Electric dipole susceptibility, nonlinear optics

A specific set of experiments which must be mentioned, being directly associated with the main topic of this paper, is the work of Bergman, et. al. (22) dealing with the second-order nonlinear optical properties of polyvinylidene fluoride (PVF2). Nonvanishing the second-order nonlinear electric dipole susceptibility, is expected in PVF2 since it exhibits other properties requiring noncentrosymmetric microscopic structure. These properties appear... 

In order to describe linear and nonlinear optical activity, it becomes necessary to consider susceptibilities other than the electric-dipole susceptibilities in Eq. (1). We will only briefly discuss such nonlocal terms. 

The coefficients in the various terms in Eqs. (2a) and (2b) are termed the nth-order susceptibilities. The first-order susceptibilities describe the linear optical effects, while the remaining terms describe the nth order nonlinear optical effects. The coefficients are the nth-order electric dipole susceptibilities, the coefficients G " are the nth-order quadrupole susceptibilities, and so on. Similar terminology is used for the various magnetic susceptibilities. For most nonlinear optical interactions, the electric dipole susceptibilities are the dominant terms because the wavelength of the radiation is usually much longer than the scattering centers. These will be the ones considered primarily from now on. 

Nonlinear Susceptibilities. Nonlinear optical effects are formally understood through the series expansion of the ith component of the polarization (average dipole moment per unit volume) P of a material in powers of the electric-field in the medium E (tjcpically on the order of 10 V/m or greater for nonlinear... 

If the electric dipole contribution dominates in the total SH response, the macroscopic response can be related to the presence of optically nonlinear active compounds at the interface. In this case, the susceptibility tensor is the sum of the contribution of each single molecule, all of them coherently radiating. For a collection of compounds, it yields ... 

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

It is important to note that the coefficients fp, gp, and hs are always nonvanishing, for both achiral and chiral isotropic films. On the other hand, fs, gs, and hp can only be nonvanishing if the isotropic film is chiral (nonracemic) because they completely depend on the chiral susceptibility components. Note that gs is always equal to zero within the electric dipole approximation. The sign of the chiral expansion coefficients changes between enantiomers, while that of the achiral expansion coefficients stays the same. Experimental determination of all expansion coefficients fully characterizes the nonlinearity and nonlinear optical activity of the sample. Once all expansion coefficients are... 

Symmetry arguments show that parity-odd, time-even molecular properties which have a non-vanishing isotropic part underlie chirality specific experiments in liquids. In linear optics it is the isotropic part of the optical rotation tensor, G, that gives rise to optical rotation and vibrational optical activity. Pseudoscalars can also arise in nonlinear optics. Similar to tlie optical rotation tensor, the odd-order susceptibilities require magnetic-dipole (electric-quadrupole) transitions to be chirally sensitive. 

The nonlinear interaction of light with matter is useful both as an optical method for generating new radiation fields and as a spectroscopic means for probing the quantum-mechanical structure of molecules [1-5]. Light-matter interactions can be formally classified [5,6] as either active or passive processes and for electric field based interactions with ordinary molecules (electric dipole approximation), both may be described in terms of the familiar nonlinear electrical susceptibilities. The nonlinear electrical susceptibility represents the material response to incident CW radiation and its microscopic quantum-mechanical formalism can be found directly by diagrammatic techniques based on the perturbative density matrix approach including dephasing effects in their fast-modulation limit [7]. Since time-independent (DC) fields can only induce a... 

In the above discussion, we have only considered the effects due to the CTE-CTE repulsion, which contribute to the resonant nonlinear absorption (as well as to other resonant nonlinearities) by the CTE themselves. Here, however, we want to mention a more general mechanism by which the nonlinear optical properties of media containing CTEs in the excited state can be enhanced. This influence is due to the strong static electric field arising in the vicinity of an excited CTE, If, for example, the CTE (or CT complex) static electric dipole moment is 20 Debye, at a distance of 0.5 nm it creates a field Ecte of order 107 V/cm. Such strong electric fields have to be taken into account in the calculation of the nonlinear susceptibilities, because they change the hyperpolarizabilities a, / , 7, etc. of all molecules close to the CTE. For instance, in the presence of these CTE induced static fields, the microscopic molecular hyperpolarizabilities are modified as follows... 

The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization PfL(2 >) is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor x (2 > >, a>) is large enough to dwarf the contribution from higher orders of the multipole expansion like the electric quadrupole contribution and is therefore the simplest approximation for the nonlinear polarization. At pure solvent interfaces, this may not be the case, since the nonlinear optical activity of solvent molecules like water, 1,2-dichloroethane (DCE), alcohols, or alkanes is rather low. The magnitude of the molecular hyperpolarizability of water, measured by DC electric field induced second harmonic... 

Other nonlinear optical spectroscopies have gained much prominence in recent years. Two techniques in particular have become quite popular among surface scientists, namely, second harmonic (SHG) [55] and sum-frequency (SFG) [56] generation. The reason why both SHG and SFG can probe interfaces selectively without being overwhelmed by the signal from the bulk is that they rely on second-order processes that are electric-dipole forbidden in centrosymmetric media by breaking the bulk symmetry, the surface places the molecular species in an environment where their second-order nonlinear susceptibility, the term responsible for the absorption of SHG and SFG signals, becomes non-zero. 

The study of amphiphile ordering at interfaces is necessary to understand many phenomena, like microemulsions, foams or interfacial reactivity. It is expected that the preferential orientation taken by these compounds at interfaces is entirely determined by their interactions with the two solvants forming the interface and the intermolecular repulsion or attraction within the monolayer. As mentioned above, the SH response at liquid/liquid interfaces is dominated by electric dipole contributions and is therefore surface specific. Neglecting the contribution from the sol-vant molecules, which usually only have a weak nonlinear optical activity, the passage from the macroscopic susceptibility tensor xP to the microscopic molecular hyperpolarizability p of the adsorbate is obtained by merely taking the SHG response of the amphiphile monolayer as the superposition of the contribution from each single moiety. Hence, it yields... 

The summation runs over repeated indices, /r, is the i-th component of the induced electric dipole moment and , are components of the applied electro-magnetic field. The coefficients aij, Pijic and Yijki are components of the linear polarizability, the first hyperpolarizability, and the second hyperpolarizability tensor, respectively. The first term on the right hand side of eq. (12) describes the linear response of the incident electric field, whereas the other terms describe the nonhnear response. The ft tensor is responsible for second order nonlinear optical effects such as second harmonic generation (SHG, frequency AotAAin, frequency mixing, optical rectification and the electro-optic effect. The ft tensor vanishes in a centrosymmetric envirorunent, so that most second-order nonlinear optical materials that have been studied so far consists of non-centrosyrmnetric, one-dimensional charge-transfer molecules. At the macroscopic level, observation of the nonlinear optical susceptibility requires that the molecular non-symmetry is preserved over the physical dimensions of the bulk stmcture. 

The 2PA nonlinear absorption process can be deseribed from the semi-classical theory, which leads to express the nonlinear electric polarisation P of an optical medium and the electronic dipole moment p induced at molecular scale following Equations 5.6 and 5.7, respectively, as a function of odd-order susceptibilities and hyperpolarisabilities, respectively [39] ... 

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