Polarization order-electric

The ENBO method, which is a method for incorporating polarization and higher order electric field-molecule interaction terms into the theory, is discussed in Section IV. Nearly all OCT experiments actually use laser pulses that give rise to strong electric fields that are sufficiently strong to significantly... 

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 ... 

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

Three synthetic approaches to donor-acceptor-substituted conjugated molecules with enhanced orientability in electric fields, potentially applicable to the preparation of electro-optic polymers via electric field poling, are summarized. The three approaches are parallel attachment of chromophores to a common framework, embedding the chromophore in a zwitterion, and head-to-tail oligomerization of chromophores. The oligomerization method as well as the use of dyes as curing agents are briefly discussed in relation to the stability of electric field-induced polar order in polymer matrices. 

Two of the most important nonlinear optical (NLO) processess, electro-optic switching and second harmonic generation, are second order effects. As such, they occur in materials consisting of noncentrosymmetrically arranged molecular subunits whose polarizability contains a second order dependence on electric fields. Excluding the special cases of noncentrosymmetric but nonpolar crystals, which would be nearly impossible to design from first principles, the rational fabrication of an optimal material would result from the simultaneous maximization of the molecular second order coefficients (first hyperpolarizabilities, p) and the polar order parameters of the assembly of subunits. (1)... 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

Application of an electric field normal to the plates (typically the plates are coated with thin films of conducting glass such as indium-tin oxide) unwinds the helix if there is one, and also may cause the polar axis to orient normal to the plates (along the field), or even flatten the chevrons. It should be stressed that any added orientation of molecular dipoles along the field direction should be a weak secondary effect — the polar order occurring in the FLC phase is a thermodynamic property of the phase and not dependent upon applied fields. 

As first realized by Meyer in 1974, when the molecules making up the C phase are non-racemic, the resulting chiral C phase can possess no reflection symmetry. Thus, the maximum possible symmetry of a C phase is C2, and the phase must possess polar order (21). One of the macroscopic manifestations of polar order can be a macroscopic electric dipole moment (the polarization P) associated with orientation of molecular dipoles along the polar axis. While the existence of polar order is not sufficient to assure an observable polarization (just as chirality does not assure optical activity), in fact many FLC materials do possess an observable P. 

It should be stated that an electric field of < 10 V/pm was applied to the cell in order to unwind the FLC helix of 3, and the observed NLO behavior is a combination of the electric field induced SHG (EFISH) and that due to the spontaneous polar order in the phase. While other FLCs give much lower SHG efficiency with the same applied fields, and achiral smectic LC phenylbenzoates in our hands give unobservable SHG under identical conditions, we cannot completely rule out at this time the possibility that a significant amount of the response from compound 3 is due to the electrical poling. Control experiments to test for this (e.g. by SHG from compound 5 and/or racemic 3) are in progress, as are further experiments aimed at obtaining the phase-matched SHG efficiency for 3. 

In this review, the focus is on electro-optic materials. Such materials are members of the more general class of second-order nonlinear optical materials, which also includes materials used for second harmonic generation (frequency doubling). The term second-order derives from the fact that the magnitude of these effects is defined by the second term of the power series expansion of optical polarization as a function of applied electric fields. The power series expansion of polarization with electric field can be expressed either in terms of molecular polarization (p Eq. 1) or macroscopic polarization (P Eq. 2)... 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

Here Pind is the induced dipole moment per unit volume, and X X and X are the first-, second-, and third-order electric susceptibilities of the sample, where the order refers to the power of electric field (not of X). Equation (1) represents the macroscopic (bulk) form for the polarization in terms of single molecule properties, the induced dipole moment per molecule is written as... 

Since the first nonlinear susceptibility is a third-rank tensor, it is only non-zero in non-centrosymmetric media. To break the centrosymmetry of the macroscopic media, poling techniques using optical and electric fields have been developed, or use was made of the inherent polar ordering in Langmuir-Blodgett films and crystals with non-centrosymmetric point groups. 

This is a manifestation of the general property of chain molecules oriented in the electric field by the mechanism of large-scale motion on the average, the three main directions in the molecule coincide the direction of the greatest geometrical length of the molecule (vector h), of the orientational-axial order (responsible for the anisotropy Ti — 72) and of the orientational polar order (determining the total dipole moment n of the molecule). 

Blinov, L. M., Palto, S. P., Tevosov, A. A., Barnik, M. 1., Weyrauch, Th., and Haase, W. Electrically and photoelectrically poled polymers for nonlinear optics Cllromophores polar order and its relaxation studied by electroabsorption. Mol. Mater. 5, 311 (1995). 

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