While analytical techniques to study electric field distribution for an electrode-pair placed on two parallel opposite faces of a crystal (or channel) exist, but for the configuration with inclined opposite crystal faces such analysis is not straightforward. Here Schwarz-Christoffel mapping method, a special form of Conformal mapping technique, is used to study electric field distribution for parallel and non-parallel electrode-pair respectively. Being an analytical technique, the simulations are fast compared to numerical methods. A scheme on how variable polarization phase can be introduced when the electrode-pair is placed on the non-parallel faces of a specially designed trapezoidal shaped electro-optic lithium niobate crystal is also given in this work. It is also shown that by using multiple strip electrodes, tunability of the polarization phase difference can be achieved. Random optimization based on genetic algorithm has been used to optimize the device structure parameters to obtain desired phase shift. © 2015 EDP Sciences.