Search results for " Nonlinear"
showing 10 items of 1224 documents
Impact of fourth-order dispersion in the modulational instability spectra of wave propagation in glass fibers with saturable nonlinearity
2010
We analyze the modulational instability (MI) of light waves in glass fibers with a local saturable nonlinear refractive index. We identify and discuss the salient features of the effect of the fourth order of the fiber dispersion, in the MI spectra. Particularly, we find that in fibers with negative sign of the second-order dispersion and positive sign of the fourth-order dispersion (FOD), the two existing types of MI processes, called processes of type I, which generate a single pair of sidebands, and processes of type II, which lead to two pairs of sidebands, become highly sensitive to the magnitude of the FOD, both quantitatively and qualitatively. We demonstrate the existence of a criti…
Metacoatings for wavelength-scale, high-numerical-aperture plano–concave focusing lenses
2016
We design plano–concave silicon lenses with coupled gradient-index plasmonic metacoatings for ultrawide apertured focusing utilizing a reduced region of ∼20λ2. The anomalous refraction induced in the planar input side of the lens and in the boundary of the wavelength-scale focal region boosts the curvature of the emerging wavefront, thus significantly enhancing the resolution of the tightly focused optical wave. The formation of a light tongue with dimensions approaching those of the concave opening is here evidenced. This scheme is expected to have potential applications in optical trapping and detection.
Inverse dispersion engineering in silicon waveguides
2014
We present a numerical tool that searches an optimal cross section geometry of silicon-on-insulator waveguides given a target dispersion profile. The approach is a gradient-based multidimensional method whose efficiency resides on the simultaneous calculation of the propagation constant derivatives with respect to all geometrical parameters of the structure by using the waveguide mode distribution. The algorithm is compatible with regular mode solvers. As an illustrative example, using a silicon slot hybrid waveguide with 4 independent degrees of freedom, our approach finds ultra-flattened (either normal or anomalous) dispersion over 350 nm bandwidth in less than 10 iterations.
CONDENSATE FRACTION IN THE DYNAMIC STRUCTURE FUNCTION OF BOSE FLUIDS
2007
We present results on the behavior of the dynamic structure function in the short wave length limit using the equation of motion method. The one-body continuity equation defines the self-energy, which becomes a functional of the fluctuating two-body correlation function. We evaluate the self-energy in this limit and show that sum rules up to the second moment, which requires the self-energy in the short wave length limit and zero frequency to be proportional to the kinetic energy per particle, are exactly satisfied. We compare our results with the impulse approximation and calculate the condensate fraction. An analytic expression for the momentum distribution is also derived.
Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization
2003
We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.
On the invariant symmetries of the D-metrics
2007
We analyze the symmetries and other invariant qualities of the $\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null congruences). We recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation, and we analyze when these invariant symmetries characterize the family of metrics. We show that the subfamily of the Kerr-NUT solutions are those admitting a Papapetrou field aligned with the Weyl tensor.
LATTICE–BOLTZMANN SIMULATION OF DENSE NANOFLOWS: A COMPARISON WITH MOLECULAR DYNAMICS AND NAVIER–STOKES SOLUTIONS
2007
In a recent work, a dense fluid flow across a nanoscopic thin plate was simulated by means of Molecular Dynamics (MD) and Lattice Boltzmann (LB) methods. It was found that in order to recover quantitative agreement with MD results, the LB simulation must be pushed down to sub–nanoscopic scales, i.e. fractions of the range of molecular interactions. In this work, we point out that in this sub–nanoscopic regime, the LB method works outside the hydrodynamic limit at the level of a single cell spacing. A quantitative comparison with the Navier–Stokes (NS) solution shows however that LB and NS results are quite similar, thereby indicating that, apart for a small region past the plate, this nano…
Hyperfine Paschen-Back regime in alkali metal atoms: consistency of two theoretical considerations and experiment
2013
Simple and efficient "\lambda-method" and "\lambda/2-method" (\lambda is the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium are implemented to study the splitting of hyperfine transitions of 85Rb and 87Rb D_1 line in an external magnetic field in the range of B = 0.5 - 0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in 85Rb (87Rb) spectra in the case of \sigma+ polarized laser radiation, only 6 (4) remain at B > 0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen-Back regime). The expressions derived in the frame of completely uncoupl…
Fluorescence of rubidium in a submicrometer vapor cell: spectral resolution of atomic transitions between Zeeman sublevels in a moderate magnetic fie…
2005
It is experimentally demonstrated that use of an extremely thin cell (ETC) with the thickness of a Rb atomic vapor column of ∼400 nm allows one to resolve a large number of individual transitions between Zeeman sublevels of the D1 line of 87Rb and 85Rb in the sub-Doppler fluorescence excitation spectra in an external magnetic field of ∼200 G. It is revealed that due to the peculiarities of the Zeeman effect for different hyperfine levels of Rb, all allowed transitions between magnetic sublevels can be clearly resolved for 87RbF_g = 1 --> F_e = 1, 2 and F_g = 2 --> F_e = 1, 2 fluorescence excitation. Also, relatively good spectral resolution can be achieved for 85RbF_g = 2 --> F_e = 2, 3 flu…
Contour detection based on nonlinear discrete diffusion in a cellular nonlinear network
2001
International audience; A contour detection based on a diffusive cellular nonlinear network is proposed. It is shown that there exists a particular nonlinear function for which, numerically, the obtained contour is satisfactory. Furthermore, this nonlinear function can be achieved using analog components.