602 research outputs found
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
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
A Framework for Verifying Data-Centric Protocols
International audienceData centric languages, such as recursive rule based languages, have been proposed to program distributed applications over networks. They simplify greatly the code, while still admitting efficient distributed execution. We show that they also provide a promising approach to the verification of distributed protocols, thanks to their data centric orientation, which allows us to explicitly handle global structures such as the topology of the network. We consider a framework using an original formalization in the Coq proof assistant of a distributed computation model based on message passing with either synchronous or asynchronous behavior. The declarative rules of the Netlog language for specifying distributed protocols and the virtual machines for evaluating these rules are encoded in Coq as well. We consider as a case study tree protocols, and show how this framework enables us to formally verify them in both the asynchronous and synchronous setting
A versatile all-optical parity-time signal processing device using a Bragg grating induced using positive and negative Kerr-nonlinearity
The properties of gratings with Kerr nonlinearity and PT symmetry are investigated in this paper. The impact of the gain and loss saturation on the response of the grating is analysed for different input intensities and gain/loss parameters. Potential applications of these gratings as
switches, logic gates and amplifiers are also shown
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)
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
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
PT-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations
Recommended from our members
Need for high-resolution genetic analysis in iPSC: results and lessons from the ForIPS consortium
Genetic integrity of induced pluripotent stem cells (iPSCs) is essential for their validity as disease models and for potential therapeutic use. We describe the comprehensive analysis in the ForIPS consortium: an iPSC collection from donors with neurological diseases and healthy controls. Characterization included pluripotency confirmation, fingerprinting, conventional and molecular karyotyping in all lines. In the majority, somatic copy number variants (CNVs) were identified. A subset with available matched donor DNA was selected for comparative exome sequencing. We identified single nucleotide variants (SNVs) at different allelic frequencies in each clone with high variability in mutational load. Low frequencies of variants in parental fibroblasts highlight the importance of germline samples. Somatic variant number was independent from reprogramming, cell type and passage. Comparison with disease genes and prediction scores suggest biological relevance for some variants. We show that high-throughput sequencing has value beyond SNV detection and the requirement to individually evaluate each clone
Outlook for inverse design in nanophotonics
Recent advancements in computational inverse design have begun to reshape the
landscape of structures and techniques available to nanophotonics. Here, we
outline a cross section of key developments at the intersection of these two
fields: moving from a recap of foundational results to motivation of emerging
applications in nonlinear, topological, near-field and on-chip optics.Comment: 13 pages, 6 figure
- …