Designing photonic topological insulators with quantum-spin-Hall edge states using topology optimization

Rasmus E. Christiansen*, Fengwen Wang, Ole Sigmund, Søren Stobbe

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Designing photonic topological insulators (PTIs) is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of PTIs as an inverse design problem and use topology optimization to maximize the transmission through an edge mode past a sharp bend. Two design domains composed of two different but initially identical C-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a PTI reminiscent of the shrink-and-grow approach to quantum-spin-Hall PTIs but with notable differences in the crystal structure as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50% larger than in previous designs. Furthermore, we find a directional β-factor exceeding 99% and very low losses for sharp bends. Our approach allows the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto-unexplored symmetry constraints.

Original languageEnglish
JournalNanophotonics
Volume8
Issue number8
Pages (from-to)1363-1369
ISSN2192-8606
DOIs
Publication statusPublished - 2019

Keywords

  • Photonic crystals
  • Photonic topological insulators
  • Top-down design
  • Topology optimization

Cite this

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title = "Designing photonic topological insulators with quantum-spin-Hall edge states using topology optimization",
abstract = "Designing photonic topological insulators (PTIs) is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of PTIs as an inverse design problem and use topology optimization to maximize the transmission through an edge mode past a sharp bend. Two design domains composed of two different but initially identical C6ν-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a PTI reminiscent of the shrink-and-grow approach to quantum-spin-Hall PTIs but with notable differences in the crystal structure as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50{\%} larger than in previous designs. Furthermore, we find a directional β-factor exceeding 99{\%} and very low losses for sharp bends. Our approach allows the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto-unexplored symmetry constraints.",
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author = "Christiansen, {Rasmus E.} and Fengwen Wang and Ole Sigmund and S{\o}ren Stobbe",
year = "2019",
doi = "10.1515/nanoph-2019-0057",
language = "English",
volume = "8",
pages = "1363--1369",
journal = "Nanophotonics",
issn = "2192-8606",
publisher = "Walterde Gruyter GmbH",
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}

Designing photonic topological insulators with quantum-spin-Hall edge states using topology optimization. / Christiansen, Rasmus E.; Wang, Fengwen; Sigmund, Ole; Stobbe, Søren.

In: Nanophotonics, Vol. 8, No. 8, 2019, p. 1363-1369.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Designing photonic topological insulators with quantum-spin-Hall edge states using topology optimization

AU - Christiansen, Rasmus E.

AU - Wang, Fengwen

AU - Sigmund, Ole

AU - Stobbe, Søren

PY - 2019

Y1 - 2019

N2 - Designing photonic topological insulators (PTIs) is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of PTIs as an inverse design problem and use topology optimization to maximize the transmission through an edge mode past a sharp bend. Two design domains composed of two different but initially identical C6ν-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a PTI reminiscent of the shrink-and-grow approach to quantum-spin-Hall PTIs but with notable differences in the crystal structure as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50% larger than in previous designs. Furthermore, we find a directional β-factor exceeding 99% and very low losses for sharp bends. Our approach allows the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto-unexplored symmetry constraints.

AB - Designing photonic topological insulators (PTIs) is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of PTIs as an inverse design problem and use topology optimization to maximize the transmission through an edge mode past a sharp bend. Two design domains composed of two different but initially identical C6ν-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a PTI reminiscent of the shrink-and-grow approach to quantum-spin-Hall PTIs but with notable differences in the crystal structure as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50% larger than in previous designs. Furthermore, we find a directional β-factor exceeding 99% and very low losses for sharp bends. Our approach allows the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto-unexplored symmetry constraints.

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KW - Photonic topological insulators

KW - Top-down design

KW - Topology optimization

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