TY - JOUR
T1 - Tutorial
T2 - Computing Topological Invariants in 2D Photonic Crystals
AU - Blanco de Paz, María
AU - Devescovi, Chiara
AU - Giedke, Geza
AU - Saenz, Juan José
AU - Vergniory, Maia G.
AU - Bradlyn, Barry
AU - Bercioux, Dario
AU - García-Etxarri, Aitzol
N1 - Funding Information:
M.B.P. thanks M. Olano for fruitful discussions. M.G.V. and A.G.-E. acknowledge the IS2016-75862-P and FIS2016-80174-P national projects of the Spanish MINECO, respectively, and DFG INCIEN2019-000356, and OF 23 /2019 (ES) from Gipuzkoako Foru Aldundia. A.G.-E. received funding from the Fellows Gipuzkoa fellowship of the Gipuzkoako Foru Aldundia through FEDER “Una Manera de hacer Europa”, and by Eusko Jaurlaritza, grant numbers, KK-2017/00089, IT1164-19, and KK-2019/00101. The work of M.B.P., G.G., J.J.S., D.B., and A.G.-E. is supported by the Basque Government through the SOPhoQua project (Grant PI2016-41). The work of D.B. is supported by the Spanish Ministerio de Ciencia, Innovation y Universidades (MICINN) under the project FIS2017-82804-P, and by the Transnational Common Laboratory QuantumChemPhys.
Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2020/2/1
Y1 - 2020/2/1
N2 - 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. The fundamental properties of wave propagation in lattices with a space-dependent periodic electric permittivity is first described. Next, an introduction to topological invariants is provided, proposing an optimal strategy to calculate them through the numerical evaluation of Maxwell's equation in a discretized reciprocal space. Finally, the tutorial is complemented 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 the magnetic permeability is also periodically modulated.
AB - 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. The fundamental properties of wave propagation in lattices with a space-dependent periodic electric permittivity is first described. Next, an introduction to topological invariants is provided, proposing an optimal strategy to calculate them through the numerical evaluation of Maxwell's equation in a discretized reciprocal space. Finally, the tutorial is complemented 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 the magnetic permeability is also periodically modulated.
KW - Berry phase
KW - Chern number
KW - Wilson loop
KW - numerical calculation
KW - photonic topological invariants
KW - topological photonics
KW - valley Chern number
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U2 - 10.1002/qute.201900117
DO - 10.1002/qute.201900117
M3 - Article
AN - SCOPUS:85084916965
SN - 2511-9044
VL - 3
JO - Advanced Quantum Technologies
JF - Advanced Quantum Technologies
IS - 2
M1 - 1900117
ER -