Spawning rings of exceptional points out of Dirac cones

• Published in: Nature (London) Vol. 525; no. 7569; pp. 354 - 358
• Main Authors: Zhen, Bo, Hsu, Chia Wei, Igarashi, Yuichi, Lu, Ling, Kaminer, Ido, Pick, Adi, Chua, Song-Liang, Joannopoulos, John D., Soljačić, Marin
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 17.09.2015; Nature Publishing Group
• Subjects: 142/126; 147/135; 639/624/399/1022; 639/624/400/1021; 639/766; charge transport; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Cone; defects; Dirac equation; Eigenvalues; Humanities and Social Sciences; Lasers; letter; Magnetic fields; materials and chemistry by design; Mathematical research; mechanical behavior; multidisciplinary; optics; phonons; Physical properties; Physics; Radiation; Rings (Algebra); Science; solar (photovoltaic); solar (thermal); SOLAR ENERGY; solid state lighting; Spawning; spin dynamics; Symmetry; synthesis (novel materials); synthesis (scalable processing); synthesis (self-assembly); thermal conductivity; thermoelectric
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/nature14889

Exceptional points are singularities in non-Hermitian systems that can produce unusual effects, and it is shown that a Dirac cone in a photonic crystal can generate a continuous ring of exceptional points through flattening the tip of the cone. Lossless parity–time symmetry Exceptional points are singularities in the energy functions of a physical system that can produce unusual effects. Until recently, they existed mainly in theory, but received renewed attention with experimental demonstrations in optical systems such as in lasers with reversed pump dependence and photonic structures with unidirectional transmission or reflection. Most studies involve systems with 'parity–time symmetry', where gain as well as artificial loss is required, an undesirable combination for practical applications. Bo Zhen et al . demonstrate, with theory and experiments, a photonic structure — a thick photonic crystal slab — in which a continuous ring of exceptional points can be created through a carefully tuned energy band structure. The approach could open the way to accessing unusual physical properties that might be exploited, for example, in advanced light sources and control of light propagation. The Dirac cone underlies many unique electronic properties of graphene 1 and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays 2 , atoms in optical lattices 3 , and through accidental degeneracy 4 , 5 . 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 6 , 7 , also known as the parity–time symmetry breaking point 8 , 9 , 10 , 11 , where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency 12 , unidirectional transmission or reflection 11 , 13 , 14 , and lasers with reversed pump dependence 15 or single-mode operation 16 , 17 . 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 18 , 19 , 20 . 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.