Tutorial: Computing Topological Invariants in 2D Photonic Crystals

@article{BlancodePaz2019TutorialCT,
  title={Tutorial: Computing Topological Invariants in 2D Photonic Crystals},
  author={Mar{\'i}a Blanco de Paz and Chiara Devescovi and G{\'e}za Giedke and J J S{\'a}enz and Maia G. Vergniory and Barry Bradlyn and Dario Bercioux and Aitzol Garc'ia-Etxarri},
  journal={Advanced Quantum Technologies},
  year={2019},
  volume={3}
}
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. Herein, a summary of numerical methods to calculate topological invariants emerging from the propagation of light in photonic crystals is provided… 
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40 Citations
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40 Citations

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References

SHOWING 1-10 OF 145 REFERENCES

Engineering fragile topology in photonic crystals: Topological quantum chemistry of light

In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport…

Photonic topological insulators.

It is shown that metacrystals-superlattices of metamaterials with judiciously designed properties-provide a platform for designing topologically non-trivial photonic states, similar to those identified for condensed-matter topological insulators.

Photonic crystal nanocavity based on a topological corner state

Topological phonics has emerged as a novel approach to engineer the flow of light and provides unprecedented means for developing diverse photonic elements, including robust optical waveguides immune…

Photonic Floquet topological insulators

This work proposes and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges.

Unconventional quantum optics in topological waveguide QED

This work predicts several unconventional quantum optical phenomena that occur when quantum emitters interact with a topological waveguide quantum electrodynamics bath, namely, the photonic analog of the Su-Schrieffer-Heeger model.

Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material.

The present work solves Maxwell equations and demonstrates the new photonic topology by revealing pseudospin-resolved Berry curvatures of photonic bands and helical edge states characterized by Poynting vectors.

Observation of photonic anomalous Floquet topological insulators

This work implements a system where chiral edge modes exist although the Chern numbers of all bands are zero, and employs periodically driven photonic waveguide lattices to demonstrate topologically protected scatter-free edge transport in such anomalous Floquet topological insulators.

Topological phase transitions and chiral inelastic transport induced by the squeezing of light

It is shown how the squeezing of light can lead to the formation of qualitatively new kinds of topological states, characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport.

Corner states of light in photonic waveguides

The recently established paradigm of higher-order topological states of matter has shown that not only edge and surface states1,2 but also states localized to corners, can have robust and exotic…

Topological phenomena in classical optical networks

This proposal proposes a scheme to realize a topological insulator with optical-passive elements and analyze the effects of Kerr nonlinearities in its topological behavior, and develops a method to analyze the scheme in the presence of a Kerr medium.
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