Experimental Evidence of Rainbow Trapping and Bloch Oscillations of Torsional Waves in Chirped Metallic Beams

A Arreola-Lucas,R A Méndez-Sánchez,A Climente,G Báez,J Sánchez-Dehesa,F Cervera

doi:10.1038/s41598-018-37842-7

Abstract

The Bloch oscillations (BO) and the rainbow trapping (RT) are two apparently unrelated phenomena, the former arising in solid state physics and the latter in metamaterials. A Bloch oscillation, on the one hand, is a counter-intuitive effect in which electrons start to oscillate in a crystalline structure when a static electric field is applied. This effect has been observed not only in solid state physics but also in optical and acoustical structured systems since a static electric field can be mimicked by a chirped structure. The RT, on the other hand, is a phenomenon in which the speed of a wave packet is slowed down in a dielectric structure; different colors then arrive to different depths within the structure thus separating the colors also in time. Here we show experimentally the emergence of both phenomena studying the propagation of torsional waves in chirped metallic beams. Experiments are performed in three aluminum beams in which different structures were machined: one periodic and two chirped. For the smaller value of the chirping parameter the wave packets, with different central frequencies, are back-scattered at different positions inside the corrugated beam; the packets with higher central frequencies being the ones with larger penetration depths. This behavior represents the mechanical analogue of the rainbow trapping effect. This phenomenon is the precursor of the mechanical Bloch oscillations, which are here demonstrated for a larger value of the chirping parameter. It is observed that the oscillatory behavior observed at small values of the chirp parameter is rectified according to the penetration length of the wave packet.

Highlights

Mechanical waves have been converted in a golden vein
We have experimentally demonstrated the mechanical analogue of rainbow trapping and Bloch oscillations in one-dimensional elastic systems
Both effects have been extensively described in different structures supporting the propagation of electronic, photonic or acoustic waves but scarcely in elastic structures

Summary

Introduction

Several physical effects emerging in quantum and classical waves, that cannot be observed in other fields of physics, can be observed with vibrations: losses and decoherence do no affect strongly them. The emergence of two effects in torsional waves, the Bloch oscillations and the rainbow trapping, is shown. The former was firstly found in quantum mechanics and the latter in metamaterials, a close relationship between both phenomena is here experimentally reported. Bloch oscillations are expected to occur on vibrating structures and experimental demonstrations of this effect for any of the different mechanical waves that can be propagated on them are of great interest.

Methods

Results

Conclusion