## 2 Electro-Optic Properties of Polymers
### Inducing of the Macroscopic Electro-Optic Properties  
Up to now, we described the nonlinear optical properties of a single molecule. However we are generally interested to the nonlinear optical response of bulk macroscopic materials made out of a large number of such molecules. In order to evaluate the nonlinear response of the whole macroscopic material it is not sufficient to know the nonlinear properties of the single molecule, but we need to consider the number of chromophores per volume unit and their orientation inside the macroscopic structure. In particular, the macroscopic nonlinear optical properties increase with the density of oriented chromophores. Considering a system constituted by molecules with large \(\beta\), if they are isotropically oriented in the space, the macroscopic second order dielectric susceptibility \(\chi^{(2)}\) is zero because the material, as a whole, is centrosymmetric. Since we are interested in electro-optic applications, we need to achieve a high \(\chi^{(2)}\) value and consequently we need to fabricate a structure in which the nonlinear molecules are oriented in a polar order. One way is to realize a solid solution of highly nonlinear molecules in a high optical quality passive polymer matrix. The matrix, in order not to interfere with the optical properties of the chromophore, is in general transparent in the wavelength used for applications and can be considered as optically linear; it is just a host material that gives mechanical stability to the ensemble of nonlinear molecules. One of the most used polymer matrices is the poly-methyl-metha-acrylate (PMMA) [12] whose chemical structure is shown in Figure 2(b). Usually, the material is deposited onto different types of substrates by spin-coating, producing amorphous thick films (1\(\sim\)2 \(\upmu\)m). The chromophores, \begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline
**Chromophore** & \(\lambda_{\text{max}}\) **(nm, CHCl\({}_{3}\))** & \(\mu_{0}\) **(Debye)** & \(\beta_{0}\) **(10\({}^{\text{-30}}\) esu)** & \(\beta_{1,9_{\text{mm}}}\) **(10\({}^{\text{-30}}\) esu)** & \(\mu_{0}\beta_{1,9_{\text{mm}}}\) **(10\({}^{\text{-48}}\) esu)** \\ \hline DR1 & 480 (497) & 7.7 (8.7) & 40 & 5,046 & 580 \\ \hline \end{tabular}
\end{table} 
Table 1: Characteristic data of the Disperse Red 1 (DR1) molecule. Figure 2: **(a)** Chemical structure of the Disperse Red 1 (DR1) and **(b)** of the (poly)-methyl-metha-acrylate (PMMA). randomly oriented at the end of the film deposition procedure, must be aligned in a non-centrosymmetric fashion after deposition by means of a poling procedure, as we shall describe later. There are several ways of introducing nonlinear optical chromophores into the polymer matrix. The two most common methods are dissolving (guest-host systems) and covalently attaching (functionalized system) the chromophores to the polymer. In the guest-host system, nonlinear optic (NLO) chromophores are dissolved, in the polymer host. The principal disadvantages of such a structure are: (i) low nonlinear activity, that it is due to the dopant maximum solubility (largest concentration is about 10% of the host weight), because greater concentrations can lead to chromophores' aggregation or crystallization; (ii) the presence of optical losses due to scattering originated by the non homogeneity of the structure; (iii) the thermal and temporal instability, in fact, the chromophores are not attached at the polymer matrix and they can move with a higher degree of freedom. In the functionalized systems, the chromophores are attached to the polymer matrix, and the relative dopant concentration can be much higher than in guest-host systems. Moreover functionalized systems are more stable since their orientational mobility is significantly hindered and the order of such systems therefore relaxes more slowly. In the functionalized systems nonlinear optical chromophores can be incorporated in the polymer matrix by chemically attaching them into the polymer main-chain (or backbone) or as a pendant side-group.