Symmetry and topology in optical and plasmonic materials

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• Matthias Saba (Université de Fribourg)
• Tuesday 22 August 2023, 14:30-15:00
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PMVW01 - 5th International Conference on Packing Problems: Packing and patterns in granular mechanics

Ever since the Cambrian explosion, the efficient manipulation and sensing of light became ubiquitous in the living world, and indeed critical for survival of most organisms. Concurrently, optical technologies are omnipresent in modern everyday live, from free-space and cable communication to medical applications, home appliances etc. Conventional optical elements such as lenses, mirrors, and polarization filters are made from natural materials such as dielectrics, metals, and liquid crystals. These are typically bulky and energy inefficient, and nature has therefore developed nanostructured geometries assembled of two or more dielectric materials. Only in the past 30 years, we have started to copy natures blueprints through bio-mimicry, and developed our own nano-structured materials in the form of so-called photonic crystals and metamaterials.   Through inverse engineering and machine learning, photonic materials have now, for example, been designed for analog computing and flat optics, with a metalens built into the next generation of the iPad and the iPhone. While inverse engineering and optical simulations are very useful tools, they do not reveal the fundamental reason for a designed optical material response. I here instead follow an approach that classifies ordered nano-structured materials according to their symmetry and associated topology to predict an optical response based on first principles. This approach can lead to generic design principles and help to understand otherwise counter-intuitive behaviour. The real-space connectedness determines, for example, the optical response of metal geometries. This explains an unexpected strong linear and circular dichroism in gyroid metamaterials that is highly sensitive to its surface termination¹. It further gives rise to so-called electron acoustic waves in metallic double-nets [2], for which light has a longitudinal polarization, reminiscent of an acoustic wave Fig. 1c-d. A group theoretical classification bulk modes, on the other hand, explains the absence of chiro-optical properties in chiral media [3]. In combination with a topological characterization, this method provides a first principle route to topologically protected edge states in flat materials [4] that can be used for lasing and on-chip photonic circuitry [5]. In 3D bulk materials, it leads to the emergence to a topologically protected near-zero refractive index [6] that gives rise to strongly spatially coherent states of light Fig. 1a-b. Figure 1: Two 3D materials designed by their symmetry and topological classification. A dielectric chiral cubic SRC net (a) gives rise to topologically protected near-zero index behavior that leads to spatially coherent states of light. A dipolar point source in a block of such a material therefore produces planewave-like emission seen from the electric field amplitude that is periodic within the structure and has planar wavefronts outside (b). The interpenetrating metallic PCU C double-net morphology© acts similar to a non-interacting double-plasma with electron that supports longitudinal electron acoustic, which cannot couple to vacuum radiation. A dipole source in a block of this material therefore produces light that is confined within the cube that acts like a resonator, as seen from the intensity heatmap in (d)

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