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.
| Original language | English |
|---|---|
| Journal | Nanophotonics |
| Volume | 8 |
| Issue number | 8 |
| Pages (from-to) | 1363-1369 |
| ISSN | 2192-8606 |
| DOIs | |
| Publication status | Published - 2019 |
Keywords
- Photonic crystals
- Photonic topological insulators
- Top-down design
- Topology optimization
Cite this
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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 journal › Journal article › Research › peer-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.
KW - Photonic crystals
KW - Photonic topological insulators
KW - Top-down design
KW - Topology optimization
U2 - 10.1515/nanoph-2019-0057
DO - 10.1515/nanoph-2019-0057
M3 - Journal article
VL - 8
SP - 1363
EP - 1369
JO - Nanophotonics
JF - Nanophotonics
SN - 2192-8606
IS - 8
ER -