(2+1)-D propagation of spatio-temporal solitary waves including higher-order corrections

We study the propagation of bright two-dimensional spatio-temporal solitary waves using a higher-order multi-dimensional non-linear Schrödinger equation. Starting directly from Maxwell's equations, a multiple-scales derivation is presented which results in a generalized first-order vectorial evolution equation that is valid for the non-linear spatio-temporal propagation of a predominantly linearly polarized electric field with large spatial and temporal bandwidths. A reduced version of this full equation including the higher-order linear and non-linear effects of third- and fourth-order dispersion, space–time focusing, shock, stimulated Raman scattering, and ultrafast quintic index saturation, is solved numerically via a modified split-step algorithm. Material parameters corresponding to those of fused silica at λf=1.55 m are used, with the addition of a negative quintic saturation term. Without quintic saturation, the non-linear spatio-temporal wave broadens under the action of the higher-order space–time effects. In addition, in the absence of Raman scattering, the wave undergoes collapse until arrested by the remaining higher-order terms. Frequency down-shifting and spatio-temporal broadening due to Raman scattering are found to have the greatest effect on non-linear spatio-temporal wave propagation. Nevertheless, we demonstrate that quintic saturation effectively stabilizes the wave such that broadening is reduced considerably, permitting nearly stationary propagation over many confocal distances, albeit with substantial down-shift. The resulting spatio-temporal solitary waves should be useful for applications in ultrafast all-optical switching and logic, and the generalized evolution equations will provide a refined starting point for the study of spatio-temporal phenomena in other areas as well.     

Least-cost network topology design for a new service

We describe an implementation of the tabu search metaheuristic that effectively finds a low-cost topology for a communications network to provide a centralized new service. Our results are compared to those of a greedy algorithm which applies corresponding decision rules, but without the guidance of the tabu search framework. These problems are difficult computationally, representing integer programs that can involve as many as 10,000 integer variables and 2000 constraints in practical applications. The tabu search results approach succeeded in obtaining significant improvements over the greedy approach, yielding optimal solutions to problems small enough to allow independent verification of optimality status and, more generally, yielding both absolute and percentage cost improvements that did not deteriorate with increasing problem size.This research was partially supported by the Air Force Office of Scientific Research and the Office of Naval Research Contract No. F49629-90-C-0033.     

Hydrogen dissociation on high-temperature tungsten

H₂ dissociation on polycrystalline tungsten is measured from 1700 to 3000 K using the filament temperature (T) change and a normalized H-atom density at the chamber surface. The dissociation probability per H₂ filament collision (P_diss) saturates at 0.40 at high T and has a 2.25 ± 0.05 eV apparent activation energy when P_diss ? 1. This activation energy is consistent with prior data and models, but the H₂ pressure dependence is not. P_diss is independent of the H₂ pressure for this entire T range and the 1-85 mTorr pressure range studied, contradicting the primary model that has been used to explain H₂ dissociation on tungsten and other metals. We show that some apparently contradictory prior measurements are actually consistent with our observations and with each other, once this pressure dependence of P_diss is recognized.     

Approximate response of a two-level system to intense multimode radiation

The rotating wave solution for a two-level atom in an intense monochromatic radiation field is extended by an approximation to the case of a multimode radiation field. Expressions for the resultant average excitation probability of the upper state are presented for rectangular and triangular pulses.     

Impedance of an electric dipole located in a cylindrical cavity in a dissipative medium

The electromagnetic fields of an electric dipole located inside a cylindrical cavity or empty tunnel are formulated. The results are used to deduce an expression for the change of self-impedance due to the presence of the cavity or tunnel walls. A numerical evaluation of the resultant convergent integral and a summation of the angular harmonic series were performed. An important finding is that the input resistance of the dipole is approximately a constant for frequencies less than about 25 MHz for a typical tunnel radius of 2 m. Such results are shown to be in qualitative agreement with an earlier analysis of an electric dipole over a dissipative half-space.     

Measurement of field effects on dielectronic recombination of Si11+ ions

Cross sections for dielectronic recombination can be influenced by the presence of external electric fields in the electron--ion collision region. In most of the previous experiments with multiply charged ions such fields were present but unknown. Therefore, comparisons of experimental results with theoretical calculations were ambiguous: for obtaining best possible agreement, theory could use the field strength as a free parameter to adjust the calculated cross sections to the experiment. In recent measurements with 10 MeV/u Si¹¹⁺ ions stored in CRYRING, controlled external motional electric fields up to 183 V/cm were introduced in the electron cooler. Significant cross section enhancements were found for Rydberg states n > 20. This revised version was published online in August 2006 with corrections to the Cover Date.     

A family of angle-moments proportional to r-n,n = 1,2,…, in free space

The moments M_n(r) ≡ 1/2 ∝^2π₀ dθ sinⁿ θ I(r,θ) of the intensity I(r, θ) in free space surrounding a spherical object emitting radiation with an arbitrary directional dependence are shown to be exactly proportional to r^-(n+1), n = 0, 1,….     

A New Class of Equations for Rotationally Constrained Flows

The incompressible Navier–Stokes equation is considered in the limit of rapid rotation (small Ekman number). The analysis is limited to horizontal scales small enough so that both horizontal and vertical velocities are comparable, but the horizontal velocity components are still in geostrophic balance. Asymptotic analysis leads to a pair of nonlinear equations for the vertical velocity and vertical vorticity coupled by vertical stretching. Statistically stationary states are maintained against viscous dissipation by boundary forcing or energy injection at larger scales. For thermal forcing direct numerical simulation of the reduced equations reveals the presence of intense vortical structures spanning the layer depth, in excellent agreement with simulations of the Boussinesq equations for rotating convection by Julien et al. (1996). Received 30 May 1997 and accepted 4 January 1998     

Observation of Zeeman degeneracy effects in collisional intense field resonance fluorescence

We report observation of the scattered spectrum from a Zeeman degenerate atom at high laser intensities. For a J = 0 to J = 1 transition in the presence of collisions we observe an asymmetric triplet in the polarization parallel to the incident laser and an asymmetric doublet in the polarization perpendicular to the incident laser.