Electronic Nonlinear Polarizations of Liquid Crystals

As we can see from this simple but general consideration of a multilevel molecule, nonlinear electronic polarizations occur naturally in all materials illuminated by an optical field. The differences among the nonlinear responses of different materials are due to differences in their electronic properties (wave functions, dipole moments, energy levels, etc.) which are determined by their basic Hamiltonian Hq. For Uquid crystals in their ordered phases, an extra factor we need to take into account are molecular correlations. 

The expressions for the molecular polarizabilities derived in the last two sections can be applied to a liquid crystal molecule if the Hamiltonian (and wave functions) of the liquid crystal molecule is known. To obtain the right Hamiltonian function and solve for the wave functions and the dipole matrix elements required for evaluating cnjj, Pyfc and of the actual liquid crystal molecule is a quautum chemistry prob- 

Several methods have beeu developed for calculating these molecular nonlinear polarizabilities. These methods have proven to be fairly reliable for predicting the second- and third-order molecular polarizabilities of organic molecules and polymers in general and liquid crystalline molecules in particular. For treating the ordered phases of liquid crystals, oue has to account for molecular correlations and ordering by introducing an orientational distribution function.  

Other important factors that should be accounted for are the local field corrections and the anisotropy of the molecules. In general, Uquid crystalUne molecules are complex and possess permanent dipole moments. Furthermore, quadrupole moments could also contribute significantly in second-order nonlinear polarizations, and thus the treatment presented in the preceding sections, which ignores these points, has to be appropriately modified. 

In the rest of this chapter, we address these and other macroscopic symmetry properties of liquid ciystalline electronic optical nonlinearities. 

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