Transmission Properties of Electromagnetic Wave in Pre-Cantor Bar: Scaling and Double-Exponetiality

Ryota SATO  Keimei KAINO  Jun SONODA  

Publication
IEICE TRANSACTIONS on Electronics   Vol.E99-C   No.7   pp.801-804
Publication Date: 2016/07/01
Online ISSN: 1745-1353
DOI: 10.1587/transele.E99.C.801
Type of Manuscript: BRIEF PAPER
Category: 
Keyword: 
electromagnetic wave,  pre-Cantor bar,  resonance,  transmission-line theory,  scaling,  staircase distribution,  

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Summary: 
Pre-Cantor bar, the one-dimensional fractal media, consists of two kinds of materials. Using the transmission-line theory we will explain the double-exponential behavior of the minimum of the transmittance as a function of the stage number n, and obtain formulae of two kinds of scaling behaviors of the transmittance. From numerical calculations for n=1 to 5 we will find that the maximum of field amplitudes of resonance which increases double-exponentially with n is well estimated by the theoretical upper bound. We will show that after sorting field amplitudes for resonance frequencies of the 5th stage their distribution is a staircase function of the index.