Conical diffraction and the dispersion surface of hyperbolic metamaterials

Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants $\epsilon_1<0$, $0<\epsilon_2\neq\epsilon_3$. In this general case the two sheets of the index surface intersect forming conical singularities. We derive the ray description of conical refraction in these materials, and show that it is topologically and quantitatively distinct from conical refraction in a conventional biaxial material. We also develop a wave optics description, which allows us to obtain the diffraction patterns formed from arbitrary beams incident close to the optic axis. The resulting patterns lack circular symmetry, and hence are qualitatively different from those obtained in conventional, positive index materials.Comment: 10 pages, 7 figure

Vortex states of a disordered quantum Hall bilayer

We present and solve a model for the vortex configuration of a disordered quantum Hall bilayer in the limit of strong and smooth disorder. We argue that there is a characteristic disorder strength below which vortices will be rare, and above which they proliferate. We predict that this can be observed tuning the electron density in a given sample. The ground state in the strong-disorder regime can be understood as an emulsion of vortex-antivortex crystals. Its signatures include a suppression of the spatial decay of counterflow currents. We find an increase of at least an order of magnitude in the length scale for this decay compared to a clean system. This provides a possible explanation of the apparent absence of leakage of counterflow currents through interlayer tunneling, even in experiments performed deep in the coherent phase where enhanced interlayer tunneling is observed.Comment: 5 pages, 3 figures. v2 slightly extended to emphasize new length scal

Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices

We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant $\epsilon_s$ of spheres is lower than the dielectric constant $\epsilon_b$ of the background medium. If $\epsilon_s> \epsilon_b$, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast $\epsilon_b/\epsilon_s$ for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two figures, and a few references adde

Polariton condensation and lasing in optical microcavities - the decoherence driven crossover

We explore the behaviour of a system which consists of a photon mode dipole coupled to a medium of two-level oscillators in a microcavity in the presence of decoherence. We consider two types of decoherence processes which are analogous to magnetic and non-magnetic impurities in superconductors. We study different phases of this system as the decoherence strength and the excitation density is changed. For a low decoherence we obtain a polariton condensate with comparable excitonic and photonic parts at low densities and a BCS-like state with bigger photon component due to the fermionic phase space filling effect at high densities. In both cases there is a large gap in the density of states. As the decoherence is increased the gap is broadened and suppressed, resulting in a gapless condensate and finally a suppression of the coherence in a low density regime and a laser at high density limit. A crossover between these regimes is studied in a self-consistent way analogous to the Abrikosov and Gor'kov theory of gapless superconductivity.Comment: 17 pages, 8 figures, submitted to PR

Global impacts of tropospheric halogens (Cl, Br, I) on oxidants and composition in GEOS-Chem [Discussion paper]

We present a simulation of the global present-day composition of the troposphere which includes the chemistry of halogens (Cl, Br, I). Building on previous work within the GEOS-Chem model we include emissions of inorganic iodine from the oceans, anthropogenic and biogenic sources of halogenated gases, gas phase chemistry, and a parameterised approach to heterogeneous halogen chemistry. Consistent with Schmidt et al. (2016) we do not include sea-salt debromination. Observations of halogen radicals (BrO, IO) are sparse but the model has some skill in reproducing these. Modelled IO shows both high and low biases when compared to different datasets, but BrO concentrations appear to be modelled low. Comparisons to the very sparse observations dataset of reactive Cl species suggest the model represents a lower limit of the impacts of these species, likely due to underestimates in emissions and therefore burdens. Inclusion of Cl, Br, and I results in a general improvement in simulation of ozone (O3) concentrations, except in polar regions where the model now underestimates O3 concentrations. Halogen chemistry reduces the global tropospheric O3 burden by 18.6 %, with the O3 lifetime reducing from 26 to 22 days. Global mean OH concentrations of 1.28  ×  106 molecules cm−3 are 8.2 % lower than in a simulation without halogens, leading to an increase in the CH4 lifetime (10.8 %) due to OH oxidation from 7.47 to 8.28 years. Oxidation of CH4 by Cl is small (∼  2 %) but Cl oxidation of other VOCs (ethane, acetone, and propane) can be significant (∼  15–27 %). Oxidation of VOCs by Br is smaller, representing 3.9 % of the loss of acetaldehyde and 0.9 % of the loss of formaldehyde

