A mathematical model to study the phase difference introduced between the two orthogonal components of light wave due to electro-optic effect in a trapezoidal shaped lithium niobate single crystal has been made. Here, the electrodes are placed on the two opposite non-parallel faces such that the field is nearly perpendicular to the light beam direction. It is found that for the said geometry of the device structure, the maximum phase difference is a function of oblique angle between the two non-parallel faces, which has a critical value. Using random optimization technique based on genetic algorithm, the device parameters can be optimized for any required phase change between the two components of light wave. The phase difference between the two orthogonal components of light can be made tunable by using a multi-strip electrode structure. The advantage of this technique is that tunability can be obtained with a constant voltage source. © 2015 Copyright SPIE.