Polarization response

NLO effects result when the polarization response of the valence electrons becomes significantly anharmonic, usually in intense light beams where the magnitude of E is very large. The magnitudes of the coefficients of the terms in equation 2 diminish rapidly at higher orders, and thus readily observable NLO effects are either second-order third-order (X ) processes. Most NLO appHcations rely on second-order processes. However,... 

An orientation-dependent asymmetry in line intensity of a quadrupole doublet is, in contrast to the aforementioned case, caused by the polarization response of... 

An important addition to the model was the inclusion of virtual particles representative of lone pairs on hydrogen bond acceptors [60], Their inclusion was motivated by the inability of the atom-based electrostatic model to treat interactions with water as a function of orientation. By distributing the atomic charges on to lone pairs it was possible to reproduce QM interaction energies as a function of orientation. The addition of lone pairs may be considered analogous to the use of atomic dipoles on such atoms. In the model, the polarizability is still maintained on the parent atom. In addition, anisotropic atomic polarizability, as described in Eq. (9-28), is included on hydrogen bond acceptors [65], Its inclusion allows for reproduction of QM polarization response as a function of orientation around S, O and N atoms and it facilitates reproduction of QM interaction energies with ions as a function of orientation. 

Over the past decade it has been learned that organic materials containing appropriately constituted or substituted conjugation systems may exhibit highly enhanced electronic nonlinear optical polarization responses Since the microscopic second-order... 

Fig. 3.5. Experimental apparatus for time-resolved THz transmission spectroscopy. The sample is excited with a visible laser pulse delivered by delay line 3. A singlecycle THz electric-field transient probes the polarization response of the sample after time delay tv scanned by delay line 1. The transmitted THz amplitude is monitored via ultrabroadband electro-optic sampling in a THz receiver as a function of time T scanned by delay line 2. From [13]...

The connection between the non-linear polarization response and the generation of optical harmonics by NLO materials can be understood by considering Figure 39, which shows a typical non-linear optical response produced by a non-centrosymmetric molecule. 

As illustrated in Figure 39a, the application of a symmetrically oscillating electric field E of frequency co makes the molecule respond with an asymmetric polarization (or the wave amplitude of the polarization response in the positive ordinate is different from that in the negative ordinate) in that the electron density can only flow in the direction donor — acceptor, and not vice versa. 

Figure 39 (a) Non-linear polarization response (P) along the direction x, as a function of... 

Just as linear polarization leads to linear optical effects, such as refractive index and birefringence, nonlinear polarization leads to other and usually more subtle (nonlinear) effects. It is precisely these effects we hope to understand and exploit. In Figure 14, application of a symmetric field (i.e., the electric field associated with the light wave) to the anharmonic potential leads to an asymmetric polarization response. This polarization wave shows diminished maxima in one direction and accentuated... 

The terms on the left are the electric force and the restoring force that is linear in the displacement. A damping term with a proportionally constant r is added to the right hand side to account for dissipation of energy during the polarization response. The solution to this equation leads to an expression for the displacement, r, as... 

Figure 3. Plot of the polarization response to an incident electromagnetic field at frequency w and the Fourier components of that response. (Reprinted with permission from ref. 4. Copyright 1975 John Wiley and Sons.)...

Figure 4. Illustration of the dependence of the amplitude of the harmonic field E(2co) on its phase relationship with the polarization response P(3co).

Estimates of the relative surface/bulk response have recently been made for Ag(100) and Ag(110) [131]. For a (110) surface, the bulk term can be isolated in the anisotropic response using appropriate polarizations. For example, the anisotropic coefficient, c(4) in the expression for the p-polarized response from a (110) crystal is comprised solely of bulk terms (Table 3.1). By measuring and fitting the data, the value for c(4) is found to be small relative to the magnitude of... 

Both the Au(100) and the Au(lll) surfaces were examined in studies aimed at measuring the relative surface/bulk response from gold surfaces [131]. For the Au(100) surface and a p-polarized incident pulse at 1064 nm, anisotropy in the p-and s-polarized responses were found to be minimal. The potential dependence for this surface was also examined. The p-polarized response was found to increase by a factor of 4 when the voltage was swept positive of the PZC from -0.1 V to +0.8 V. The s-polarized response which was very small and isotropic showed no change with bias voltage. All of the data from this surface is consistent with a dominance of the surface response relative to the bulk. 

Thus, without any doubt, the situation of a polar solute in a polar solvent is very different from the situation of a solute in a dielectric continuum. The solvent is neither homogeneous, nor does it give a linear polarization response. Hence, the considerable success of dielectric continuum solvation models for the... 

In PI, the slow and fast indices are replaced by the subscripts or and el referring to orientational and electronic response of the solvent, respectively, while in PII the subscripts in and dyn refer now to an inertial and a dynamic polarization response of the solvent, respectively. 

Figure 3.31 As (due to orientational response of aqueous solvent) versus e, calculated for ET in a large binuclear transition metal complex (D (Ru2+/3+) and A (Co2+/3+) sites bridged by a tetraproline moiety) molecular-level results obtained from a nonlocal polarization response theory (NRFT, solid lines) continuum results are given by dashed lines, referring to numerical solution of the Poisson equation with vdW (cont./vdW) and SAS (cont./SAS) cavities, or as the limit of the NRFT results when the full k-dependent structure factor (5(k)) is replaced by 5(0) 5(k) for bulk water was obtained from a fluid model based on polarizable dipolar spheres (s = 1.8 refers to ambient water (square)). For an alternative model based on TIP3 water (where, nominally, 6 = ), ambient water corresponds to the diamond. (Reprinted from A. A. Milishuk and D. V. Matyushov, Chem Phys., 324, 172. Copyright (2006), with permission from Elsevier).

Electro- and magnetooptical phenomena in colloids and suspensions are widely used for structure and kinetics analysis of those media as well as practical applications in optoelectronics [143,144]. The basic theoretical model used to study optical anisotropy of the disperse systems is the noninteracting Brownian particle ensemble. In the frame of this general approximation, several special cases according to the actual type of particle polarization response to the applied field may be distinguished (1) particles with permanent dipole moments, (2) linearly polarizable particles, (3) nonlinearly polarizable particles, and (4) particles with hysteretic dipole moment reorientation. 

The presence of different solvation regimes is due to the time dependence of the solvent polarization response to sudden changes ( 10-13 s) in the solute charge distribution. In most cases, the solvent polarization response may be decomposed into two terms, one describing a fast (electronic) response and the other a slow (orientational) response. Here, fast indicates the part of the solvent response that is instantaneously equilibrated to the dynamical change of the solute charge distribution, while the slow refers to the remaining inertial component. 

Qualitatively similar polarization responses are apparent for both microfiltration and ultrafiltration processes, but for microfiltration, additional more complex can occur as is discussed below (Belfort, Davis, and Zydney, 1994 Segre and Silberberg, 1962). The rejection parameter mentioned earlier can be written as either an observed, R0, or an intrinsic, R , value ... 

Equation (8.3) provides a common basis for the major computational methods used in low-energy electron scattering theory. The terms containing Q(H — E)Q 1 in this equation describe polarization response and other correlation effects in terms of a matrix optical potential. Singularities due to this energy denominator cancel out exactly [264, 265, 270],... 

Since only a relatively small number of coupled equations can be solved in practice, the target states p must be selected carefully. Virtual target excitation into the ionization continuum must be approximated by inclusion of closed-channel pseudostates that cannot be target eigenstates but have the character of wave packets in the continuum. Target polarization response is treated by including polarization pseudostates y(P). 

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