Models of coherent exciton condensation

That excitons in solids might condense into a phase-coherent ground state was proposed about 40 years ago, and has been attracting experimental and theoretical attention ever since. Although experimental confirmation has been hard to come by, the concepts released by this phenomenon have been widely influential. This tutorial review discusses general aspects of the theory of exciton and polariton condensates, focussing on the reasons for coherence in the ground state wavefunction, the BCS to Bose crossover(s) for excitons and for polaritons, and the relationship of the coherent condensates to standard lasers.Comment: 27 pages, 6 figures. Submitted for a special issue of J. Phys. Cond. Matt. associated with the EU network "Photon-mediated phenomena in semiconductor nanostructures

Conducting sexualities research: An outline of emergent issues and case studies from ten wellcome-funded projects [version 1; peer review: 3 approved]

© 2019 Kneale D et al. This letter seeks to synthesise methodological challenges encountered in a cohort of Wellcome Trust-funded research projects focusing on sexualities and health. The ten Wellcome Trust projects span a diversity of gender and sexual orientations and identities, settings; institutional and non-institutional contexts, lifecourse stages, and explore a range of health-related interventions. As researchers, we originate from a breadth of disciplinary traditions, use a variety of research methods and data sources. Despite this breadth, four common themes are found across the projects: (i) inclusivity representations and representativeness, (ii) lumping together of diverse groups, (iii) institutions and closed settings (iv) ethical and governance barriers

On occurrence of spectral edges for periodic operators inside the Brillouin zone

The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the (reduced) Brillouin zone only, rather than the whole zone? Or, do the edges of the spectrum occur necessarily at the set of ``corner'' high symmetry points? This is known to be true in 1D, while no apparent reasons exist for this to be happening in higher dimensions. In many practical cases, though, this appears to be correct, which sometimes leads to the claims that this is always true. There seems to be no definite answer in the literature, and one encounters different opinions about this problem in the community. In this paper, starting with simple discrete graph operators, we construct a variety of convincing multiply-periodic examples showing that the spectral edges might occur deeply inside the Brillouin zone. On the other hand, it is also shown that in a ``generic'' case, the situation of spectral edges appearing at high symmetry points is stable under small perturbations. This explains to some degree why in many (maybe even most) practical cases the statement still holds.Comment: 25 pages, 10 EPS figures. Typos corrected and a reference added in the new versio

Ki-67 and outcome in clinically localised prostate cancer: analysis of conservatively treated prostate cancer patients from the Trans-Atlantic Prostate Group study

Treatment decisions after diagnosis of clinically localised prostate cancer are difficult due to variability in tumour behaviour. We therefore examined one of the most promising biomarkers in prostate cancer, Ki-67, in a cohort of 808 patients diagnosed with prostate cancer between 1990 and 1996 and treated conservatively. Ki-67 expression was assessed immunohistochemically, in two laboratories, by two different scoring methods and the results compared with cancer-specific and overall survival. The power of the biomarker was compared with Gleason score and initial serum prostate-specific antigen (PSA). Both methods showed that Ki-67 provided additional prognostic information beyond that available from Gleason score and PSA: for the semi-quantitative method, Δχ2 (1 d.f.)=24.6 (P<0.0001), overall survival χ2=20.5 (P<0.0001), and for the quantitative method, Δχ2 (1 d.f.)=15.1 (P=0.0001), overall survival χ2=10.85 (P=0.001). Ki-67 is a powerful biomarker in localised prostate cancer and adds to a model predicting the need for radical or conservative therapy. As it is already in widespread use in routine pathology, it is confirmed as the most promising biomarker to be applied into routine practice