PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Experimental Observation of Topological Fano Resonances forAudible Sound
Farzad Zangeneh-Nejad1; and Romain Fleury1;
1

Laboratory of Wave Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne,Switzerland

ABSTRACTThe Fano resonance is a widespread wave scattering phenomenon observed in many different systems,
from cold atom physics, to electromagnetics, electronic circuits, and acoustics. It is characterized by a very
sharp and asymmetric scattering cross-section spectrum that switches from a zero to a maximum value fortwo close by frequencies. Such extraordinary feature has established Fano resonances as the basic principle
for many applications including efficient sources and emitters, switches, interferometers, or supersensitive
sensors. Yet, these resonances are difficult to achieve in practice, as they require tight geometricaltolerances and large fabrication precision to guarantee their occurrence in the desired frequency range, andthe absence of parasitic peaks. In this talk, we will discuss a route for leveraging one-dimensional
topological insulators to generate a novel form of sturdy Fano resonances, and experimentally demonstrate
their robustness for audible sound waves. Extension to other physical systems will be briefly discussed.
Keywords: Topological insulators, Fano resonances, Acoustics, Metamaterials.

1. INTRODUCTION
Fano resonance occurs as a result of constructive and destructive interferences between two resonatingstates: a continuous or “bright” state and a discrete, “dark” one. Such resonances, characterized by theirasymmetric and ultra-sharp line shapes, have recently drawn considerable amount of attention for realizing
a large variety of optical devices with unprecedented features, including ultra-compact electromagneticallyinduced transparency devices, highly efficient lasers, ultra-fast switches and modulators, ultra-sharp filters,
ultrathin perfect absorbers, and highly precise interferometers [1]. The ultra-sharp line shape of the Fano
resonance has further been of utmost interest in sensing applications. More specifically, the peculiar line
shape of the Fano resonance has been found to be extremely sensitive to geometrical and environmental
perturbations. This property has established a fertile ground for realizing ultra-sensitive and accurate
sensors based on such resonances [2].
The extreme sensitivity of the Fano resonance, albeit useful for sensing, is often associated with vexing
practical issues. In particular, it often implies tight geometrical tolerances and large fabrication precision toguarantee its occurrence in the desired frequency range, and the absence of parasitic peaks. As a result, theadvantageous properties of Fano-based devices are often mitigated by the costs associated with the required

1

Corresponding author: Romain.fleury@epfl.ch2100

fabrication technology.
In a seemingly unrelated field of research, topological insulators [3-7], materials with non-trivial
topological orders, have been found to provide an unconventional robustness to perturbations. In fact, it has
been widely demonstrated that edge modes flowing along the boundaries of such phases of matter areprotected to certain classes of defects. Such protection has enabled realization of a broad range of classicalwave devices with an unusual immunity against imperfections. Following these advances, an importantquestion naturally arises: Can the abstract concept of topology also be leveraged for building a novel formof Fano resonances with strong robustness to disorder? In this contribution, we answer positively to thisquestion, reporting our recent findings on the observation of a novel class of sturdy Fano resonances,
dubbed as topological Fano resonances [8].

2. TOPOLOGICAL FANO RESONANCES
To achieve topological Fano resonances, we consider the configuration shown in Fig. 1a, consisting of an
acoustic waveguide in which a Su-Schrieffer-Heeger (SSH) array [9] of cylindrical obstacles isimplemented. Considering the reflection symmetry of the structure with respect to the centerline of thewaveguide, one can divide the corresponding modal solutions into even and odd types. Likewise, the edge
modes of the SSH array are either even or odd with respect to the centerline of the guide. The odd edge
mode, originating from the so-called bound states in the continuum, is completely decoupled from thecontinuum of waveguide modes and serves as a discrete (dark) state. The even edge mode, on the contrary,originates from multiple scattering of sound, and serves as the slowly varying background state. By slightly
breaking the reflection mirror symmetry of the system, these two topological edge states can couple to eachother. This creates the Fano line shape as shown in the inset of Fig. 1a. The corresponding mode profiles ofthe dark and bright edge states are also shown in the inset.
Since the existences of dark and bright edge modes are guaranteed by the topological properties of thesurrounding insulators, the Fano line shape inherits some form of immunity against disorder. Todemonstrate such salient feature, we randomly change the position of the cylinders and calculate thecorresponding transmission coefficient (Fig. 1b). As it is observed in the figure, the Fano resonance is stillpreserved, constituting an evidence of its strong robustness to disorder.
Based on these findings we built a prototype to experimentally demonstrate topological Fano resonancesand validate their robustness (Fig .2a). The sample is built from an plexiglass pipe, guiding sound waves,and nylon plastic cylindrical rods which are manually put on their specific places inside the waveguide. The
waveguide is excited with a loudspeaker, and the corresponding transmitted pressure field is measured. The
bottom panel of the figure illustrates the measured transmission coefficients, extracted from analyzing thecorresponding standing wave pattern. As we expected from our numerical findings, the interferences
between the dark and bright edge modes creates a Fano-like resonance around the frequency 2.2 kHz. In
order to study the effect of disorder on the Fano line shape, we randomly move some of the obstacles fromtheir original places as seen in Fig. 2b, and repeat our scattering test. Inset of the figure shows thecorresponding transmission coefficient. It is seen that the Fano line shape is still present and no parasitic

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peaks are introduced to the spectrum. Yet, the Fano line shape can still shift, holding great promises forsensing applications.

Fig.1: Topological Fano resonances, (top) A SSH array of cylinders is implemented inside an acoustic waveguide.
(Middle) Profiles of the corresponding even and dark edge states, (bottom) Transmission Spectrum of thewaveguide, manifesting the Fano line shape around 1.5 kHz. b, Same as a) except that some disorder is added

to the sample. The Fano line shape shows strong immunity against disorder.

3. CONCLUSIONSIn summary, we showed how topology, the mathematics of conserved quantities under continuousdeformation, can be leveraged to form a new form of sturdy Fano resonances, dubbed as topological Fanoresonances, with an unprecedented robustness against geometrical tolerances. While we observed such typeof resonances in acoustics, topological Fano resonances can also be observed in other physical platforms.
For instance, by implementing a SSH array of dielectric rods inside a conventional microwave waveguide,
one can realize topological Fano resonances based on electromagnetic waves. These findings altogether
hold great promises for a new generation of acoustic device such as switches, sasers, modulators, etc.,
thereby enriching the toolkit of modern acoustic engineering [10-15].

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Fig. 2: Experimental demonstration of topological Fano resonances for audible sound, a, (top) A SSH arrayof nylon plastic cylindrical rods is implemented inside a pipe made of acrylic glass. (bottom) The spectrum
exhibits the Fano line-shape caused by the interference between the bright and dark edge modes. b, Same as
panel a except that some disorder is added to the configuration.

ACKNOWLEDGEMENTS
The authors would like to acknowledge support from Swiss National Science Foundation (SNSF)
under Grant No. 172487.

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