Modes of a symmetric slab optical waveguide in birefringent media - Part II: Slab with coplanar optical axis

We study the modes of a symmetric thin-film slab waveguide composed of birefringent crystalline material in the film and in the equivalent substrate and superstrate. In addition we assume that the optical axes of the uniaxial materials of film and substrate are parallel to each other and also parallel (coplanar) to the plane of the film. This simple anisotropic waveguide has interesting properties. It supports only hybrid modes but in the limit of propagation along the optical axis and at right angles to it the modes become almost of the TE and TM type. Moreover, some of the modes become leaky waves as they propagate at increasingly larger angles relative to the optical axis of the dielectric material. For guides made of materials whose ordinary refractive index nois larger than the extraordinary index ne, the extraordinary wave modes, which approximate TE modes, become leaky; and fornₑ > nₒ, the ordinary wave modes, which approximate TM modes, become leaky. The leakage losses are large near a "critical angle," where leakage begins to appear but may be insignificant at larger angles, measured between the optical axis and the direction of propagation.