<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-symmetry in honeycomb photonic lattices

Szameit, Alexander; Rechtsman, Mikael C.; Bahat-Treidel, Omri; Segev, Mordechai

doi:10.1103/physreva.84.021806

Cited by 283 publications

(265 citation statements)

References 37 publications

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“…These include studies of i) P Tsymmetry (i.e. symmetry under the combined operations of parity and time reversal), ii) nonlinear wave dynamics, iii) the persistence of the Klein effect, and iv) the breakdown of conical diffraction due to nonlinear interactions [54][55][56]. Perhaps the culmination of these studies has been presented in Refs.…”

Section: Confining Photonsmentioning

confidence: 99%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.

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Section: Confining Photonsmentioning

confidence: 99%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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“…[6]. Under balanced gain and loss, the real conical spectrum becomes complex, emulating superluminal "tachyonic" dispersion [40,81]. This superluminal dispersion is associated with the appearance of the non-Hermitian analogue of a conical intersection, "exceptional point" degeneracies [82], which form generically from any accidental conical intersection when open boundary conditions are applied [83].…”

Section: Applicationsmentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective Dirac equation, with electron spin replaced by a "fermionic" half-integer pseudospin. However, in many systems such as metamaterials, modal symmetries result in the formation of higher order conical intersections with integer or "bosonic" pseudospin. The ability to engineer lattices with these qualitatively different singular dispersion relations opens up many applications, including superior slab lasers, generation of orbital angular momentum, zeroindex metamaterials, and quantum simulation of exotic phases of relativistic matter.

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“…For example, in the PT -symmetric plasmonic waveguides, EPs can close the gap formed by two branches of surface plasmon polaritons [28]. EPs can also close band gaps in PT -symmetry honeycomb PCs [29,30]. A ring of EPs can exist near a Dirac-like cone in two-dimensional (2D) PCs [33].…”

Section: Introductionmentioning

confidence: 99%

“…For systems with continuous spectra, various PT -symmetric photonic crystals (PCs) have been considered by studying their complex band structures. For each Bloch * Corresponding author: phchan@ust.hk k, the coalescence of two eigenstates in a discrete spectrum is normally called an EP [28][29][30][31][32][33]. For example, in the PT -symmetric plasmonic waveguides, EPs can close the gap formed by two branches of surface plasmon polaritons [28].…”

Section: Introductionmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

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Non-Hermitian systems with parity-time-(PT )-symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT -symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of PT symmetry transitions are found. One is that a PT -broken phase can reenter into a PT -exact phase at a higher degree of non-Hermiticity. The other is that two EPs, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some k point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the PT -exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems.

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PT-symmetry in honeycomb photonic lattices

Cited by 283 publications

References 37 publications

Artificial honeycomb lattices for electrons, atoms and photons

Artificial honeycomb lattices for electrons, atoms and photons

Conical intersections for light and matter waves

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

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