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Topological properties of sub-wavelength crystalline metamaterials

Periodic Reporting for period 1 - ToPSeCRET (Topological properties of sub-wavelength crystalline metamaterials)

Reporting period: 2018-06-01 to 2020-05-31

Waves, such as electromagnetic signals or acoustic vibrations, are privileged carriers of information and energy that are ubiquitously used in modern technologies, from advanced imaging and prospections methods to telecommunications. Their emission, propagation, processing and reception are carried out using wave devices that are typically built from standard natural materials. The restricted pool of available natural materials used to be considered as an ultimate limitation on the functionality and performance of these systems. However, it has been discovered that by judiciously structuring and arranging natural materials, one could build artificial materials, called metamaterials (MM), with wave properties that are not found in any known natural material, including in its own constituents. This opened a wealth of new potentialities in wave device engineering, such as the possibility to manipulate waves at scales smaller than their wavelength, of boosting wave-matter interactions for ultra-sensitive sensing schemes, or of imaging objects with unprecedented resolution.
Among the fascinating properties that one can engineer, particular interest has been put on so-called topological properties. A topological property is a property of a wave system or material that cannot be annihilated by any continuous modification. An example would be the presence of, for example, a transparency window, that would be immune to any continuous modification of the material dispersion relation induced, for instance, by geometrical perturbations. Such robust properties are interesting from the standpoint of technological applications because they are guaranteed by their topological nature, leading to devices that continue to work even if they are not perfectly manufactured or are subject to damage. However, topological wave properties have so far been largely restricted to scenarios involving large and bulky structures, directly inspired from similar properties known in electronic systems.
In this project, our aim is to explore the possibility to obtain topological wave properties at scales much smaller than the wavelength, in order to unleash the full potential of topology for the realization of sturdy compact devices. For this, we will search for topological phases in metamaterial crystals (MMC) which are a special class of locally-resonant metamaterials that have proven their ability to manipulate energy at subwavelength scales. Our objectives are:
(G1) Investigating topological properties of sub- scaled MMC while understanding and physically interpreting the respective role and interplay of structure and resonant composition at the sub- scale of the elementary unit cell.
G1-A) Extend actual theories/analytical models to study topological properties of media composed of resonant elements coupled through a far field MS based coupling (the vast majority of MM) and apply it to sub-wavelength scaled MMC. Nowadays, topological order in resonators arrays, as MM, is indeed severely restricted to TB coupled resonators media.
G1-B) Use the developed theoretical tools of (G1-A) to link the topological macroscopic properties of a given MMC and the microscopic response of its elementary unit cell. While topological properties are almost exclusively derived from mathematical complex calculations, a specific attention will be paid to bring out simple and general physical interpretations of topological trivial and non-trivial properties in terms of wave/matter and wave/structure interactions in the MMC unit cell.
(G2) Use this novel microscopic understanding of MMC topological properties (G1-B) to straightforwardly conceive elementary MMC sub- unit cells with appropriate composition and structure to explore, design and experimentally realize a new class of topologically non-trivial two-dimensional MMC. These novel materials will be leveraged to designing a sub- edge-state waveguide at the interface of two topologically different MMCs.
(G3) The fundamental discoveries of G1 and G2 will be exploited for a more applied-oriented purpose. An innovative design for a disorder immune sub- slow wave waveguide will be proposed.
Before a brief summary of the work performed, it must be stressed that due to serious medical reasons, the fellow was constrained to several sick leave or part-time employment. The deterioration of the medical condition of the fellow led to the early termination of the grant agreement.

G1 was achieved with a publication (Physical Review B, DOI : 10.1103/PhysRevB.102.134303) by the fellow, for the first time exploring the physics of a locally-resonant topological one-dimensional metamaterial, and studying the differences with the standard Su-Schreffer-Heeger scheme.

While some designs and full-wave numerical simulations toward G2 were proposed in this publication, the fellow did not have the chance to experimentally verify these concepts.

G3 has also partially be investigated, as reported in another publication (Physical Review Applied, DOI : 10.1103/PhysRevApplied.10.054069 selected as Editors' suggestion), which does include an experimental realization of 2D topological subwavelength guiding performed in collaboration with another postdoc.
We have explored and unveiled the physics of a locally-resonant topological one-dimensional metamaterial, studying the differences with the standard Su-Schreffer-Heeger scheme (Physical Review B, DOI : 10.1103/PhysRevB.102.134303).

We have demonstrated numerically and experimentally the possibility of 2D sub-wavelength guiding and studied the robustness of the propagation against disorder in the position of the metamaterial elements and in their resonant frequency (Physical Review Applied, DOI : 10.1103/PhysRevApplied.10.054069 , selected as Editor's choice).