Wave propagation through Cantor-set media: Chaos, scaling, and fractal structures

Abstract

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 ${\mathrm{C}}_{\infty }$. 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 $\kappa ={\kappa }^{\ast }$ with a rational ${\kappa }^{\ast }/\pi$. The scaling function is obtained analytically by using the Euler's totient function, and the local scaling behavior is confirmed numerically.

arXiv comment30 pages, 18 figures; added Sec.3C discussing further details about optical experiments

References in corpus (2)

• Strong Resonance of Light in a Cantor Set
• Electronic transport in a Cantor stub waveguide network

Cited by in corpus (6)

• Octonacci Photonic Crystals with Negative Refraction Index Materials
• Local symmetry dynamics in one-dimensional aperiodic lattices
• Photonic Properties of Metallic-Mean Quasiperiodic Chains
• Dyadic Cantor set and its kinetic and stochastic counterpart
• Light Transmission Through Metallic-Mean Quasiperiodic Stacks with Oblique Incidence
• Tunneling from general Smith-Volterra-Cantor potential