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

A set of two-dimensional electromagnetic equations is derived for guided waves in a dielectric plate surrounded by free space. In these equations, the interaction of the vibrating field in the plate with the evanescent field in free space is taken into account by satisfying the continuity conditions at the faces of the plate. Dispersion relations for straight-crested waves are obtained from the two-dimensional equations as a series of algebraic equations instead of the transcendental equations from the three-dimensional Maxwell´s equations. It is shown that the agreement is close between the approximate and exact dispersion curves for various orders of waves and for different values of refractive index