Nonlinear optical molecular coefficients

However, its was found possible to infer all four microscopic tensor coefficients from macroscopic crystalline values and this impossibility could be related to the molecular unit anisotropy. It can be shown that the molecular unit anisotropy imposes structural relations between coefficients of macroscopic nonlinearities, in addition to the usual relations resulting from crystal symmetry. Such additional relations appear for crystal point group 2,ra and 3. For the monoclinic point group 2, this relation has been tested in the case of MAP crystals, and excellent agreement has been found, triten taking into account crystal structure data (24), and nonlinear optical measurements on single crystal (19). This approach has been extended to the electrooptic tensor (4) and should lead to similar relations, trtten the electrooptic effect is primarily of electronic origin. 

Theoretical estimations and experimental investigations tirmly established (J ) that large electron delocalization is a perequisite for large values of the nonlinear optical coefficients and this can be met with the ir-electrons in conjugated molecules and polymers where also charge asymmetry can be adequately introduced in order to obtain non-centrosymmetric structures. Since the electronic density distribution of these systems seems to be easily modified by their interaction with the molecular vibrations we anticipate that these materials may possess large piezoelectric, pyroelectric and photoacoustic coefficients. 

In this paper, an overview of the origin of second-order nonlinear optical processes in molecular and thin film materials is presented. The tutorial begins with a discussion of the basic physical description of second-order nonlinear optical processes. Simple models are used to describe molecular responses and propagation characteristics of polarization and field components. A brief discussion of quantum mechanical approaches is followed by a discussion of the 2-level model and some structure property relationships are illustrated. The relationships between microscopic and macroscopic nonlinearities in crystals, polymers, and molecular assemblies are discussed. Finally, several of the more common experimental methods for determining nonlinear optical coefficients are reviewed. 

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)... 

Nonlinear optical properties depend upon the molecular environment as well as the individual molecular prop erties. In particular, at the molecular level, second harmonic generation depends upon the magnitude of p (the quadratic hyperpolarizability), which is the coefficient... 

We have seen how the molecular properties in nonlinear optics are defined by the expansion of the molecular polarization in orders of the external electric field, see Eq. (5) beyond the linear polarization this definition introduces the so-called nonlinear hyperpolarizabilities as coupling coefficients between the two quantities. The same equation also expresses an expansion in terms of the number of photons involved in simultaneous quantum-mechanical processes a, j3, y, and so on involve emission or absorption of two, three, four, etc. photons. The cross section for multiphoton absorption or emission, which takes place in nonlinear optical processes, is in typical cases relatively small and a high density of photons is required for these to occur. 

X-ray data showed that the molecular arrangement in the crystal is drastically different for 2-(3,5-dimethyl-lH-l,2,4-triazolyl)-5-nitropyri-dine and 3,5-dimethyl-l-(4-nitrophenyl)-lH-l,2,4-triazole despite the same crystal space group. The difference in molecular arrangement influences the nonlinear optical coefficients for a blue light second-harmonic generation device (94BCJ1936). 

Polycondensation and imidization of w,w -diaminobenzophenone and pyromellitic dianhydride under microwave radiation was also carried out. The product polyimide was obtained in a two-step process. It is claimed that this product of microwave radiation polymerization compares favorably with a product of conventional thermal polymerization, because it exhibits third-order nonlinear optical coefficient of 1.642 x 10 esu and response time of 24 ps. The third-order optical nonlinearity of this polymer is dependent on the chain length and the molecular structure. 

A wide variety of molecular properties can be accurately obtained with ADF. The time-dependent DFT implementation " yields UV/Vis spectra (singlet and triplet excitation energies, as well as oscillator strengths), frequency-dependent (hyper)polarizabilities (nonlinear optics), Raman intensities, and van der Waals dispersion coefficients. Rotatory strengths and optical rotatory dispersion (optical properties of chiral molecules ), as well as frequency-dependent dielectric functions for periodic structures, have been implemented as well. NMR chemical shifts and spin-spin couplingsESR (EPR) f-tensors, magnetic and electric hyperfme tensors are available, as well as more standard properties like IR frequencies and intensities, and multipole moments. Relativistic effects (ZORA and spin-orbit coupling) can be included for most properties. 

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