Tutorial: Computing topological invariants in two-dimensional photonic crystals

Abstract

The field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple methods for diagnosing the topology of optical systems remain elusive for an important part of the community. In this tutorial, we provide a summary of numerical methods to calculate topological invariants emerging from the propagation of light in photonic crystals. We first describe the fundamental properties of wave propagation in lattices with a space-dependent periodic electric permittivity. Next, we provide an introduction to topological invariants; proposing an optimal strategy to calculate them through the numerical evaluation of Maxwell's equation in a discretized reciprocal space. Finally, we will complement the tutorial with a few practical examples of photonic crystal systems showing different topological properties, such as photonic valley-Chern insulators, photonic crystals presenting an "obstructed atomic limit", photonic systems supporting fragile topology and finally photonic Chern insulators, where we also periodically modulated the magnetic permeability.

arXiv comment13 pages, 11 figures. Accepted for publication in Advanced Quantum Technologies for special issue of Photonic Quantum Technologies

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Cited by in corpus (34)

• Quantifying the robustness of topological slow light
• Second-harmonic generation via double topological valley-Hall kink modes in all-dielectric photonic crystals
• On the robustness of topological corner modes in photonic crystals
• Topological Phases of Photonic Crystals under Crystalline Symmetries
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