Two-peaked and flat-top perfect bright solitons in epsilon-near-zero nonlinear metamaterials: novel Kerr self-trapping mechanisms

We analytically investigate transverse magnetic (TM) spatial bright solitons, as exact solutions of Maxwell's equations, propagating through nonlinear metamaterials whose linear dielectric permittivity is very close to zero and whose effective nonlinear Kerr parameters can be tailored to achieve values not available in standard materials. Exploiting the fact that, in the considered medium, linear and nonlinear polarization can be comparable at feasible and realistic optical intensities, we identify two novel self-trapping mechanisms able to support two-peaked and flat-top solitons, respectively. Specifically, these two novel mechanisms are based on the occurrence of critical points at which the effective nonlinear permittivity vanishes, the two mechanisms differing in the way the compensation between linear and nonlinear polarization is achieved through the non-standard values of the nonlinear parameters.Comment: 7 pages, 4 figure

|\epsilon|-Near-Zero materials in the near-infrared

We consider a mixture of metal coated quantum dots dispersed in a polymer matrix and, using a modified version of the standard Maxwell-Garnett mixing rule, we prove that the mixture parameters (particles radius, quantum dots gain, etc.) can be chosen so that the effective medium permittivity has an absolute value very close to zero in the near-infrared, i.e. |Re(epsilon)|<<1 and |Im (epsilon)|<<1 at the same near-infrared wavelength. Resorting to full-wave simulations, we investigate the accuracy of the effective medium predictions and we relate their discrepancy with rigorous numerical results to the fact that |epsilon|<<1 is a critical requirement. We show that a simple method for reducing this discrepancy, and hence for achieving a prescribed value of |\epsilon|, consists in a subsequent fine-tuning of the nanoparticles volume filling fraction.Comment: 3 pages, 3 figure

Analisis Proses Blanking Dengan Simple Press Tool

Blanking production process will be required for mass production due to good product quality and lower production costs. For mini wrench products, blanking process can be done with a simple press tool. This analysis starting with design, manufacturing and than analysis. It's concluded that the construction of simple press tool are Plate Material (ST 60), Pillar Material (ST 60), Punch and Dies Material (SKD 11 with 15 mm thickness and 0.108 mm clearance), stripper material (ST 37), the punch holder material (ST 37), and the stopper material (ST 37). Forces acting on the machine press tool are cutting force (37 kN), clamping force (371 N), and power press machine (8.5 kW)

Introduction to special issue: Aesthetics in mathematics

Mathematicians often appreciate the beauty and elegance of particular theorems, proofs, and definitions, attaching importance not only to the truth but also to the aesthetic merit of their work. As Henri Poincaré [1930, p. 59] put it, mathematical beauty is a ‘real aesthetic feeling that all true mathematicians recognise’. Others went further, regarding mathematical beauty as a key motivation driving the formulation of mathematical proofs and even as a criterion for choosing one proof over another. As Hermann Weyl famously and provocatively declared, ‘My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful’ (cited [Chandrasekhar, 1987, p. 52])....Talk of the beauty of mathematical theorems, proofs, and definitions may thus be commonplace

Directions in entrepreneurship education in Europe

An extraordinary proliferation of entrepreneurship courses and programs was and still is underway in colleges and universities worldwide. In Europe this phenomenon has been further stimulated by the focus on Entrepreneurship as key objective for the implementation of the Europe2020 strategy (EC, 2010). This paper provides a systematized overview of patterns and directions in EE in Europe in recent years. We conduct a review of the published research of the theme with an European focus in an attempt to organize the literature along precise lines. When possible we use empirical findings to sustain our arguments. Systematizing the existing literature is a necessary step in developing the field. For researchers, this overview will be constructive in providing an analysis of the directions of published research and in setting up a research agenda for the future. It also raises awareness with regard to entrepreneurship, and in particular, to its potential contribution to the individuals and to the competitiveness of economies. The empirical analysis adds to our knowledge about the current situation of EE in practice in Europe

Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity

We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. The behavior of the electromagnetic field in the extreme nonlinear regime is very peculiar and characterized by novel features as, for example, the transverse power flow reversing. In order to probe the novel regime, we consider a class of fields (transverse magnetic nonlinear guided waves) admitting full analytical description and we show that these waves are allowed to propagate even in media with $\epsilon0$ since the nonlinear polarization produces a positive overall effective permittivity. The considered nonlinear waves exhibit, in addition to the mentioned features, a number of interesting properties like hyper-focusing induced by the phase difference between the field components.Comment: 12 pages, 7 figure

Collision and fusion of counterpropagating micron-sized optical beams in non-uniformly biased photorefractive crystals

We theoretically investigate collision of optical beams travelling in opposite directions through a centrosymmetric photorefractive crystal biased by a spatially non-uniform voltage. We analytically predict the fusion of counterpropagating solitons in conditions in which the applied voltage is rapidly modulated along the propagation axis, so that self-bending is suppressed by the "restoring symmetry" mechanism. Moreover, when the applied voltage is slowly modulated, we predict that the modified self-bending allows conditions in which the two beams fuse together, forming a curved light-channel splice.Comment: 12 page