Resumen de Engineering non-hermitian and topological flow of sound
Acoustics is the branch of science responsible for studying the propagation of sound and vibrational waves. Among all the existing disciplines in acoustics the one related with sound propagation is precisely the most known. However, depending on the type of waves, the medium of propagation or the physical application of the study done, we can talk about aeroacoustics, noise, psychoacoustics, and engineering acoustics among other disciplines. The applications are so wide that they can be related with non-destructive evaluation of precision components, medical instruments such as the sonography, detection of danger, language, or other forms of communications and creation and appreciation of music. Nevertheless, the control of waves remains a challenge in all these domains since sound waves are not easy to treat.
Researchers started to make analogies between condense matter physics and classical physical theories more than 5 decades ago, giving rise to new disciplines in electromagnetics, optics, mechanics and also in acoustics. At first glance, one can think that condense matter physics and acoustics are not correlated. However, making use of mathematics, we can model completely different systems by similar mathematical equations. Schrödinger equation is a partial differential equation that governs the wave function of a quantum-mechanical system, whereas the acoustic wave equation governs the sound propagation through a fluid media. From a purely mathematical point of view both are wave equations.
In the last decades, acoustic and phononic metamaterial research was focused on finding new ways to modify the flow of sound waves at will. Through this project, we focus on exploring novel properties of sound by developing numerical code and theoretical methods to understand the acoustic analogy to non-Hermitian systems, topological insulators, and other exciting phenomena in condensed matter physics such as the magic angle in twisted bilayer graphene. Succinctly, we wish to translate these common notions of quantum mechanics into classical acoustics to find new properties for the case of sound.
Non-Hermitian acoustic structures can be achieved by balancing acoustic loss and gain units. Commonly known as Parity-Time (PT) symmetric structures, they have neither parity symmetry nor time-reversal symmetry but are nevertheless symmetric in the product of both. In particular, the doctoral research project aims at designing acoustic PT symmetry and demonstrating the extraordinary scattering characteristics of the acoustic PT medium based on exact theoretical predictions and numerical analysis. Hence, we investigate the possibilities to realize one-way cloaks of invisibility and broken symmetry properties with amplifying or attenuating behaviour by studying two different structures.
The first one is a periodic and finite one-dimensional non-Hermitian sonic crystal where we can find new ways to design unusual wave propagation in dependence to the balanced gain and loss strength. Beyond the coalescence of complex Bloch modes, we conduct in-depth transient analysis to find that asymmetrically reflected pulses can be readily tuned by means of the non-Hermiticity parameter and we discuss how one is able to engineer supersonic group velocities in the vicinity of an exceptional point hosting almost entirely vertical dispersion bands. We foresee that our findings can advance sonar and echo control applications in the non-destructive community and in medicine.
In the second non-Hermitian study done, we derive a theoretical recipe to realize an acoustic unhearability cloak via PT-symmetry. By combining loss and gain structures, we show that reflected sound is eliminated from an insonifed body to be concealed and how it is reconstructed at the rear side of it. Full-wave simulations and measurement data support the theoretical predictions in creating a cloak based on a single but non-Hermitian shell structure. We can indeed say that the use of parity-time symmetry enables unique cloaking properties useful in the audible range but also applicable to hide submarines from sonar detection.
After the non-Hermitian studies, we focus on topological acoustics, that combines the knowledge of topology in mathematics and electronics with sound waves. Knowing that artificial sonic lattices have been widely used to explore topological phases of sound and its properties, we propose to study the properties of Second Order Topological Insulators when non-Hermiticity is involved. Deriving a semi-numerical tool, based on the Multiple Scattering Theory (MST), that allows us to compute the spectral dependence of corner states in the presence of defects, we illustrate the limits of the topological resilience of the confined non-Hermitian acoustic states.
The predicted spectral locations of the corner states in response to an acoustic point source that we model with MST, agree very well with eigenfrequencies computations done by a FEM. Our simulations further confirm the topological robustness of these corner states in the presence of interstitial cylindrical crystal defects. Interestingly, depending on the geometrical arrangement of the non-Hermitian components we are able to excite corner states of variable acoustic energy. Hence, our powerful semi-numerical predictions can reliably pave the way for the design of new acoustic devices where topological protection in combination with lossy and amplifying ingredients are in great demand.
Beyond its academic importance, we anticipate that the results obtained could be used to focus acoustic energy. Potential applications include the development of new waveguides, that we can achieve without the need for a physical channel, but rather simply through the topology of the study system. This case of sound transport is relevant for filtering and conducting applications. Unlike traditional passive systems, this one is highly robust against imperfections. Another potential application is acoustic-electric conversion. Since we are able to concentrate the sound in the corners, harvest the acoustic energy, concentrate it in the corners and then convert it into electrical energy. These advances could also have applications in industrial ultrasound technologies or in the improvement of certain medical diagnostic tests such as ultrasound, for example.
An attractive motivation of all these acoustic structures compared to their electronic counterparts, is their easy fabrication and tunability, allowing the experimental verification of this quantum analogies as well as the development of many numerical studies. Thereby, in the last part of this thesis we mimic twisted bilayer physics in a mechanical twisted bilayer configuration and, also, in an acoustical bilayer. Designing the mathematical models to describe the physics involved, we show how the twist angle is related to the flat band formation as happens in twisted bilayer graphene.
During the study of twisted bilayer mechanical system, we demonstrate not only the flat band formation like that on the twisted bilayer graphene, but a very similar modulation of group velocity with twist angle and spatial eigenmode profiles in both. The exploration of the magic angle sequence and velocity modulation of TBG using the mechanical double-plate analogue would allow far easier parameter uniformity and control than in TBG. Mechanical analogues could not only help shed light on the rich TBG physics but would also enable ultrasonics devices for slow-sound operations and RF signal buffering.
In the second part of this study, we focus on holey twistsonic media, i.e., the acoustic counterpart of twisted bilayer graphene has been demonstrated semi-numerically thanks to a modal expansion approach. Holey plates are highly flexible and tunable structures for metamaterials, topological and twistsonic applications. Hence, we believe that our tool should serve as solid basis to conduct experimental studies along this line. We showed how these acoustic twisted media not only host these flat moiré dispersion bands, but moreover, that they can be straightforwardly altered through the involved geometry.
