We show that light pulses can be stopped and stored coherently, with an all-optical adiabatic and reversible pulse bandwidth compression process. Such a process overcomes the fundamental bandwidth-delay constraint in optics and can generate arbitrarily small group velocities for any light pulse with a given bandwidth, without any coherent or resonant light-matter interactions. We exhibit this process in optical resonators, where the bandwidth compression is accomplished only by small refractive-index modulations performed at moderate speeds.

We have observed filamentation due to azimuthal modulational instabilities in spinning ring solitons with orbital angular momentum $m\hslash$ in sodium vapor. We show experimentally that vortex beams with $m$ values of 1, 2, and 3 tend to break into two, four, and six filaments, respectively. Treating the sodium vapor as a Doppler broadened two-level atomic system, we find that we can accurately model the propagation and breakup of these beams with numerical simulations.

The dynamics of passive Lagrangian tracers in three-dimensional quasigeostrophic turbulence is studied numerically and compared with the behavior of two-dimensional barotropic turbulence. Despite the different Eulerian properties of the two flows, the Lagrangian dynamics of passively advected tracers in three-dimensional quasigeostrophic turbulence is very similar to that of barotropic turbulence. In both systems, coherent vortices play a major role in determining the mixing and dispersion properties. This work indicates that recent results on particle dynamics in barotropic, two-dimensional turbulence carry over to more realistic baroclinic flows, such as those encountered in the large-scale dynamics of the atmosphere and ocean.

We study experimentally the snake instability of the bright soliton stripe of the $(2+1)$-dimensional hyperbolic nonlinear Schrödinger equation. The instability is observed, through spectral measurements, on spatially extended femtosecond pulses propagating in a normally dispersive self-defocusing semiconductor planar waveguide.

We study a simple model of shear banding in which the flow-induced phase is destabilized by coupling between flow and microstructure (wormlike micellar length). By varying the strength of instability and the applied shear rate, we find a rich variety of oscillatory and chaotic shear banded flows. At low shear and weak instability, the induced phase pulsates next to one wall of the flow cell. For stronger instability, high shear pulses ricochet across the cell. At high shear we see oscillating bands on either side of central defects. We discuss our results in the context of recent experiments.

Using elementary cellular automata (CA) as an example, we show how to coarse grain CA in all classes of Wolfram’s classification. We find that computationally irreducible physical processes can be predictable and even computationally reducible at a coarse-grained level of description. The resulting coarse-grained CA which we construct emulate the large-scale behavior of the original systems without accounting for small-scale details. At least one of the CA that can be coarse grained is irreducible and known to be a universal Turing machine.

We demonstrate that multiphoton-induced photoelectron emission from a gold surface caused by low-energy (unamplified) 4-fs, 750-nm laser pulses is sensitive to the timing of electric field oscillations with respect to the pulse peak. This observation confirms recent theoretical predictions and opens the door to measuring the absolute value of the carrier-envelope phase difference of few-cycle light pulses with a solid-state detector.

In a network of neuronal oscillators with time-delayed coupling, we uncover a phenomenon of enhancement of neural synchrony by time delay: a stable synchronized state exists at low coupling strengths for significant time delays. By formulating a master stability equation for time-delayed networks of Hindmarsh-Rose neurons, we show that there is always an extended region of stable synchronous activity corresponding to low coupling strengths. Such synchrony could be achieved in the undelayed system only by much higher coupling strengths. This phenomenon of enhanced neural synchrony by delay has important implications, in particular, in understanding synchronization of distant neurons and information processing in the brain.

We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. Using equilibrium and nonequilibrium molecular dynamics, three types of thermal conducting behaviors are found: a logarithmic divergence with system sizes for large transverse coupling, $1/3$ power law at intermediate coupling, and $2/5$ power law at low temperatures and weak coupling. The results are consistent with a simple mode-coupling analysis of the same model. We suggest that the $1/3$ power-law divergence should be a generic feature for models with transverse motions.

