Periodic strings: a mechanical analogy to photonic and phononic crystals

TL;DR

This paper introduces a periodic string system that mimics photonic and phononic crystals, demonstrating wave bandgaps and exploring parameter effects, providing an accessible physics laboratory model.

Contribution

It presents a novel mechanical analogy to photonic and phononic crystals using a finite periodic string system suitable for undergraduate labs.

Findings

Identification of frequency bandgaps in the string system

Effect of physical parameters on bandgap properties

Analogies with electronic wave propagation in crystals

Abstract

We study a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a configuration that can mimic the properties of photonic or phononic crystals and could be implemented in undergraduate physics laboratories. We demonstrate that this configuration displays frequency intervals for which wave propagation is not allowed (frequency bandgaps), in close analogy to photonic and phononic crystals. We discuss the behavior of these bandgaps when varying physical parameters, such as the values of the linear mass densities, the oscillation frequency, and the number of strings constituting the entire system. Some analogies with the propagation of electronic waves through a crystal lattice in condensed matter physics are also explored.