An operator-based approach to topological photonics
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches...
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-11-01
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| Series: | Nanophotonics |
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| Online Access: | https://doi.org/10.1515/nanoph-2022-0547 |
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| _version_ | 1846157364414119936 |
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| author | Cerjan Alexander Loring Terry A. |
| author_facet | Cerjan Alexander Loring Terry A. |
| author_sort | Cerjan Alexander |
| collection | DOAJ |
| description | Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure’s topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system’s Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system’s crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities. |
| format | Article |
| id | doaj-art-23ca64b1b16e48fbb081319d0e3d0b7f |
| institution | Kabale University |
| issn | 2192-8614 |
| language | English |
| publishDate | 2022-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nanophotonics |
| spelling | doaj-art-23ca64b1b16e48fbb081319d0e3d0b7f2024-11-25T11:19:08ZengDe GruyterNanophotonics2192-86142022-11-0111214765478010.1515/nanoph-2022-0547An operator-based approach to topological photonicsCerjan Alexander0Loring Terry A.1Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM87185, USADepartment of Mathematics and Statistics, University of NM, Albuquerque, NM87131, USARecently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure’s topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system’s Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system’s crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities.https://doi.org/10.1515/nanoph-2022-0547photonic crystalstopological photonics topology |
| spellingShingle | Cerjan Alexander Loring Terry A. An operator-based approach to topological photonics Nanophotonics photonic crystals topological photonics topology |
| title | An operator-based approach to topological photonics |
| title_full | An operator-based approach to topological photonics |
| title_fullStr | An operator-based approach to topological photonics |
| title_full_unstemmed | An operator-based approach to topological photonics |
| title_short | An operator-based approach to topological photonics |
| title_sort | operator based approach to topological photonics |
| topic | photonic crystals topological photonics topology |
| url | https://doi.org/10.1515/nanoph-2022-0547 |
| work_keys_str_mv | AT cerjanalexander anoperatorbasedapproachtotopologicalphotonics AT loringterrya anoperatorbasedapproachtotopologicalphotonics AT cerjanalexander operatorbasedapproachtotopologicalphotonics AT loringterrya operatorbasedapproachtotopologicalphotonics |