抄録
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 εr2 > 1 where εr2 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)| ≤ εr22n−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⋅3k)| ≤ εr22n−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.
