An alternative description of multidimensional optics in liquid crystals and uniaxial media, which combines the geometrical optics approximation. (GOA) with the beam propagation method (BPM), is presented. In. this description, the two orthogonal GOA eigenmodes are used as a basis for development of beam propagation equations for the fields. The general treatment of this approach is developed both theoretically and numerically. The formalism is applied to liquid crystal devices with pixilated structures, and numerical results are compared with the GOA results.