Using the transmission-line theory, we will investigate properties of wave propagation and resonance in fractal pre-Cantor multilayers called pre Cantor Bars as shown in Fig.1. When the stage number
n increases, the pre-Cantor bar will not transmit almost anywhere for ε
r2 > 1 where ε
r2 is the ratio of dielectric constants of two kinds of layers. For resonance frequencies of the
n-th pre-Cantor bar, the largest amplitude of voltages at the midpoint of the bar,
V(
L⁄2), increases double-exponentially because of the inequality |
V(
L⁄2)| ≤ ε
r22n−2. For such a resonance frequency, an amplitude of the voltage at the midpoint of a white region in Fig.1 is given by |
V(
L⁄2⋅3
k)| ≤ ε
r22n−k−2 . Because the voltage |
V(χ)| is localized around χ =
L⁄2, the EM localization occurs for the resonance frequency of the pre-Cantor bar of the higher stages.
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