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

The Action of Certain Organic Silver Compounds on the Potato Root Eelworm, Heterodera schachtii, Schmidt, With Notes on the Biology of the Parasite, and Additional Papers

Abstract Not Provided

Variational analysis of self-focusing of intense ultrashort pulses in gases

By using perturbation theory we derive an expression for the electrical field of a Gaussian laser pulse propagating in a gas medium. This expression is used as a trial solution in a variational method to get quasianalytical solutions for the width, intensity and self-focusing distance of ultrashort pulse. The approximation gives an improved agreement with results of numerical simulations for a broad range of values of the input power of the pulse than previous analytical results available in the literature.Comment: 19 pages, 8 figure

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

Strong nonlinear optical response of graphene flakes measured by four-wave mixing

We present the first experimental investigation of nonlinear optical properties of graphene flakes. We find that at near infrared frequencies a graphene monolayer exhibits a remarkably high third-order optical nonlinearity which is practically independent of the wavelengths of incident light. The nonlinear optical response can be utilized for imaging purposes, with image contrasts of graphene which are orders of magnitude higher than those obtained using linear microscopy.Comment: 4 pages, 5 figure

Ultraslow light propagation in an inhomogeneously broadened rare-earth ion-doped crystal

We show that Coherent Population Oscillations effect allows to burn a narrow spectral hole (26Hz) within the homogeneous absorption line of the optical transition of an Erbium ion-doped crystal. The large dispersion of the index of refraction associated with this hole permits to achieve a group velocity as low as 2.7m/s with a ransmission of 40%. We especially benefit from the inhomogeneous absorption broadening of the ions to tune both the transmission coefficient, from 40% to 90%, and the light group velocity from 2.7m/s to 100m/s

A note on Burgers' turbulence

In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for the velocity-difference PDF, with the exciting force correlation function $\kappa (y)\sim1-y^{\alpha}$ is analyzed. Several solvable cases are considered, which are in a good agreement with available numerical results. Then it is shown how the method developed by A. Polyakov can be applied to turbulence with short-scale-correlated forces, a situation considered in models of self-organized criticality.Comment: 11 pages, Late

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.Comment: 16 pages, 5 figure

Analytical model of brittle destruction based on hypothesis of scale similarity

The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys the power law with the exponent between -4 and -1. The model of destruction has much in common with the fractal theory. The power exponent can be expressed in terms of the fractal dimension. Reasonable assumptions on the shape of fragments concretize the power exponent, and vice versa possible destruction laws can be inferred on the basis of measured size distributions.Comment: 10 pages, 3 figure

Power dependence of pure spin current injection by quantum interference

We investigate the power dependence of pure spin current injection in GaAs bulk and quantum-well samples by a quantum interference and control technique. Spin separation is measured as a function of the relative strength of the two transition pathways driven by two laser pulses. By keeping the relaxation time of the current unchanged, we are able to relate the spin separation to the injected average velocity. We find that the average velocity is determined by the relative strength of the two transitions in the same way as in classical interference. Based on this, we conclude that the density of injected pure spin current increases monotonically with the excitation laser intensities. The experimental results are consistent with theoretical calculations based on Fermi's golden rule.Comment: 6 pages, 4 figure