Second-order susceptibility coefficient

Actually, it has been shown that the highest second order susceptibility coefficients (macroscopic nonlinearity), for a given chromophore (microscopic nonlinearity), can be reached in the (polar) crystal classes 1, 2, m and mm2, while other polar crystal classes are less favourable [21]. 

We have heretofore had ample discussion of linear optical properties of ZnO and related materials. In this section, the nonlinear processes in ZnO are discussed, a topic that has been investigated in some detail. The research on nonlinear optical properties of semiconductors is motivated by electro-optic devices that can be used in telecommunications and optical computing as efficient harmonic generators, optical mixers, and tunable parametric oscillators, among others. The nonlinear optical properties such as second harmonic generation (SHG), that is, (2(0i, 2(02), and the sum frequency generation (SFG), that is, (materials characterization, particularly surfaces, because the second-order susceptibility coefficient is very sensitive to the change in symmetry (178,179). The crystal should be... 

To fit the experimental results, it is necessary to fix the overall phase. This can be done, for example, by defining h as a real quantity (/ / = 0). The values found for the coefficients /, g, and h can then subsequently be used to calculate the values of the components of the second-order susceptibility, X(2). This is done in detail for a Langmuir-Blodgett film of a poly(isocyanide) in the following section. Note that both phase and magnitude of all tensor components are relative values. The absolute phase cannot be determined... 

The electro-optic coefficient in a poled polymer film can be related to the second-order susceptibility as shown in Equation 5. 

Based upon the method of calculation adopted, a complete computer programme consisting of three main parts can easily be written for support of such calculations. The three parts are as follows (a) the CNDO part or EHMO part with Madelung correction for calculation of the localized electron orbitals in the anionic group (b) the transition matrix element calculation part and (c) the second-order susceptibility part for the calculation of the microscopic susceptibility of the anionic group followed by the calculation of the macroscopic SHG coefficients of the crystal. 

SHG coefficients of KB5 amount only to one tenth that of KDP. In case there exists a crystal consisting of the same basic structural unit [Bd06(0H)4] but crystallizing in point group either C2 or D2, the component X-/25 of the microscopic second-order susceptibility will make its contribution to the overall SHG effect of the crystal and exhibit as large an overall effect as half of that of KDP. This is left for further consideration. 

The odd order susceptibilities are nonzero in all materials. However, owing to the fact that x is a third rank tensor, the second order susceptibility is nonzero only in noncentrosym-metric materials, that is, materials possessing no center of symmetry. The focus of this paper is on second order processes, and the relationships between the bulk susceptibility, second harmonic generation, and the linear electro-optic effect. For second harmonic generation, Xijl is symmetric in ij, leading to the relationship between the second harmonic coefficient dijk and the bulk second order susceptibility x 2)[i2l... 

The steps to be followed may be summarized. Secular determinants must be constructed for each of the doubly degenerate levels in both directions. First-order Zeeman coefficients must be evaluated for each direction. Matrix elements connecting the three secular determinants must be evaluated to yield second-order Zeeman coefficients. The first-and second-order Zeeman coefficients must be substituted into the Van Vleck equation to yield the anisotropic magnetic susceptibilities x and x - Generally, anisotropic magnetic properties are discussed in terms of /x and n since the variation of these anisotropic components are much more easily visuaUzed. 

As can be inferred from Equation 11.1, for a transparent medium at frequency CO and taking into account the losses by absorption with coefficient a at frequency 2co, the light-induced second-order susceptibility can be written as... 

Since the ground state second order Zeeman coefficient is proportional to — 1/A, this vibronic interaction has a profound influence on the magnetic properties of the [Ti(OH2)6] + cation [50, 54, 55], With just the ground state populated, the susceptibility and effective magnetic moment have the form ... 

The three principal magnetic susceptibilities Xx, Xy and %z can then be calculated through the Van Vleck equation, which requires the eigenvalues and eigenfunctions of % defined in Eq. (55), and the first and second order Zeeman coefficients. 

This expression shows that the electiooptic coefficients are proportional to the second order susceptibility. In the centrosymmetric materials, ryt constitues the component of a third order coefficient. Values of t33 and na can be calculated and measured. 

Several techniques have been developed for determining the second-order susceptibility [24]. Of practical importance are methods that may be employed for aligned polymeric systems containing polar moieties [4, 8]. Methods making use of the Pockels or linear electro-optic (EO) effect are based on the measurement of the variation in the refractive index of thin polymer films induced by an external electric field. In this way, values of the electro-optic coefficients rss and in are obtained, which are related to the corresponding values through Eq. (3.16). 

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