We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons with different symmetries through the intermediate states resembling generalized Hermite-Laguerre-Gaussian modes.

We report the experimental observation of temporal vector soliton propagation and collision in a linearly birefringent optical fiber. To the best of the authors’ knowledge, this is both the first demonstration of temporal vector solitons with two mutually incoherent component fields, and of vector soliton collisions in a Kerr nonlinear medium. Collisions are characterized by an intensity redistribution between the two components, and the experimental results agree with numerical predictions of the coupled nonlinear Schrödinger equation.

We report on measured statistics of pulsed radio-frequency fields inside a dynamic (mode-stirred) reverberant cavity. Unlike for time-harmonic excitation, the early transient received power during the buildup of energy is quasiperiodic with respect to the stir angle and exhibits unusually long correlations. These correlations decay at the same exponential rate as the increase of energy. By contrast, the probability distribution of the power reaches its asymptotic form in a more rapid but oscillatory manner.

Transitions in the dynamics of complex systems can be characterized by changes in the synchronization behavior of their components. Taking the human cardiorespiratory system as an example and using an automated procedure for screening the synchrograms of 112 healthy subjects we study the frequency and the distribution of synchronization episodes under different physiological conditions that occur during sleep. We find that phase synchronization between heartbeat and breathing is significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and reduced during REM sleep. Our results suggest that the synchronization is mainly due to a weak influence of the breathing oscillator upon the heartbeat oscillator, which is disturbed in the presence of long-term correlated noise, superimposed by the activity of higher brain regions during REM sleep.

We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is analogous to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the kinetic theory of plasmas and gases. To calculate the lowest order system size effect, we truncate this hierarchy at second order and solve the resulting closed equations for the two-oscillator correlation function around the incoherent state. We use this correlation function to compute the fluctuations of the order parameter, including the effect of transients, and compare this computation with numerical simulations.

Interfaces moving in a disordered medium exhibit stochastic velocity fluctuations obeying universal scaling relations related to the presence or absence of conservation laws. For fluid invasion of porous media, we show that the fluctuations of the velocity are governed by a geometry-dependent length scale arising from fluid conservation. This result is compared to the statistics resulting from a nonequilibrium (depinning) transition between a moving interface and a stationary, pinned one.

Surfactants lower surface tension and are used to facilitate breakup and spreading. How much surfactant remains where a filament of initial radius $R$ breaks is set by the ratio of convection, which sweeps surfactant away, to diffusion, which replenishes it, or Peclet number $\mathrm{Pe}\propto R$. Thus, as is well known, surfactant concentration $\Gamma \to 0$ when a macroscale filament breaks. Here theory and simulation are used to investigate pinch-off of microscopic filaments. At breakup, $\Gamma$ is shown to be nonzero but uniform on a filament of negligible Pe. Since $R$ must be finite, the zero-Pe limit is transitory and yields to a final regime. Two such regimes with distinct dynamics characterized by different scaling exponents are reported.

Non-Oberbeck-Boussinesq (NOB) effects are measured experimentally and calculated theoretically for strongly turbulent Rayleigh-Bénard convection of ethane gas under pressure where the material properties strongly depend on the temperature. Relative to the Oberbeck-Boussinesq case we find a decrease of the central temperature as compared to the arithmetic mean of the top- and bottom-plate temperature and an increase of the Nusselt number. Both effects are of opposite sign and greater magnitude than those for NOB convection in liquids like water.

In this Letter, we report the confinement of a uniform beam of light (${\lambda }_1=400\mathrm{nm}$) at the nodes of a standing wave (${\lambda }_2=532\mathrm{nm}$) via absorbance modulation. In the present implementation of absorbance modulation, a thin polymer film containing a photochromic azobenzene side chain is exposed to a standing wave at ${\lambda }_2$ and a uniform beam at ${\lambda }_1$, resulting in alternate regions of high and low absorbance. Light at ${\lambda }_1$ is localized around the low-absorbance regions. Using photoresist exposures, we mapped out the localized light intensity distribution, which agrees well with our theoretical model. Since the width of this distribution is primarily determined by the ratio of the intensities at the two wavelengths, this technique opens up the possibility of localizing light fields below the diffraction limit using far-field optics.

