Spawning rings of exceptional points out of Dirac cones
The Dirac cone underlies many unique electronic properties of graphene1 and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of...
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| Format: | Article |
| Language: | en_US |
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Nature Publishing Group
2017
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| Online Access: | http://hdl.handle.net/1721.1/108256 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0003-2691-1892 https://orcid.org/0000-0002-7244-3682 https://orcid.org/0000-0002-7184-5831 |
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| author | Lu, Ling Pick, Adi Chua, Song-Liang Zhen, Bo Hsu, Chia Wei Igarashi, Yuichi Kaminer, Ido Efraim Joannopoulos, John Soljacic, Marin |
| author2 | Massachusetts Institute of Technology. Research Laboratory of Electronics |
| author_facet | Massachusetts Institute of Technology. Research Laboratory of Electronics Lu, Ling Pick, Adi Chua, Song-Liang Zhen, Bo Hsu, Chia Wei Igarashi, Yuichi Kaminer, Ido Efraim Joannopoulos, John Soljacic, Marin |
| author_sort | Lu, Ling |
| collection | MIT |
| description | The Dirac cone underlies many unique electronic properties of graphene1 and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point also known as the parity–time symmetry breaking point where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency unidirectional transmission or reflection and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an ‘exceptional ring’ in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity–time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain. |
| first_indexed | 2024-09-23T16:08:24Z |
| format | Article |
| id | mit-1721.1/108256 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:08:24Z |
| publishDate | 2017 |
| publisher | Nature Publishing Group |
| record_format | dspace |
| spelling | mit-1721.1/1082562022-09-29T18:30:45Z Spawning rings of exceptional points out of Dirac cones Lu, Ling Pick, Adi Chua, Song-Liang Zhen, Bo Hsu, Chia Wei Igarashi, Yuichi Kaminer, Ido Efraim Joannopoulos, John Soljacic, Marin Massachusetts Institute of Technology. Research Laboratory of Electronics Zhen, Bo Hsu, Chia Wei Igarashi, Yuichi Kaminer, Ido Efraim Joannopoulos, John Soljacic, Marin The Dirac cone underlies many unique electronic properties of graphene1 and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point also known as the parity–time symmetry breaking point where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency unidirectional transmission or reflection and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an ‘exceptional ring’ in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity–time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain. United States. Army Research Office (W911NF-07-D0004) United States. Army Research Office (W911NF-13-D-0001) Solid-State Solar-Thermal Energy Conversion Center National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (DMR-1419807) 2017-04-19T17:17:33Z 2017-04-19T17:17:33Z 2015-09 2015-04 Article http://purl.org/eprint/type/JournalArticle 0028-0836 1476-4687 http://hdl.handle.net/1721.1/108256 Zhen, Bo; Hsu, Chia Wei; Igarashi, Yuichi; Lu, Ling; Kaminer, Ido; Pick, Adi; Chua, Song-Liang; Joannopoulos, John D. and Soljačić, Marin. “Spawning Rings of Exceptional Points Out of Dirac Cones.” Nature 525, no. 7569 (September 9, 2015): 354–358. © 2015 Macmillan Publishers Limited, part of Springer Nature https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0003-2691-1892 https://orcid.org/0000-0002-7244-3682 https://orcid.org/0000-0002-7184-5831 en_US http://dx.doi.org/10.1038/nature14889 Nature Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Nature Publishing Group arXiv |
| spellingShingle | Lu, Ling Pick, Adi Chua, Song-Liang Zhen, Bo Hsu, Chia Wei Igarashi, Yuichi Kaminer, Ido Efraim Joannopoulos, John Soljacic, Marin Spawning rings of exceptional points out of Dirac cones |
| title | Spawning rings of exceptional points out of Dirac cones |
| title_full | Spawning rings of exceptional points out of Dirac cones |
| title_fullStr | Spawning rings of exceptional points out of Dirac cones |
| title_full_unstemmed | Spawning rings of exceptional points out of Dirac cones |
| title_short | Spawning rings of exceptional points out of Dirac cones |
| title_sort | spawning rings of exceptional points out of dirac cones |
| url | http://hdl.handle.net/1721.1/108256 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0003-2691-1892 https://orcid.org/0000-0002-7244-3682 https://orcid.org/0000-0002-7184-5831 |
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