Analytical solutions are derived for the electromagnetic E and H modes mn in a cylindrical wave guide of radius a and infinite length which is filled axially with media of different dielectric permittivity (ϵ) and magnetic permeability (μ) such that ϵ=ϵ1, μ=μ1 for -∞?z≪-d; ϵ=ϵ2, μ=μ2 for -d≪z≪+d; and ϵ=ϵ3, μ=μ3 for +d≪z?+∞. The power and the reflection and transmission coefficients of the E and H modes mn are given as functions of their frequency ω and the guide parameters ϵi, μi, a, and d. It is shown that the reflection and transmission coefficients exhibit a periodic fine structure for frequencies ω above the cutoff frequency ωmn, as a result of the spatial eigenvalue nature of the field solutions.
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