Electric field dependence of polarization and dipole moment

Electric field dependence of polarization and dipole moment 

Electric field-induced changes in refractive index can be explained with the aid of the following model under the influence of the electric field, the charge distribution in the molecules is perturbed and the molecules are polarized. The dipole moment pi induced by an electric field along the molecular axis can be expressed by an expansion [see Eq. (3-3)] [15]. 

/uq denotes the permanent dipole moment. The coefficients are tensors termed as linear polarizabihty, , and first and second molecular hyp erpolariz-abilities, and yijki, respectively. The indices refer to the tensor elements expressed in the frame of the molecule using Cartesian coordinates. Ej, E, and Ei denote the applied electric field strength components. Commonly, the response time ranges from picoseconds to femtoseconds. Therefore, if an alternating electric field with a frequency of less than 10 Hz is appHed, the direction of the polarization alternates with the oscillations of the appHed field. 

The polarization induced at the molecular level can cause a polarization in the bulk of the sample and lead to macroscopicaUy detectable property changes, for instance in the refractive index. The macroscopic polarization Pi induced by the electric field can be expressed by the expansion given by Eq. (3-4). 

Pq is the permanent polarization, and and denote the second- and third-order nonlinear optical three-dimensional susceptibility tensors. The indices attached to the x tensors refer to the tensor elements, and the indices associated with the E values refer to the components of the electric field strength, here expressed in the laboratory frame. 

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