Optical characterization polarizability tensor

An axially symmetric molecule is characterized by its linear polarizability in the principal axes a x and a y = a" and a" = af/. It is a good approximation to assume that its second- and third-order polarizability tensors each have only one component and respectively, which is parallel to the z principal axis of the molecule. For linear and nonlinear optical processes, the macroscopic polarization is defined as the dipole moment per unit volume, and it is obtained by the linear sum of the molecular poiarizabilities averaged over the statistical orientational distribution function G(Q). This is done by projecting the optical fields on the molecular axis the obtained dipole is projected on the laboratory axes and orientational averaging is performed. The components of the linear and nonlinear macroscopic polarizabilies are then given by ... 

O Equation 11.84 defines the components of the dynamic electric dipole polarizability tensor, cCf,v -coa-, o)i), those of the first electric dipole hyperpolarizabUity,j8 v(/ (-Wa wi, W2), and those of the second electric dipole hyperpolarizabUity yf,v ((-coa coi, C02, (03). The combination of frequencies and the presence or absence of static fields characterize various nonlinear processes. The calculations can be done for any combination of frequencies satisfying O Eq. 11.85, but only selected examples of the most commonly studied optical phenomena will be discussed below (see, e.g., Willets et al. 1992 and Bogaard and Orr 1975 for more details). 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

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