Susceptibility tensor elements

Notice that /pijn = nonlinear susceptibility tensor elements... 

Eq. 12), Eq. (25) is valid in the Fourier domain and relates the components of the susceptibility tensor elements and the complex components of the electric field and polarization. All quantities are frequency dependent. The general expression of the second-order nonlinear polarization is given by [10] ... 

In the case of second-harmonic generation, the second-order nonlinear susceptibility tensor elements are symmetric in their last two Cartesian indices and are unchanged by the permutation of their second and third frequency arguments because they are identical. Thus, Eq. (28) can be rewritten in the simplified form... 

To understand and optimize the electro-optic properties of polymers by the use of molecular engineering, it is of primary importance to be able to relate their macroscopic properties to the individual molecular properties. Such a task is the subject of intensive research. However, simple descriptions based on the oriented gas model exist [ 20,21 ] and have proven to be in many cases a good approximation for the description of poled electro-optic polymers [22]. The oriented gas model provides a simple way to relate the macroscopic nonlinear optical properties such as the second-order susceptibility tensor elements expressed in the orthogonal laboratory frame X,Y,Z, and the microscopic hyperpolarizability tensor elements that are given in the orthogonal molecular frame x,y,z (see Fig. 9). 

O.S.Thus, for small poling fields, when the linear approximation for the Langevin functions holds, the two independent susceptibility tensor elements given by Eqs. (66) and (67) give... 

In the case of second harmonic generation, for example, the second-order susceptibility tensor elements are symmetrical in their last two indices. Therefore, the number of independent tensor elements is reduced from 27 to 18. Moreover, the tensor elements be expressed in contracted form [j The index I takes... 

The symmetry group of ZnO is P63mc (Hermann-Mauguin notation) and (Schoenflies notation). In optical nonlinearity nomenclature, hexagonal ZnO has class 6 mm symmetry. This being the case, many of the susceptibility tensor elements vanish. The only nonvanishing components are dn, di4 = dn, dn, dn = dn, and dn . 

Second-order nonlinear optical properties describe the coupling interaction between two electric fields (as described in Equation 3.129) and the crystal. For the ideal wurtzite ZnO, with the 6 mm symmetry, there are four nonvanishing second-order nonlinear susceptibility tensor elements, = Xm- and... 

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