The electro-optical effect of the fourth order

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Abstract
The sixth-rank tensor K describing the nonlinear electro-optical fourth-order effect has been calculated. A relationship between the non-zero components of the above tensor for all 32 crystallographic classes is shown. The calculations were executed with the aid of a tensor function describing the dependence of the dielectrical impermeability tensor on the electrical field tensor. It has been shown that changes in the optical properties of crystals due to the fourth-order electro-optical effect are similar to those brought about by the Kerr effect.