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

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Abstract
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/ΣPk, where Pk denotes the fractional power carried in the k th region, is equal to 1/νpνg. Another main result is that the partial derivative ∂(β2)/ω2∂(∊kμk) is close to Pk/ΣPk in a weakly guiding dielectric waveguide. Applications of them to analysis of a dielectric surface waveguide are discussed.

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