Induced dipole moment second-harmonic generation

Experimental and theoretical results are presented for four nonlinear electrooptic and dielectric effects, as they pertain to flexible polymers. They are the Kerr effect, electric field induced light scattering, dielectric saturation and electric field induced second harmonic generation. We show the relationship between the dipole moment, polarizability, hyperpolarizability, the conformation of the polymer and these electrooptic and dielectric effects. We find that these effects are very sensitive to the details of polymer structure such as the rotational isomeric states, tacticity, and in the case of a copolymer, the comonomer composition. 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

Both theoretical analysis and dipole moment measurements indicated that sulfonyl-substituted compounds may have ft coefficients similar in magnitude to their nitro analogues. Therefore, we have measured p for several sulfonyl- and nitro-substituted compounds using electric-field-induced second-harmonic generation method (EFISH) (11,25). In this experiment, one measures an effective third-order nonlinearity rEFISH for a solution containing the compound of interest, given by... 

Fig. 3.25. The degree of order induced by poling can be determined using the results above to analyse the variation in second harmonic intensity as the poled sample is rotated about an axis normal to the fundamental beam. Generally, the low field limit, given by Equation (3.106), is found to apply and the degree of orientation is low. However, for molecules with large dipole moments th,e divergence from the low field limit shown in Fig. 3.25 can be observed, anil much higher orientation is obtained. The experimentally determined non-linearities are usually the electro-optical (r) and the second harmonic generation (d) coefficients. These are related to the hyperpolarisabilities by ...

The most traditional experimental determination of p is the electric field-induced second harmonic (EEISH) method, which requires the molecules to be aligned in solution by an electric field, by means of their static dipole moment (po). The EEISH signal is therefore proportional to po and to p <>c (projection of p on po), which is assumed to be equal to p in most cases. The bulk NLO properties are frequently evaluated as the efficiency of a powdered sample in second-harmonic generation (SHG), or as the d components of the x tensor. 

The lack of a permanent dipole moment in the cryptand-based molecules makes the classical electric field-induced second harmonic generation (EFISH) experiment (154) unsuitable for the determination of molecular nonlinearity p which, however, can be obtained in solution employing the hyper-Rayleigh scattering (HRS) technique (155). The powder SHG measurements were carried... 

Suslick et al. measured the first hyperpolarizabilities ()S) of porphyrins having electron-donor (amino) and -acceptor (nitro) groups in the para-position of 5,10,15,20-substituted tetraphenylporphyrins (Figure 25) using electric field induced second harmonic generation (EFISH) technique at 1.19 pm with chloroform solutions. The dipole moment (p) and P values were affected by the position of donor and acceptor groups. A P value of 30 x 10 esu and dipole moment of 7 x 10 esu were measured for the porphyrin having R = R = NO2, R = R = NH2 and the porphyrin... 

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2 > = > - - third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect co = co + 0), or the quadratic electrooptic (Kerr) effect ( > = > - - 0 -I- 0). These electrooptic effects are discussed extensively in the article Electrooptical Applications (qv). EFISH is... 

The earliest studied main-chain polymers consisted of chromophores with their dipole moments oriented head-to-tail along the polymer chain [127-129]. It was expected that this head-to-tail arrangement of the molecular dipole moments might result in a coherent enhancement of the second-order nonlinear properties [130]. Williams et al. [131,132] reported a series of head-to-tail materials based on 2-cyano-3-(4-hydroxyphenyl)-2-propenoate ester random copolymers [Structure (15)] prepared by transesterification. The homopolymers are insoluble, intractable materials, whereas copolymers are soluble and can be spun to form thin films. In those polymers, in which the dipoles of the individual chromophores point in one direction, large dipole enhancement will be observed. By electric field-induced second-harmonic generation (EFISH) measurements in solution, enhancement was observed but when extended to the polymer films, the expected enhancement in dipole moments and stability have been not realized. 

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. 

Molecular crystals are among the most efficient second- and higher-harmonic generating materials. An external electric field E, upon interacting with a molecule, will induce a dipole moment p. If the field is strong, the response may not be linear, in which case the components of p can be developed in increasing powers of E as described by the expansion (i = 1, 2, 3)... 

Most of the studies on push-pull phthalocyanines have been carried out by means of Electric Field Induced Second Harmonic (EFISH) Generation experiments in solution. Since only one experimental condition is favorable for EFISH, namely, parallel polarizations for all optical and static fields, these experiments lead to only one observable the vector component along the charge transfer axis assuming that the dipole moment vector and the vector part of the third-rank tensor along tlie molecular z-axis are collinear). 

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