The spray formed when a fast gas stream blows over a liquid volume presents a wide distribution of fragment sizes. The process involves a succession of changes of the liquid topology, the last being the elongation and capillary breakup of ligaments torn off from the liquid surface. The coalescence of the liquid volumes constitutive of a ligament at the very moment it detaches from the liquid bulk produces larger drops. This aggregation process has its counterpart on the shape of the size distribution associated with the ligament breakup, found to be very well represented by gamma distributions. The exponential shape of the overall distribution in the spray coincides with the large excursion wing of these elementary distributions, underlying the crucial role played by the ligament dynamics in building up the broad statistics of sprays.

We demonstrate experimentally and theoretically the existence of canard orbits and excitable quasiharmonic limit cycles in the thermo-optical dynamics of semiconductor optical amplifiers. We also observe the phase locking of the noise-induced spikes to the small-amplitude Hopf quasiharmonic oscillations, recently predicted by Makarov, Nekorkin, and Velarde [Phys. Rev. Lett. 86, 3431 (2001)].

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and remains finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.

Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant to physical and biological applications, can thus be expected to occur more commonly in dynamical systems than previously thought.

For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these firing patterns persist until a critical temporal extent is reached that is of the order of the interaction delay. For stronger disorder the periodic firing patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from a network of given connectivity and heterogeneity. Moreover, we show how to design heterogeneous coupling architectures to create an arbitrary prescribed pattern.

Heat conduction in a one-dimensional chain of equivalent rigid particles in the field of the external on-site potential is considered. The zero diameters of the particles correspond to the integrable case with the divergent heat conduction coefficient. By means of a simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters, and good agreement is observed.

The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated and a realistic experimental setup is suggested. The beam is injected in a single boundary waveguide, linear refractive index of which ($n_0$) is larger than refractive indexes ($n$) of other identical waveguides in the array. Particularly, the effect holds if $\omega (n_0-n)/c>2Q$, where $Q$ is a linear coupling constant between array waveguides, $\omega$ is a carrier wave frequency, and $c$ is a light velocity. Numerical experiments show that the energy transfers from the boundary waveguide to the waveguide array above a certain threshold intensity of the injected beam. This effect is due to the creation and the propagation of gap solitons in full analogy with a similar phenomenon in sine-Gordon lattice [F. Geniet and J. Leon, Phys. Rev. Lett. 89, 134102 (2002)].

Lasers that provide an energy encompassed in a focal volume of a few cubic wavelengths (${\lambda }^3$) can create relativistic intensity with maximal gradients, using minimal energy. With particle-in-cell simulations we found, that single 200 attosecond pulses could be produced efficiently in a ${\lambda }^3$ laser pulse reflection, via deflection and compression from the relativistic plasma mirror created by the pulse itself. An analytical model of coherent radiation from a charged layer confirms the pulse compression and is in good agreement with simulations. The novel technique is efficient ($\sim 10\%$) and can produce single attosecond pulses from the millijoule to the joule level.

We show that modes of axially uniform waveguides of arbitrary cross section can be made to have anomalous dispersion relations resulting from strong repulsion between two modes. When the axial wave vector $k$ is 0, the two modes have different TE/TM symmetry and thus can be brought arbitrarily close to an accidental frequency degeneracy. For nonzero $k$, the symmetry is broken causing the modes to repel. When the modes are sufficiently close together this repulsion leads to unusual features such as extremely flattened dispersion relations, backward waves, zero group velocity for nonzero $k$, atypical divergence of the density of states, and nonzero group velocity at $k=0$.

Propagation loss can occur in photonic crystal waveguides without complete optical confinement. We employ a highly efficient transfer-matrix method which allows for accurate and reliable extraction of the propagation loss even at an extremely low level. The results for a two-dimensional photonic crystal waveguide shows that the loss exponentially decays via the waveguide wall thickness. An anomalous phenomenon is found where the loss for guided modes near the upper band gap edge can be several orders of magnitude smaller than that for modes in the middle of the band gap. This anomaly can be well explained by the localization degree of guided modes at different frequency domains.

The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field-strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the self-similarity is to be expected with a finite flow scale and system size. In the nonlinear saturated state, intermittency is reduced and the PDF is exponential. Parallels are noted with self-similar behavior recently observed for passive-scalar mixing and for map dynamos.