The slab-coupled waveguide, consisting of a dielectric rod lying on a slab that in turn covers a substrate, is a multidielectric waveguide that includes such special cases as the single-material fiber, the rib waveguide, and the strip-loaded film guide. These guides have recently become known as potentially useful either for long-distance optical transmission or for integrated optics. Simple, closed-form, approximate solutions have been found to describe the following properties of the guide: number of modes, their field configurations and propagation constants, numerical aperture, requirements for single-mode operation, field penetration in the slab, tolerance to curvature of the guide axis, dispersion, and impulse response.