Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2009-01-24
Phys. Rev. E 79, 056226 (2009)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
30 pages, 18 figures; added Sec.3C discussing further details about optical experiments
Scientific paper
10.1103/PhysRevE.79.056226
Propagation of waves through Cantor-set media is investigated by renormalization-group analysis. For specific values of wave numbers, transmission coefficients are shown to be governed by the logistic map, and in the chaotic region, they show sensitive dependence on small changes of parameters of the system such as the index of refraction. For other values of wave numbers, our numerical results suggest that light transmits completely or reflects completely by the Cantor-set media ${\rm C}_{\infty}$. It is also shown that transmission coefficients exhibit a local scaling behavior near complete transmission if the complete transmission is achieved at a wave number $\kappa=\kappa^*$ with a rational $\kappa^*/\pi$. The scaling function is obtained analytically by using the Euler's totient function, and the local scaling behavior is confirmed numerically.
Esaki Kenta
Kohmoto Mahito
Sato* Masatoshi
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