Strong Resonance of Light in a Cantor Set(Condensed Matter : Electronic Structure, Electrical, Magnetic and Optical Properties)

概要

論文の詳細を見る
The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately 6/|η_r|, where η_r is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime τ_r=4.3ms and of the enhancement factor M=7.8×10^7 is found at the resonant frequency ω_r=367GHz for the Cantor set of the fourth generation of length L=10cm made of a medium of the dielectric constant ε=10.
社団法人日本物理学会の論文
2005-11-15