Monochromatic energy exchanges in thin-film dielectric waveguides can be understood in terms of a zig-zag ray picture that includes Goos-Haenchen shifts that occur at the film boundaries, as pointed out by Burke. Recently, Kogelnik and Weber have shown that, in order to predict the correct modal group velocity, the ray model should also include the time delay associated with the ray shifts at the film boundaries. In this paper, we explore in detail the ray-optical descriptions of anisotropic film waveguides that consist of three-layered biaxial materials with one of the principal axes of the crystal in each of the three media oriented in the direction of propagation and the other two parallel and perpendicular to the plane of the film. We show that the Burke-Kogelnik-Weber (BKW) ray model provides a complete description of energy flow in such anisotropic structures. Expressions for the ray shift, group velocity, power flow, and stored energy, applicable to both TE and TM modes, are presented.
V. Ramaswamy, "Ray model of energy and power flow in anisotropic film waveguides," J. Opt. Soc. Am. 64, 1313-1320 (1974)