NLO coefficients

The calculated values of third-order NLO coefficients are tabulated in Section III,B, together with experimental comparison when possible. 

It is of particular interest from both NLO and chemical perspectives to understand how the polarizability changes in the evolution from an isolated atom to a molecule, a cluster of atoms or molecules, an extended array, and ultimately the bulk. Intuitively, one would expect that if the effective potential for the electron extends over several atomic sites, the polarizability and nonlinear optical coefficients might be larger. Indeed, the largest NLO coefficients have been found for semiconductors and unsaturated extended organic molecules both of which have highly delocalized electrons (2). 

This equation shows that when two light beams of frequencies 1 and 2 interact with the atom(s) in the NLO material, polarization occurs at sum ( 1 + 2) and difference ( 1 - 2) frequencies. This electronic polarization will therefore, re-emit radiation at these frequencies, with contributions that depend on the relative magnitudes of the NLO coefficient, %(2)- This combination of frequencies leads to sum frequency generation (SFG). 

Table I lists the properties of several organic materials which have been studied as single crystals. The materials are listed alphabetically according to the acronym applied to them in order to avoid the appearance of prejudice with respect to any one material. Listed are the molecular P (if known), space group and point group of the crystal, SHG powder intensity relative to urea, NLO coefficients for SHG, its transparency cutoff, and the figure of merit for SHG if known. Other aspects are...

Based on the expression for, a large increase in the useful NLO coefficient for a fixed wavelength is predicted in the case where the absorbance of the NLO dye lies between the fundamental and second harmonic. Residual absorption at the second harmonic is the limiting factor in the practical application of this technique, and has been addressed through the synthesis of new dyes. Improvement of lOx in reducing this absorbance has been achieved, and another factor of 5-lOx is estimated to be required before practical devices can be fabricated. Franck-Condon effects (vibronic structure) appear to be responsible for this residual absorption because small, rigid chromophores are often correlated with the lowest amounts of absorption. Chromophores based loosely on... 

In 1969, Hubner[35] reported that the space group of the low-temperature form of barium borate is C2/C, a centrosymmetric structure. However, in 1979, by using a powder second-harmonic generation (SHG) test, my group found that the low-temperature form of barium borate possesses a large NLO coefficient, about six times... 

Correction vectors[40], as introduced by Dirac[41], provide a model-exact approach to dynamical NLO coefficients of Hubbard or PPP models with a large but... 

Higher-order NLO coefficients are given by higher-order correction vectors, starting with It satisfies the inhomogeneous linear equation... 

During the past decade, theoretical calculations of hyperpolarizabilities have been performed to help synthetic chemists design optimum NLO structures. Although extremely accurate calculations are still out of reach, it is now possible to predict the influence of structural changes on the NLO coefficients. In the case of photochromes, theoretical calculations may be useful for predicting 3 values of thermally unstable colored forms. The theoretical methods generally employed to calculate molecular hyperpolarizabilities are of two types those in which the electric field is explicitly included in the Haniiltonian, frequently labeled as Finite Field (FF) and those which use standard time dependent perturbation theory, labeled Sum Over State (SOS) method. 

Meier et al. [98] have shown that DAST crystal is also a very interesting material for phase-matched parametric oscillation around the telecommunication wavelength at A = 1318 and 1542 nm. Their results (as shown in Table 9) indicate that the second-order NLO coefficient dill = lOlOpm/V at 1318nm for DAST crystal. 

The dendritic ruthenium alkynyl complexes have very large cubic NLO coefficients. Inspection of y values for trazi -[Ru(C=CCgH4-4-C=CPh(C=CPh) (dppe)2] and [1, 3, 5-CgH3-trans - C=C-4-C=CCgH4C=C[Ru(C=CPh)(dppe)2] 3]... 

Morrall et al. review NLO properties of iron, ruthenium, osmium, nickel, and gold alkynyl complexes, which the authors have prepared. HRS (at 1.064 p,m) and Z-scan (at 0.8 p,m) measurements have been employed. Structure-property relations have been established. Static first hyperpolarizability values have also been computed employing the two-state model. They relate the NLO coefficients to several factors and properties (e.g. ease of oxidation, ir-system length, dimensionality ). 

In order to achieve high NLO coefficients and x 3 the medium must follow two criteria the constituent blocks must have high NLO polarizabilities, depending on the chemical structure and the medium must have the appropriate symmetry. For those possessing the center-symmetry, vanishes. Among them are amorphous and isotropic materials. However, these media may have non-zero x -3 - In the presence of an electric field, some of these materials may change from center-symmetrical to non-center symmetrical. 

The relation between the molecular polarizabilities to the bulk susceptibilities depends on the molecular density, N, and the local internal field factor F. Particularly, it relates to the molecular orientation. For example, the second NLO coefficient is expressed as... 

Figure 6.30. The NLO coefficients for different molecular orientation configurations. (Modified from Donald and Windle, 1992.)...

Table 6.11. The second NLO coefficients of several important NLO inorganic materials and the organic crystal MNA (The Chemical Rubber Company, 1971) (unit 10-12m/V).

The third NLO susceptibility may not be zero even though the molecular orientation is completely randomly distributed, i.e., in an isotropic state. The highly ordered phase usually has a high value for the third NLO coefficient. For example, the highly ordered nematic phase has a third NLO coefficient five times that in the isotropic phase. 

The NLO materials used so far are mainly inorganic materials, such as quartz, KDP, zinc oxide, LiNbOs, etc. The ions in these inorganic materials are responsible for the NLO properties. The ions have a great mass so that the NLO coefficients of these NLO materials are small at high frequency. Table 6.11 lists elements of the NLO tensors of the Pockel effect and of the second harmonic generation for some widely used NLO materials, Xp and x(d ... 

In order to achieve high second NLO coefficients, a concept of the following conjugate molecules was proposed ... 

The organic materials with the appropriate second NLO coefficient are classified as three different kinds ... 

The side chain polymeric liquid crystal (as host) is doped with NLO active small molecules (as guest). In the matrix of side chain polymeric liquid crystals, the NLO active molecules are aligned along the director. The system is then poled and processed. Meredish et al. (1982) adopted a side chain polymeric liquid crystal as the host and DANS as the dopant, as shown in Figure 6.32. The pole field is 1.3KV/mm. The resultant second NLO coefficient reached 6 x 10-9 esu. The glass temperature of the polymers is low (Tg < 50 °C) thus the orientation is not good enough. 

Figure 6.33. The NLO coefficient (I33 of a side chain liquid crystalline polymer PMMA as a function of restore time. (Modified from Singer et al., 1988.)...

Amorphous side chain polymers with NLO active side groups have an appropriate second NLO coefficient. But further study revealed that these side chain polymers if in the liquid crystal phases have better NLO behavior. For the side chain polymer shown below, x = 8 x 10 9esu in a liquid crystal phase which is greater than the value in the amorphous phase by a factor 1.5. The poling field in both cases is 15KV/mm (Amano et al., 1990). 

In general, the ways to promote the third NLO coefficient is consistent with the methods that promote the second NLO coefficients. For the former, it is not necessary to pole samples. The molecule does not necessarily have to have a non-symmetrically electronic structure. According to recent calculation by Medrano (1989) the molecules with donor (or acceptor) groups at their terminal exhibit high molecular NLO polarizability 7 and hence a high third NLO coefficient x. ... 

Figure 6.36. The comparison of the Pockel coefficient 733 and the second NLO coefficient d33. (Modified from Dubois et al., 1993.)...

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