We present measurements of first- and second-order coherence of quantum-dot micropillar lasers together with a semiconductor laser theory. Our results show a broad threshold region for the observed high-$\beta$ microcavities. The intensity jump is accompanied by both pronounced photon intensity fluctuations and strong coherence length changes. The investigations clearly visualize a smooth transition from spontaneous to predominantly stimulated emission which becomes harder to determine for high $\beta$. In our theory, a microscopic approach is used to incorporate the semiconductor nature of quantum dots. The results are in agreement with the experimental intensity traces and the photon statistics measurements.

Intense multiphoton electron emission is observed from sharp ($\sim 20\mathrm{nm}$ radius) metallic tips illuminated with weak 100-pJ, 7-fs light pulses. Local field enhancement, evidenced by concurrent nonlinear light generation, confines the emission to the tip apex. Electrons are emitted from a highly excited nonequilibrium carrier distribution, resulting in a marked change of the absolute electron flux and its dependence on optical power with the tip bias voltage. The strong optical nonlinearity of the electron emission allows us to image the local optical field near a metallic nanostructure with a spatial resolution of a few tens of nanometers in a novel tip-enhanced electron emission microscope.

It is shown how surface plasmons that travel between the slits in Young’s interference experiment can change the state of spatial coherence of the field that is radiated by the two apertures. Surprisingly, the coherence can both be increased and decreased, depending on the slit separation distance. This results in a modulation of the visibility of the interference fringes. Since many properties of a light field—such as its spectrum, polarization, and directionality—may change on propagation and are dependent on the spatial coherence of the source, our results suggest that the use of surface plasmons provides a new way to alter or even tailor the statistical properties of a light field.

We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number $R_m\sim 30$. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

We investigate high-order difference-frequency mixing in plasmas, taking into account the microscopic rescattering physics and propagation effects for the first time. We show that phase matching can occur over a broad frequency range, up to very high photon energies, and that it is confined to specific temporal and spatial windows. This gated phase matching mechanism is driven by the continuous phase slip between two driving fields and can be employed for manipulating the temporal, spatial, and spectral properties of high harmonic emission.

A second plateau in the harmonic spectra of laser-driven two-electron atoms is observed both in the numerical solution of a low-dimensional model helium atom and using an extended strong field approximation. It is shown that the harmonics well beyond the usual cutoff are due to the simultaneous recombination of the two electrons, which were emitted during different, previous half-cycles. The new cutoff is explained in terms of classical trajectories. Classical predictions and the time-frequency analysis of the ab initio quantum results are in excellent agreement. The mechanism corresponds to the inverse single photon double ionization process in the presence of a (low frequency) laser field.

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.

Using an integrated colliding-pulse mode-locked semiconductor laser, we demonstrate the existence of nonlinear dynamics and chaos in photonic integrated circuits (PICs) by demonstrating a period-doubling transition into chaos. Unlike their stand-alone counterparts, the dynamics of PICs are more stable over the lifetime of the system, reproducible from batch to batch and on faster time scales due to the small sizes of PICs.

We observe a new type of behavior in a shear-thinning yield stress fluid: freestanding convection rolls driven by vertical oscillation. The convection occurs without the constraint of container boundaries, yet the diameter of the rolls is spontaneously selected for a wide range of parameters. The transition to the convecting state occurs without hysteresis when the amplitude of the plate acceleration exceeds a critical value. We find that a nondimensional stress, the stress due to the inertia of the fluid normalized by the yield stress, governs the onset of the convective motion.

We investigate quasi-Bragg-matched counterpropagating spatial solitons in a reflection grating in the presence of a longitudinally modulated Kerr nonlinearity. The physical interplay of linear reflection and Kerr self-focusing with the modulation in the nonlinearity yields a variety of elaborate self-action mechanisms. We first analytically predict the existence of symmetric soliton pairs supported by a pure Kerr-like effective nonlinearity. We then analytically derive two families of solitons, associated with the linear grating eigenmodes, supported by an effective “incoherent” Kerr-like coupling arising from the exact balance between the modulation in the nonlinearity and the Kerr interaction due to beam interference.