Relation between dispersion and power-flow distribution in a dielectric waveguide

Abstract

This paper considers a dielectric waveguide that is uniform in the z direction and composed of N homogeneous regions with ∊ = ∊_k and μ = μ_k (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 μ_k. We present a few simple general relations between dispersion and power-flow distribution. For example, the sum of ∊_kμ_k’s weighted by P_k/ΣP_k, where P_k denotes the fractional power carried in the k th region, is equal to 1/ν_pν_g. Another main result is that the partial derivative ∂(β²)/ω²∂(∊_kμ_k) is close to P_k/ΣP_k in a weakly guiding dielectric waveguide. Applications of them to analysis of a dielectric surface waveguide are discussed.