Optical mesh lattices with PT-symmetry

We investigate a new class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response is studied in both the passive and parity-time (PT) symmetric regime. The possibility of band merging and the emergence of exceptional points along with the associated optical dynamics are considered in detail both above and below the PT-symmetry breaking point. Finally unidirectional invisibility in PT-synthetic mesh lattices is also examined along with possible superluminal light transport dynamics.Comment: 14 pages, 17 figures, published in Physical Review

Experimental Measurement of the Berry Curvature from Anomalous Transport

Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can be related to global topological invariants such as those classifying quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a wave packet. Here, we experimentally demonstrate for the first time that wave packet dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time-evolution of a wave packet in a 1D geometrical "charge" pump, where the Berry curvature leads to an anomalous displacement of the wave packet under pumping. This is both the first direct observation of Berry curvature effects in an optical system, and, more generally, the proof-of-principle demonstration that semi-classical dynamics can serve as a high-resolution tool for mapping out geometrical properties

Spawning rings of exceptional points out of Dirac cones

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. Deformations of the Dirac cone often reveal 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. These two fields of research are in fact connected: here we discover the ability of a Dirac cone to evolve into a ring of exceptional points, which we call an "exceptional ring." We experimentally demonstrate this concept 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 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 that exists in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain

Bypass surgery versus stenting for the treatment of multivessel disease in patients with unstable angina compared with stable angina

BACKGROUND: Earlier reports have shown that the outcome of balloon angioplasty or bypass surgery in unstable angina is less favorable than in stable angina. Recent improvements in percutaneous treatment (stent implantation) and bypass surgery (arterial grafts) warrant reevaluation of the relative merits of either technique in treatment of unstable angina. Methods and Results- Seven hundred fifty-five patients with stable angina were randomly assigned to coronary stenting (374) or bypass surgery (381), and 450 patients with unstable angina were randomly assigned to coronary stenting (226) or bypass surgery (224). All patients had multivessel disease considered to be equally treatable by either technique. Freedom from major adverse events, including death, myocardial infarction, and cerebrovascular events, at 1 year was not different in unstable patients (91.2% versus 88.9%) and stable patients (90.4% versus 92.6%) treated, respectively, with coronary stenting or bypass surgery. Freedom from repeat revascularization at 1 year was similar in unstable and stable angina treated with stenting (79.2% versus 78.9%) or bypass surgery (96.3% versus 96%) but was significantly higher in both unstable and stable patients treated with stenting (16.8% versus 16.9%) compared with bypass surgery (3.6% versus 3.5%). Neither the difference in costs between stented or bypassed stable or unstable angina ($2594 versus$3627) nor the cost-effectiveness was significantly different at 1 year. CONCLUSIONS: There was no difference in rates of death, myocardial infarction, and cerebrovascular event at 1 year in patients with unstable angina and multivessel disease treated with either stented angioplasty or bypass surgery compared with patients with stable angina. The rate of repeat revascularization of both unstable and stable angina was significantly higher in patients with stents

Parity-time symmetric coupled microresonators with a dispersive gain/loss

The paper reports on the coupling of Parity-Time (PT)-symmetric whispering gallery resonators with realistic material and gain/loss models. Response of the PT system is analyzed for the case of low and high material and gain dispersion, and also for two practical scenarios when the pump frequency is not aligned with the resonant frequency of the desired whispering gallery mode and when there is imbalance in the gain/loss profile. The results show that the presence of dispersion and frequency misalignment causes skewness in frequency bifurcation and significant reduction of the PT breaking point, respectively. Finally, we demonstrate a lasing mode operation which occurs due to an early PT-breaking by increasing loss in a PT system with unbalanced gain and loss

Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

International audienceWe consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay

Evidence for the η_b(1S) Meson in Radiative Υ(2S) Decay

We have performed a search for the η_b(1S) meson in the radiative decay of the Υ(2S) resonance using a sample of 91.6 × 10^6 Υ(2S) events recorded with the BABAR detector at the PEP-II B factory at the SLAC National Accelerator Laboratory. We observe a peak in the photon energy spectrum at E_γ = 609.3^(+4.6)_(-4.5)(stat)±1.9(syst) MeV, corresponding to an η_b(1S) mass of 9394.2^(+4.8)_(-4.9)(stat) ± 2.0(syst) MeV/c^2. The branching fraction for the decay Υ(2S) → γη_b(1S) is determined to be [3.9 ± 1.1(stat)^(+1.1)_(-0.9)(syst)] × 10^(-4). We find the ratio of branching fractions B[Υ(2S) → γη_b(1S)]/B[Υ(3S) → γη_b(1S)]= 0.82 ± 0.24(stat)^(+0.20)_(-0.19)(syst)

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Spatial Kramers-Kronig relations and the reflection of waves

Copyright © 2015, Rights Managed by Nature Publishing GroupAuthor version of article. The version of record is available from the publisher via DOI: 10.1038/nphoton.2015.106When a planar dielectric medium has a permittivity profile that is an analytic function in the upper or lower half of the complex position plane x=x'+ix'' then the real and imaginary parts of its permittivity are related by the spatial Kramers-Kronig relations. We find that such a medium will not reflect radiation incident from one side, whatever the angle of incidence. Using the spatial Kramers-Kronig relations, one can derive a real part of a permittivity profile from some given imaginary part (or vice versa) such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories and may have relevance for designing materials that efficiently absorb radiation or for the creation of a new type of anti-reflection surface.Engineering and Physical Sciences Research Council (EPSRC