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

TL;DR

This paper investigates wave propagation in Cantor-set media using a renormalization-group approach, revealing fixed points for reflection and transmission, and identifying wave numbers with chaotic transmission behaviors, applicable to optical experiments.

Contribution

Introduces a renormalization-group method to analyze wave behavior in fractal media, uncovering fixed points and chaos in transmission properties.

Findings

Fixed points for complete reflection and transmission identified.

Chaotic behaviors in transmission coefficients at specific wave numbers.

Method applicable to various wave types in Cantor-set media.

Abstract

Propagation of waves in the Cantor-set media is investigated by a renormalization-group type method. We find fixed points for complete reflection, $T^*=0$, and for complete transmission, $T^*=1$. 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.