Automated Discovery and Optimization of 3D Topological Photonic Crystals

Kim, Samuel; Christensen, Thomas; Johnson, Steven G.; Soljačić, Marin

doi:10.1021/acsphotonics.2c01866

Cited by 5 publications

(1 citation statement)

References 91 publications

(173 reference statements)

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“…We have demonstrated that this fractionalization comes from a counting mismatch of states and that the boundary-localized states associated with it are the consequence of the conservation of the number of degrees of freedom in the system, and do not require a fixed band filling (i.e., Fermi level). We have further demonstrated The framework presented here is readily generalizable to three-dimensional PhCs under crystalline symmetries [89,122]. Such three-dimensional PhCs, now a subject of active experimental exploration [123][124][125][126][127], exhibit several unique topological phases with associated bulk and boundary signatures.…”

Section: Discussionmentioning

confidence: 75%

Topological phases of photonic crystals under crystalline symmetries

et al. 2023

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Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological bands in one-and two-dimensional photonic crystals, with and without time-reversal symmetry. Our approach exploits the symmetry representations of field eigenmodes at high-symmetry points in momentum space, allowing for the efficient design of a wide range of topological PhCs. In particular, we show that the complete classification provided here is useful for diagnosing photonic crystal analogs of obstructed atomic limits, fragile phases, and stable topological phases that include bands with Dirac points and Chern numbers.

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Section: Discussionmentioning

confidence: 75%

Topological phases of photonic crystals under crystalline symmetries

et al. 2023

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Topological photonics in three and higher dimensions

Han,

Xi,

Meng

et al. 2024

APL Photonics

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Topological photonics is a rapidly developing field that leverages geometric and topological concepts to engineer and control the characteristics of light. Currently, the research on topological photonics has expanded from traditional one-dimensional (1D) and two-dimensional (2D) to three-dimensional (3D) and higher-dimensional spaces. However, most reviews on topological photonics focus on 1D and 2D systems, and a review that provides a detailed classification and introduction of 3D and higher-dimensional systems is still missing. Here, we review the photonic topological states in 3D and higher-dimensional systems on different platforms. Moreover, we discuss internal connections between different photonic topological phases and look forward to the future development direction and potential applications of 3D and higher-dimensional systems.

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Chern, dipole, and quadrupole topological phases of a simple magneto-optical photonic crystal with a square lattice and an unconventional unit cell

Lan,

Chen,

et al. 2024

Phys. Rev. B

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For the study of topological phases in photonics, while quantum-Hall-type first-order chiral edge states are routinely realized in magneto-optical photonic crystals, higher-order topological states are mostly explored in all-dielectric photonic crystals. In this work, we study both first- and second-order topological photonic states in magneto-optical photonic crystals. In specific, we revisit a simple magneto-optical photonic crystal in a square lattice with one gyromagnetic cylinder in each unit cell. However, rather than investigating the conventional unit cell where the cylinder is at the center of the square unit cell as previous works have done, we consider a configuration where the cylinders are located at the four corners of the square unit cell and show that this configuration hosts rich topological phases, such as dual-band Chern, dipole, and quadrupole topological phases. Our detailed characterizations of these topological states are based on the Wannier bands and their polarizations via the Wilson loop and nested Wilson loop methods. We study in detail both the edge and corner states of the different topological phases and show that they exhibit a special feature of “spectrum robustness.” For example, though the edge and corner states of the dipole phases living in a band gap could be pushed into the bulk bands by tuning the boundary conditions, they can pass through the bulk bands and reappear within a different band gap. For dual-band quadrupole phases, we can find a regime where both band gaps host a set of corner states simultaneously and, intriguingly, the filling anomaly of one set of corner states can leave their signatures in the filling anomaly of the other set of corner states though they are separated by an extensive number of bulk states. The rich topological physics revealed in a simple magneto-optical photonic crystal not only provides new insights on higher-order topological phases in time-reversal symmetry-broken photonic systems, the results may also find promising applications by harnessing the potentials of both edge and corner states. Published by the American Physical Society 2024

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Automated Discovery and Optimization of 3D Topological Photonic Crystals

Cited by 5 publications

References 91 publications

Topological phases of photonic crystals under crystalline symmetries

Topological phases of photonic crystals under crystalline symmetries

Topological photonics in three and higher dimensions

Chern, dipole, and quadrupole topological phases of a simple magneto-optical photonic crystal with a square lattice and an unconventional unit cell

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