polarization

From a symmetry viewpoint the second-order surface polarization in the linear (-in-M) approach can be written as... 

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

The first two terms are electric quadrupole in character while the last term is magnetic dipolar. Under excitation by a single plane wave, the first term vanishes. In a homogeneous medium the second term vanishes by Gauss Law. The third term describes the induced polarization which is along the propagation direction. It can only radiate at the discontinuity of the surface. The full expression for the second-order nonlinear polarization in an isotropic medium is then written as the sum of the surface and bulk polarizations [78] ... 

The electronic wave function has now been removed from the first two terms while the curly bracket contains tenns which couple different electronic states. The first two of these are the first- and second-order non-adiabatic coupling elements, respectively, vhile the last is the mass polarization. The non-adiabatic coupling elements are important for systems involving more than one electronic surface, such as photochemical reactions. 

To analyze the second-order susceptibility, the symmetry of the films was first analyzed by measuring the intensities of the second-harmonic light. The sample was irradiated with polarized light from a Nd YAG laser incident at 45°, and the second-harmonic light emanating from the sample was detected while the sample was rotated around its surface normal. No variation in the second-harmonic intensity was observed as the sample was rotated, indicating... 

Optical frequency up-conversion, or second harmonic generation (SHG), in nanostructured surfaces can be also considered as a kind of field enhance-menf [61]. In general, SHG efficiency is proportional to the square of nonlinear polarization ha (x [P (2second order susceptibility. For a nanostructured surface, the incident field is transformed to the local field given by Eq. 19, yielding ... 

Having resolved the molecular perception problem and achieved a unique representation of all atoms, bonds, and rings in the molecule, the second major step is the definition of the most useful measure for local similarity of atoms and atomic environment. For the purpose of COSMO/rag, we need to achieve the state that atoms are considered as most similar, if their partial molecular surfaces and surface polarities, i.e., polarization charge densities, are most similar. But since the latter is not known, at least for the new molecule under consideration, we have to ensure that the local geometries and the electronic effects of the surrounding atoms are most similar. Obviously, two similar atoms should at legist be identical with respect to their element and their hybridization. Turning this information into a unique real number, a similarity index of the lowest order (zeroth order) can be defined for each atom from the atom element numbers and... 

When the electron is partially delocalized, one should switch to the adiabatic representation in which the upper and lower CT surface are split by an energy gap depending on P. If this energy gap is expanded in P with truncation after the second-order term, we come to the model of a donor-acceptor complex whose dipolar polarizabilities are different in the ground and excited states. The solute-solvent interaction energy then attains the energy of solute polarization that is quadratic in P... 

The inherent surface-specificity of SFG originates from its second-order nonlinearity. The beam mixing process induces a nonlinear polarization... 

In ATR-FTIR excitation occurs only in the immediate vicinity of the surface ol the reflection element, in an evanescent wave resulting from total internal reflection. The intensity of the evanescent field decays exponentially in the direction normal to the interface with a penetration depth given by (1.7.10.121, which for IR radiation is of the order of a few hundreds of nm. Absorption leads to an attenuation of the totally reflected beam. The ATR spectrum is similar to the IR transmission spectrum. Only for films with a thickness comparable to, or larger than, the penetration depth of the evanescent field, do the band intensities depend on the film thickness. Information on the orientation of defined structural units can be obtained by measuring the dichroic ratio defined as R = A IA, where A and A are the band absorbances for radiation polarized parallel and perpendicular with respect to the plane of incidence, respectively. From this ratio the second-order parameter of the orientation distribution (eq. [3.7.13]) can be derived ). ATR-FTIR has been extensively used to study the conformation and ordering in LB monolayers, bilayers and multilayers of fatty acids and lipids. Examples of various studies can be found... 

It is not surprising therefore that the optical properties of small metal particles have received a considerable interest worldwide. Their large range of applications goes from surface sensitive spectroscopic analysis to catalysis and even photonics with microwave polarizers [9-15]. These developments have sparked a renewed interest in the optical characterization of metallic particle suspensions, often routinely carried out by transmission electron microscopy (TEM) and UV-visible photo-absorption spectroscopy. The recent observation of large SP enhancements of the non linear optical response from these particles, initially for third order processes and more recently for second order processes has also initiated a particular attention for non linear optical phenomena [16-18]. Furthermore, the paradox that second order processes should vanish at first order for perfectly spherical particles whereas experimentally large intensities were collected for supposedly near-spherical particle suspensions had to be resolved. It is the purpose of tire present review to describe the current picture on the problem. 

The first order term of Eq. (8) is reduced to the field r ), the electric dipole field, whereas the second order term, linear with the parameter order x = a/X, is the sum of tire fields ( >, ) and ( >, ), respectively the electric quadrupole and the magnetic dipole fields. The surface nonlinear polarization of the form of Eq. (3) is now a series expansion with respect to the parameter x = a/X too. Its general expression is ... 

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