Abstract

This paper considers a dielectric waveguide that is uniform in the <i>z</i> direction and composed of <i>N</i> homogeneous regions with ∊ = ∊<i><sub>k</sub></i> and µ = µ<i><sub>k</sub></i> (<i>k</i> = 1, 2, …, <i>N</i>). If the electromagnetic field of a specified mode is tightly confined in the vicinity of the <i>k</i> th region, the phase constant β would be mainly determined by ∊<i><sub>k</sub></i> and µ<i><sub>k</sub></i>. We present a few simple general relations between dispersion and power-flow distribution. For example, the sum of ∊<i><sub>k</sub></i>µ<i><sub>k</sub></i>’s weighted by <i>P<sub>k</sub></i>/∑<i>P<sub>k</sub></i>, where <i>P<sub>k</sub></i> denotes the fractional power carried in the <i>k</i> th region, is equal to 1/<i>v<sub>p</sub> v<sub>g</sub></i>. Another main result is that the partial derivative ∂(β<sup>2</sup>)/ω<sup>2</sup>∂(∊<i><sub>k</sub></i>µ<i><sub>k</sub></i>) is close to <i>P<sub>k</sub></i>/∑<i>P<sub>k</sub></i> in a weakly guiding dielectric waveguide. Applications of them to analysis of a dielectric surface waveguide are discussed.

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