The refractive index changes due to the electroptic effect are discussed when external electric fields $E_x, E_y, E_2$ are applied on $LiNbO_3$, a typical anisotropic material. Derived are approximate equations for principal axis' rotations and index changes, results of which are compared with exact results by te computer simulations. In each useful application of $LiNbO_3$substrate, the results of the approximate equations are confirmed to agree with exact solutions.
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