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Séminaire de Nadège Kaina

Locally resonant metamaterials: deep subwavelength photonic/phononic crystals

23/02/2018 Nice Valrose
Publication : 23/02/2018
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Many properties of natural materials (their color, electric or heat conductivity, transparency or opacity...) can be directly derived from how they can interact with waves, be it optical ones (as light), acoustic ones (as sound) or mechanical ones. One can easily understand that this interaction should be very different from a material to the other; indeed, copper is not the same color as silver, nor wood conduct heat as well as metals. This difference of behavior lies in fact that each material can be described unequivocally by two main properties: its composition (that is its constitutive atoms) and its structure (how these atoms are organized in space). Both the structure and the composition capture the extreme richness of the physical properties of natural materials, which are extensively studied within the field of solid-state physics. For instance, the color of a material can be explained by its atomic constituents through absorption, such as for metals or by its crystalline structure, as is the case in opals. Similarly, the spatial organization of atoms in materials, while governing the electron propagation, is responsible for their electrical properties. To be complete, the propagation of heat or shocks is again entirely ruled by the same parameters: the atoms type and their organization.

Starting from Lord Rayleigh in the beginning of the 20th century, scientists have been interested in studying such composition and structure based interactions but at larger scales and lower frequencies (since natural materials are scaled at the angstrom and constrained to optical frequencies). To do so, they devised new composite, manufactured materials that can not only mimic behavior of natural materials (propagation, reflection, diffraction, absorption...) yet at larger wavelengths but can also display exotic properties unfound in nature. These researches have led to two major concept proposals in the community of wave physics within the last 30 years, each one principally dealing with one of the two elementary properties: photonic crystals that account for the structure and metamaterials that relies on the composition. The former reproduces the crystalline nature of materials, by structuring periodically composite media with periods corresponding to the wavelength the material is sensitive to. This results in interferences effects from multiply reflected waves and in turns on the apparition of frequency bands of allowed and forbidden propagation of waves. This phenomenon, called Bragg scattering, is very similar to electron propagation in crystals that periodically encounter atoms, which is at the origin of the conducting or insulating properties of natural materials. Metamaterials on the other hand refer to media structured at spatial scales that are much smaller than the wavelength, and their properties are usually derived from the resonant nature of their building blocks, as atoms display resonant behaviour in natural materials. Because of their sub-wavelength scale organization, that can be periodic or not, metamaterials are commonly considered as effective homogeneous media whose properties solely result from the mean response of all their unit cells to incoming waves, similarly to dielectric materials acting on light.

Up to now, the physics of photonic crystals and metamaterials were thought to be extremely different and their properties not mixable. Indeed, while the first one requires that the wavelength scales with the physical scale of the medium for Bragg scattering to occur, the second is inherently structured much more finely, which was always thought to forbid any effect based on Bragg scattering and interferences, hence

completely disregarding the role of the structure. As a result, current manmade materials cannot cumulate the advantages of the two main families; in other words, they are unable to reproduce the amazing richness encountered in natural media.

In this work, we show that, contrarily to common beliefs and despite the very deep-subwavelength spatial organization of the resonators, the wave propagation in some metamaterials can actually be reinterpreted at the light of two physical phenomena analogous to those usually attributed to photonic/phononic crystals alone: interferences and multiple scattering. Adopting this novel point of view opens many exciting, and up to now unconceivable, possibilities to control the wave propagation at subwavelength scales. First, taking advantage of interferences effects, we show that waves can be spatially and temporally manipulated, at the subwavelength scale of the metamaterials unit cell, by inserting locally resonant defects. The second consequence of our approach, addressing the multiple scattering phenomenon, consists in evidencing the crucial role of structure, i.e. of the subwavelength spatial organization of resonators, to tailor the metamaterials macroscopic properties. We hence prove that a so-called single negative metamaterial (presenting only one negative effective property) can be turned into a double negative one (hence presenting a negative index of refraction), simply by smartly organizing the building blocks of the metamaterial, at scales much smaller than the wavelength.