We study acoustical vortices (AVs) and their connection with optical vortices (OVs). We show that AVs and OVs have the same properties if the concept of pseudomomentum is used. Radiation stress and conservation of topological charge are obtained with the pseudomomentum rule. In a weak nonlinear regime, the conservation of pseudo angular momentum imposes a linear increase of the topological charge with the harmonic order. This last result is experimentally verified.

We show that any amount of anisotropy moves the Oslo model to another known universality class, the exponents of which can be derived exactly. This amounts to an exact solution of the quenched Edwards-Wilkinson equation with a drift term. We argue that anisotropy is likely to be experimentally relevant and may explain why consistent exponents have not been extracted in the rice pile experiments.

It is shown that hexagonal convection cells in a rotating horizontal fluid layer heated from below will in general exhibit a drift in contrast to convection rolls except in the case of a vertical axis of rotation. The direction of the drift is prograde (retrograde) for cells with rising (descending) motion in the center of the convection cell. In addition a mean flow generated by convection is derived. An application to solar convection is discussed.

We propose a dual electromagnetically induced transparency (EIT) based multiwave mixing scheme that retains the significantly enhanced conversion efficiency enabled by ultraslow propagation of pump waves, yet is also capable of inhibiting and delaying the onset of the detrimental three-photon destructive interference that limits the further growth of the four-wave mixing (FWM) field. We show that the new scheme exhibits a wave-matching condition that is fundamentally different from the conventional FWM without EIT, and the efficient generation of the mixing wave is not critically dependent upon the FWM detuning to achieve constructive interference as required in the conventional FWM. These are significant steps forward in enabling applications of ultraslow wave nonlinear optics.

We study segregation and coarsening dynamics of dry granular materials and slurries in tubes with circular and square cross sections. Space-time plots show key differences between the four cases, including band splitting and wave formation, depending upon the rotational speed. However, the fraction of the surface occupied by bands of small-rich particles is nearly constant in all experiments, leading to quasi-1D behavior, and the rate of coarsening, when it occurs, is logarithmic in all cases. Coarsening rates are very similar except in the case with the longest development time.

We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explain earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.

We experimentally demonstrate for the first time that a radially polarized field can be focused to a spot size significantly smaller [$0.16(1){\lambda }^2$] than for linear polarization ($0.26{\lambda }^2$). The effect of the vector properties of light is shown by a comparison of the focal intensity distribution for radially and azimuthally polarized input fields. For strong focusing, a radially polarized field leads to a longitudinal electric field component at the focus which is sharp and centered at the optical axis. The relative contribution of this component is enhanced by using an annular aperture.

We examine the mutual synchronization of a one-dimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby a global nontrivial behavior emerges. A propensity criterion for networking is introduced, consisting in the coexistence within the attractor of a localized chaotic region, which displays high sensitivity to external stimuli, and an island of stability, which provides a reliable coupling signal to the neighbors in the chain. Based on this criterion, we compare homoclinic chaos, recently explored in lasers and conjectured to be typical of a single neuron, with Lorenz chaos.

We report experiments on the characterization of a train of attosecond pulses obtained by high-harmonic generation, using mixed-color ($\mathrm{X}\mathrm{U}\mathrm{V}+\mathrm{I}\mathrm{R}$) atomic two-photon ionization and electron detection on a velocity map imaging detector. We demonstrate that the relative phase of the harmonics is encoded both in the photoelectron yield and the angular distribution as a function of XUV-IR time delay, thus making the technique suitable for the detection of single attosecond pulses. The timing of the attosecond pulse with respect to the field oscillation of the driving laser critically depends on the target gas used to generate the harmonics.

We consider the circularly polarized localized modes of chiral photonic structures with combined central twist and isotropic layer defects. The general filter is shown to suffer from anomalous remittance and saturation of linewidth as the thickness of the structure is increased. However, by choosing parameters that phase match the elements of the round-trip matrix of the isotropic layer defect, we demonstrate the existence of supermodes that maintain exceptional purity of polarization state and exponential decrease in linewidth as the thickness is increased.

We study the diffusive propagation of multiply scattered light in an optically thick cloud of cold rubidium atoms illuminated by a quasiresonant laser beam. In the vicinity of a sharp atomic resonance, the energy transport velocity of the scattered light is almost 5 orders of magnitude smaller than the vacuum speed of light, reducing strongly the diffusion constant. We verify the theoretical prediction of a frequency-independent transport time around the resonance. We also observe the effect of the residual velocity of the atoms at long times.

In isotropic bistable media, a vortex pair typically evolves into rotating spiral waves. In an anisotropic system, instead of spiral waves, the vortices can form wave fragments that propagate with a constant speed in a given direction determined by the system’s anisotropy. The fragments may propagate invariably, shrink, or expand. We develop a kinematic approach for the study of vortex-pair dynamics in anisotropic bistable media and use it to capture the wave fragment dynamics.

Superpersistent chaotic transients are characterized by an exponential-like scaling law for their lifetimes where the exponent in the exponential dependence diverges as a parameter approaches a critical value. So far this type of transient chaos has been illustrated exclusively in the phase space of dynamical systems. Here we report the phenomenon of noise-induced superpersistent transients in physical space and explain the associated scaling law based on the solutions to a class of stochastic differential equations. The context of our study is advective dynamics of inertial particles in open chaotic flows. Our finding makes direct experimental observation of superpersistent chaotic transients feasible. It also has implications to problems of current concern such as the transport and trapping of chemically or biologically active particles in large-scale flows.

A family of three-dimensional traveling waves for flow through a pipe of circular cross section is identified. The traveling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as $1250$. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.

We investigate the propagation of short, intense laser pulses in arrays of coupled silica waveguides, in the anomalous dispersion regime. The nonlinearity induces trapping of the pulse in a single waveguide, over a wide range of input parameters. A sharp transition is observed for single waveguide excitation, from strong diffraction at low powers to strong localization at high powers.

Drying aqueous suspensions of monodisperse silica nanoparticles can fracture in remarkable patterns. As the material solidifies, evenly spaced cracks invade from the drying surface, with individual cracks undergoing intermittent motion. We show that the growth of cracks is limited by the advancement of the compaction front, which is governed by a balance of evaporation and flow of fluid at the drying surface. Surprisingly, the macroscopic dynamics of drying show signatures of molecular-scale fluid effects.

We study various families of two-dimensional discrete or lattice solitons, and show that they are possible only when their power level exceeds a critical threshold. In addition, we show that gap-lattice solitons exist only when the lattice possesses a complete 2D band gap. Our results suggest that these conditions are universally valid, irrespective of the nature of the nonlinearity or the specific structure of the index lattice. The analysis explains fundamental aspects of behavior of two-dimensional discrete solitons that have been very recently observed in photosensitive optical crystals.

We show theoretically and experimentally that for sum-frequency vibrational spectroscopy near electronic transitions, resonant enhancement of the chiral response can be much stronger than that of the achiral response. The doubly resonant spectrum selectively enhances the vibrational modes through their different electron-vibration couplings. The unusually strong resonant enhancement significantly improves sensitivity of chiral spectroscopy and allows detection of the chiral vibrational spectrum of a molecular monolayer for the first time.

We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective frequency components or stabilize their excitations. These MFGSs form a new class of stable gap solitons.