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Title: Spawning rings of exceptional points out of Dirac cones

Abstract

The Dirac cone underlies many unique electronic properties of graphene 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 enclosedmore » 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. In this study, 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.« less

Authors:
 [1];  [2];  [3];  [1];  [1];  [4];  [5];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics; Yale Univ., New Haven, CT (United States). Dept. of Applied Physics
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics; NEC Corporation, Tsukuba, Ibaraki (Japan). Smart Energy Research Lab.
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Research Lab. of Electronics; Harvard Univ., Cambridge, MA (United States). Dept. of Physics
  5. DSO National Lab. (Singapore)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1371039
Grant/Contract Number:  
SC0001299; FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Nature (London)
Additional Journal Information:
Journal Name: Nature (London); Journal Volume: 525; Journal Issue: 7569; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; Journal ID: ISSN 0028-0836
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
14 SOLAR ENERGY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; solar (photovoltaic); solar (thermal); solid state lighting; phonons; thermal conductivity; thermoelectric; defects; mechanical behavior; charge transport; spin dynamics; materials and chemistry by design; optics; synthesis (novel materials); synthesis (self-assembly); synthesis (scalable processing)

Citation Formats

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. United States: N. p., 2015. Web. doi:10.1038/nature14889.
Zhen, Bo, Hsu, Chia Wei, Igarashi, Yuichi, Lu, Ling, Kaminer, Ido, Pick, Adi, Chua, Song-Liang, Joannopoulos, John D., & Soljačić, Marin. Spawning rings of exceptional points out of Dirac cones. United States. doi:10.1038/nature14889.
Zhen, Bo, Hsu, Chia Wei, Igarashi, Yuichi, Lu, Ling, Kaminer, Ido, Pick, Adi, Chua, Song-Liang, Joannopoulos, John D., and Soljačić, Marin. Wed . "Spawning rings of exceptional points out of Dirac cones". United States. doi:10.1038/nature14889. https://www.osti.gov/servlets/purl/1371039.
@article{osti_1371039,
title = {Spawning rings of exceptional points out of Dirac cones},
author = {Zhen, Bo and Hsu, Chia Wei and Igarashi, Yuichi and Lu, Ling and Kaminer, Ido and Pick, Adi and Chua, Song-Liang and Joannopoulos, John D. and Soljačić, Marin},
abstractNote = {The Dirac cone underlies many unique electronic properties of graphene 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. In this study, 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.},
doi = {10.1038/nature14889},
journal = {Nature (London)},
number = 7569,
volume = 525,
place = {United States},
year = {2015},
month = {9}
}

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