Ferroelectrics have anisotropic electronic bonds Birefringence

1 Ferroelectrics have anisotropic electronic bonds Birefringence 

How do we describe the polarization states of light, which are not polarized parallel to one of the main crystalline axes We have to look at the different components of E parallel to the main axes, evaluate their propagation and at the end of the optical path add them up to the resulting beam. 

With respect to the crystal, this is visualized by the index ellipsoid or indicatrix. (In a homogeneous medium this would be a sphere.) Without external field, the indicatrix is oriented along the main crystallographic directions. 

The subject may become a little involved, if an external electrical field is applied Ions move, bonds are deformed and even the first-order equations for the change of the indicatrix must include the cross-terms, which describe the rotation of the ellipsoid. We follow the notation of [2] and write for the indicatrix in the presence of an electric field 

This ellipsoid is tilted with respect to the x, y, z-axes and the parameters By are a function of the electric field E. In order to couple the six constants By to the three components of E, 18 coefficients are needed. They are arranged in the form of a 3 x 6 matrix, which is sometimes called the electro-optic tensor  

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