This paper considers a dielectric waveguide that is uniform in the z direction and composed of N homogeneous regions with ∊ = ∊k and µ = µk (k = 1, 2, …, N). If the electromagnetic field of a specified mode is tightly confined in the vicinity of the k th region, the phase constant β would be mainly determined by ∊k and µk. We present a few simple general relations between dispersion and power-flow distribution. For example, the sum of ∊kµk’s weighted by Pk/∑Pk, where Pk denotes the fractional power carried in the k th region, is equal to 1/vp vg. Another main result is that the partial derivative ∂(β2)/ω2∂(∊kµk) is close to Pk/∑Pk in a weakly guiding dielectric waveguide. Applications of them to analysis of a dielectric surface waveguide are discussed.
Shojiro Kawakami, "Relation between dispersion and power-flow distribution in a dielectric waveguide," J. Opt. Soc. Am. 65, 41-45 (1975)