Wave Propagation in the Cantor-Set Media: Chaos from Fractal

Abstract

Propagation of waves in the Cantor-set media is investigated by a renormalization-group type method. We find fixed points for complete reflection, $T^{\ast }=0$, and for complete transmission, $T^{\ast }=1$. In addition, the wave numbers for which transmission coefficients show chaotic behaviors are reported. The results obtained are for optical waves, and they can be tested in optical experiments. Our method could be applied to any wave propagation through the Cantor set.

arXiv comment4 pages, 6 figures

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