Nonlinear second-order optical nonlinearity

Nonlinear second order optical properties such as second harmonic generation and the linear electrooptic effect arise from the first non-linear term in the constitutive relation for the polarization P(t) of a medium in an applied electric field E(t) = E cos ot. 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

For obtaining the information on fabrication of noncentrosymmetric LB films with highly efficient second-order optical nonlinearity, six azobenzene-linked amphiphiles were synthesized as a model compound, and their molecular hyperpolarizabilities (3, monolayer-formation at the air-water interface, and molecular orientation and second-order susceptibilities of the azobenzene-linked amphiphiles LB films were evaluated. The molecular structures of the azobenzene-linked amphiphiles are shown in Fig.2. 

Using the alternating deposition of the amphiphiles with a carboxyl substituent and arachidic add, noncentrosymmetric LB films (hetero Y-type) were prepared, and molecular orientation and second-order optical nonlinearity in the LB films were evaluated with the linear dichroism [4] and the second-harmonic generation (SHG) measurements, respectively. The SHG measurement procedure is mentioned in the section 1.3. 

The presence of only one Si(OR )3 unit per chromophore makes the formation of a highly crosslinked sol-gel network very difficult. The high mobility of the NLO dye in the free volume of the host network causes relaxation of the poling-induced order. Presently, the most promising approach to improve the stability of the second-order optical nonlinearity is therefore the use of multiple-substituted dyes, such as 2083. 

Second-order optical nonlinearities result from introduction of a cubic term in the potential function for the electron, and third-order optical nonlinearities result from introduction of a quartic term (Figure 18). Two important points relate to the symmetry of this perturbation. First, while negative and positive p both give rise to the same potential and therefore the same physical effects (the only difference being the orientation of the coordinate system), a negative y will lead to a different electron potential than will a positive y. Second, the quartic perturbation has mirror symmetry with respect to a distortion coordinate as a result, both centrosymmetric and noncentrosymmetric materials will exhibit third-order optical nonlinearities. If we reconsider equation 23 for the expansion of polarization of a molecule as a function of electric field and assume that the even-order terms are zero (i.e., that the molecule is centrosymmetric), we see that polarization at a given point in space is ... 

In general, the optimization of organic molecules for third order nonlinear optical applications has enjoyed much less success than for second order optical nonlinearities. The major reason for this has been the questionable validity of the two-level model for y, and the difficult assessment of the contribution of two-photon states for the more acceptable three-level model. 

Since the dipoles of chromophore molecules are randomly distributed in an inert organic matrix in amorphous PR materials, the material is centrosymmet-ric and no second-order optical nonlinearity can be observed. However, in the presence of a dc external field, the dipole molecules tend to be aligned along the direction of the field and the bulk properties become asymmetric. Under the assumption that the interaction between the molecular dipoles is negligible compared to the interaction between the dipoles and the external poling field (oriented gas model), the linear anisotropy induced by the external field along Z axis at weak poling field limit (pE/ksT <[Pg.276]

Assessing thermal and photochemical stability is important. Thermal stability can be readily measured by measuring properties such as second harmonic generation as a function of heating at a constant rate (e.g., 4-10 °C/min) [121]. The temperature at which second-order optical nonlinearity is first observed to decrease is taken as defining the thermal stability of the material [2,3,5,63,63]. It is important to understand that the loss of second-order nonlinear optical activity measured in such experiments is not due to chemical decomposition of the electro-optic material but rather is due to relaxation of poling-induced acentric... 

Kanis DR, Ratner MA, Marks TJ (1994) Design and construction of molecular assemblies with large second-order optical nonlinearities. Quantum mechanical aspects. Chem. Rev. 94 195—242... 

Teng, C.C. and Garito A.F., Dispersion of the nonlinear second-order optical susceptibility of organic systems. Phys. Rev. B (1983) 28 6766-6773. 

However, as far as interplay of conductivity and second-order NLO in hybrid molecular materials is concerned, very few studies are available (534, 535). As previously mentioned, both conducting and second-order NLO properties are formally connected to the same concept of charge transfer, though intermole-cular in conductors but intramolecular in compounds exhibiting second-order optical nonlinearity. Attempts to associate the [Ni(dmit)2] anion with cationic cyanine dyes known to exhibit second-order optical non-linearity such as DAMS+ (4-dimethylamino-l-methylstibazolium), DAMP+ (4-dimethylamino-1-methylpyridinium) and NOMS+ (4 -nitro-l-methylstibazolium) (Scheme 28)... 

Second order optical nonlinearity can be induced in polymeric systems containing dipolar (donor-acceptor) chromophores. The chromophore can be a molecular species attached to the host chain or it can be incorporated in the polymeric structure itself. In general, a good chromophore has an electron donating group connected to an electron... 

Second harmonic is a convenient in situ probe of the dynamics of photoisomers in a polymer environment if the photoisomers have a second-order optical nonlinearity. A corona discharge is used to apply a large electrostatic field to align the molecules. When a change in the orientation of the photoisomers is induced through photoisomerization, second harmonic generation is used to follow the changes in the state and orientation of the photoisomers. 

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