Curved Gratings as Plasmonic Lenses for Linearly Polarised Light

The ability of curved gratings as sectors of concentric circular gratings to couple linearly polarized light into focused surface plasmons is investigated by theory, simulation and experiment. Curved gratings, as sectors of concentric circular gratings with four different sector angles, are etched into a 30-nm thick gold layer on a glass coverslip and used to couple linearly-polarised free space light at nm into surface plasmons. The experimental and simulation results show that increasing the sector angle of the curved gratings decreases the lateral spotsize of the excited surface plasmons, resulting in focussing of surface plasmons which is analogous to the behaviour of classical optical lenses. We also show that two faced curved gratings, with their groove radius mismatched by half of the plasmon wavelength (asymmetric configuration), can couple linearly-polarised light into a single focal spot of concentrated surface plasmons with smaller depth of focus and higher intensity in comparison to single-sided curved gratings. The major advantage of these structures is the coupling of linearly-polarised light into focused surface plasmons with access to and control of the plasmon focal spot, which facilitates potential applications in sensing, detection and nonlinear plasmonics.Comment: 15 pages and 12 figure

Synchronizing retinal activity in both eyes disrupts binocular map development in the optic tectum

Spatiotemporal correlations in the pattern of spontaneous and evoked retinal ganglion cell (RGC) activity are believed to influence the topographic organization of connections throughout the developing visual system. We have tested this hypothesis by examining the effects of interfering with these potential activity cues during development on the functional organization of binocular maps in the Xenopus frog optic tectum. Paired recordings combined with cross-correlation analyses demonstrated that exposing normal frogs to a continuous 1 Hz of stroboscopic illumination synchronized the firing of all three classes of RGC projecting to the tectum and induced similar patterns of temporally correlated activity across both lobes of the nucleus. Embryonic and eye-rotated larval animals were reared until early adulthood under equivalent stroboscopic conditions. The maps formed by each RGC class in the contralateral tectum showed normal topography and stratification after strobe rearing, but with consistently enlarged multiunit receptive fields. Maps of the ipsilateral eye, formed by crossed isthmotectal axons, showed significant disorder and misalignment with direct visual input from the retina, and in the eye-rotated animals complete compensatory reorientation of these maps usually induced by this procedure failed to occur. These findings suggest that refinement of retinal arbors in the tectum and the ability of crossed isthmotectal arbors to establish binocular convergence with these retinal afferents are disrupted when they all fire together. Our data thus provide direct experimental evidence that spatiotemporal activity patterns within and between the two eyes regulate the precision of their developing connections

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Selective demarketing: When customers destroy value.

Selective demarketing is a strategic option for firms to manage customers who are or are likely to be a poor fit with its offering. Research has investigated related areas such as customer profitability and relationship dissolution but, as yet, studies have not offered a robust conceptualisation of selective demarketing. Based on research into value co-destruction, this study argues that these customers effectively destroy value by misusing or misunderstanding how to integrate their operant resources with those of the firm. As firms exist within a wider service system, this failure to integrate resonates throughout the system. To demarket selectively, firms use higher order operant resources to disengage and discourage these customers. This study offers a novel conceptualisation of selective demarketing and extends research on value destruction through adopting a firm and systems perspective

A critical evaluation of systematic reviews assessing the effect of chronic physical activity on academic achievement, cognition and the brain in children and adolescents: A systematic review

Background. International and national committees have started to evaluate the evidence for the effects of physical activity on neurocognitive health in childhood and adolescence to inform policy. Despite an increasing body of evidence, such reports have shown mixed conclusions. We aimed to critically evaluate and synthesise the evidence for the effects of chronic physical activity on academic achievement, cognitive performance and the brain in children and adolescents in order to guide future research and inform policy. Methods. MedLine, Embase, PsycINFO, Cochrane Library, Web of Science, and ERIC electronic databases were searched from inception to February 6th, 2019. Articles were considered eligible for inclusion if they were systematic reviews with or without meta-analysis, published in peer-reviewed (English) journals. Reviews had to be on school-aged children and/or adolescents that reported on the effects of chronic physical activity or exercise interventions, with cognitive markers, academic achievement or brain markers as outcomes. Reviews were selected independently by two authors and data were extracted using a pre-designed data extraction template. The quality of reviews was assessed using AMSTAR-2 criteria. Results. Of 908 retrieved, non-duplicated articles, 19 systematic reviews met inclusion criteria. One high-quality review reported inconsistent evidence for physical activity-related effects on cognitive- and academic performance in obese or overweight children and adolescents. Eighteen (critically) low-quality reviews presented mixed favourable and null effects, with meta-analyses showing small effect sizes (0.1–0.3) and high heterogeneity. Low-quality reviews suggested physical activity-related brain changes, but lacked an interpretation of these findings. Systematic reviews varied widely in their evidence synthesis, rarely took intervention characteristics (e.g. dose), intervention fidelity or study quality into account and suspected publication bias. Reviews consistently reported that there is a lack of high-quality studies, of studies that include brain imaging outcomes, and of studies that include adolescents or are conducted in South American and African countries. Conclusions. Inconsistent evidence exists for chronic physical activity-related effects on cognitive-, academic-, and brain outcomes. The field needs to refocus its efforts towards improving study quality, transparency of reporting and dissemination, and is urged to differentiate between intervention characteristics for its findings to have a meaningful impact on policy

Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR