Wave propagation in a quasi-periodic waveguide network

TL;DR

This paper studies how classical waves, electromagnetic or acoustic, propagate through a Fibonacci quasi-periodic waveguide network, revealing conditions for resonant transmission and patterns of wave intensity.

Contribution

It introduces a general formulation for wave transport in Fibonacci waveguides and identifies local correlations responsible for resonant transmission and mode patterns.

Findings

Resonant transmission depends on local positional correlations.

Wave intensity patterns can be periodic or self-similar.

Extended modes are observed in certain configurations.

Abstract

We investigate the transport properties of a classical wave propagating through a quasi-periodic Fibonacci array of waveguide segments in the form of loops. The formulation is general, and applicable for electromagnetic or acoustic waves through such structures. We examine the conditions for resonant transmission in a Fibonacci waveguide structure. The local positional correlation between the loops are found to be responsible for the resonance. We also show that, depending on the number of segments attached to a particular loop, the intensity at the nodes displays a perfectly periodic or a self-similar pattern. The former pattern corresponds to a perfectly extended mode of propagation, which is to be contrasted to the electron or phonon characteristics of a pure one dimensional Fibonacci quasi-crystal.