Two-dimensional equations for guided electromagnetic waves in anisotropic dielectric plates surrounded by free space

Two-dimensional governing equations for guided electromagnetic waves in an anisotropic dielectric plate surrounded by free space are deduced from the three-dimensional Maxwell´s equations by expanding the electromagnetic vector potential in a series of trigonometric functions of thickness coordinate in the plate and in exponentially decaying functions of thickness coordinate in the upper and lower halves of free space. By further satisfying the continuity conditions of the electromagnetic field at the interfaces between the plate and free spaces, a single system of two-dimensional governing equations is obtained. Dispersion relations are obtained from the two-dimensional equations and computed for the doubly rotated cut of lithium niobate (yxlt)45°/5°. These dispersion curves are then compared with the corresponding ones obtained from the exact solutions of the three-dimensional Maxwell´s equations. It is shown that the agreement between the approximate and exact dispersion curves is very close