The combined experimental and numerical study finds a complex mechanism of $Z_2$ symmetry breaking involving global bifurcations for the first time in hydrodynamics. In addition to symmetry breaking via pitchfork bifurcation, the $Z_2$ symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a $Z_2$-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. Instead of symmetry breaking due to a SNIP bifurcation, we find a more complex mechanism of $Z_2$ symmetry breaking involving nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations and complex dynamics in the vicinity of this global bifurcation.

We demonstrate low-threshold lasing in random amplifying layered medium via photon localization. Lasing is facilitated by resonant excitation of localized modes at the pump laser wavelength, which are peaked deep within the sample with greatly enhanced intensity. Emission occurs into long-lived localized modes overlapping the localized gain region. This mechanism overcomes a fundamental barrier to reducing lasing thresholds in diffusive random lasers, in which multiple scattering restricts the excitation region to the proximity of the sample surface.

Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schrödinger equation, are shown to exist to all nonparaxial orders as exact solutions of Maxwell’s equations in the presence of the vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell’s equations, while exact linearly polarized $(2+1)$D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one-fourth of the wavelength.

Chaotic diffusion often represents a severe obstacle for the setup of experiments, e.g., in fusion plasmas or particle accelerators. We present a complete test of a method of control of Hamiltonian chaos, with both its numerical test and its first experimental realization on a paradigm for wave-particle interaction, i.e., a travelling wave tube. The core of our approach is a small apt modification of the system which channels chaos by building barriers to diffusion. Its experimental realization opens the possibility to practically achieve the control of a wide range of systems at a low additional cost of energy.

We demonstrate theoretically and subsequently observe in experiment a novel type of soliton interaction when a pair of closely spaced spatial optical solitons as a whole is made partially incoherent. We explain how the character of the soliton interaction can be controlled by the total partial incoherence, and show a possibility to change the soliton interaction from attractive to repulsive, or vice versa, near a certain threshold in the coherence parameter.

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number ${\widehat{\mathrm{R}\mathrm{a}}}_s$. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness ${\delta }^{*}$ at the onset of convection. We show that the dimensionless boundary layer thickness $\delta ={\delta }^{*}/d$ scales as ${\mathrm{R}\mathrm{a}}_s^{-p}$, where ${\mathrm{R}\mathrm{a}}_s={\widehat{\mathrm{R}\mathrm{a}}}_s\delta$ is a modified solutal Rayleigh number for convection which accounts for the actual density unbalance and $d$ is the thickness of the sample layer. This scaling behavior is analogous to that reported at steady state for turbulent convection in simple fluids. We find $p=0.35$, a value compatible with the exponent $1/3$, reported for turbulent heat convection in simple fluids at steady state.

Distributed feedback microstructures play a fundamental role in confining and manipulating light to obtain lasing in media with gain. Here, we present an innovative array of organic, color-tunable microlasers which are intrinsically phase locked. Dye-doped helixed liquid crystals were embedded within periodic, polymeric microchannels sculptured by light through a single-step process. The helical superstructure was oriented along the microchannels; the lasing was observed along the same direction at the red edge of the stop band. Several physical and technological advantages arise from this engineered heterostructure: a high quality factor of the cavity, ultralow lasing threshold, and thermal and electric control of the lasing wavelength and emission intensity. This level of integration of guest-host systems, embedded in artificially patterned small sized structures, might lead to new photonic chip architectures.

The first electromagnetic metamaterials (${\mathrm{E}\mathrm{M}}^3$) produced by microfabrication are reported. They are based on the rod–split-ring-resonator design as proposed by Pendry et al. [IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)] and experimentally confirmed by Smith et al. [Phys. Rev. Lett. 84, 4184 (2000)] in the GHz frequency range. Numerical simulation and experimental results from far infrared (FIR) transmission spectroscopy support the conclusion that the microfabricated composite material is ${\mathrm{E}\mathrm{M}}^3$ in the range 1–2.7 THz. This extends the frequency range in which ${\mathrm{E}\mathrm{M}}^3$ are available by about 3 orders of magnitude well into the FIR, thereby widely opening up opportunities to verify the unusual physical implications on electromagnetic theory as well as to build novel electromagnetic and optical devices.

We show that the recently demonstrated technique for generating stationary pulses of light [M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature (London) 426, 638 (2003)] can be extended to localize optical pulses in all three spatial dimensions in a resonant atomic medium. This method can be used to dramatically enhance the nonlinear interaction between weak optical pulses. In particular, we show that an efficient Kerr-like interaction between two pulses can be implemented as a sequence of several purely linear optical processes. The resulting process may enable coherent interactions between single photon pulses.

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

The wake in the flow past a circular cylinder has posed a long-standing challenge to scientists since the late 19th century. Many aspects of this seemingly simple phenomenon remain unexplained. Of particular interest is the relationship between the dimensionless vortex shedding frequency (the Strouhal number St) and the ratio of inertial to viscous forces in the fluid (the Reynolds number Re). We propose a new St-Re relation based on the observations of the structure of a vortex street in flowing soap films. The measurements suggest a simple two-parameter form $\mathrm{S}\mathrm{t}=1/(A+B/\mathrm{R}\mathrm{e})$ that describes laminar vortex shedding remarkably well for bulk fluids as well as for two-dimensional flowing soap films.

It is widely believed that the velocity of information ${\upsilon }_i$ encoded on an optical pulse is equal to the group velocity ${\upsilon }_g$, at least when ${\upsilon }_g$ is less than the speed of light in vacuum $c$. On the other hand, several authors suggest that ${\upsilon }_i=c$, although the size of the signal traveling at this velocity may be small, thereby making it difficult to measure. Here, we measure ${\upsilon }_i$ for pulses propagating through a resonant “slow-light” medium where ${\upsilon }_g\approx 0.006c$. We find ${\upsilon }_i=1.03c_{-0.25c}^{+0.49c}$, or that ${\upsilon }_i\approx 168{\upsilon }_g$, clearly demonstrating that the speed of information cannot be generally described by ${\upsilon }_g$, but is characterized by its own velocity.

The cracks observed in the glaze of ceramics form networks, which divide the 2D plane into domains. It is shown that, on the average, the number of sides of these domains is four. This contrasts with the usual 2D space divisions observed in Voronoi tessellation or 2D soap froths. In the latter networks, the number of sides of a domain coincides with the number of its neighbors, which, according to Euler’s theorem, has to be six on average. The four sided property observed in cracks is the result of a formation process which can be understood as the successive divisions of domains with no later reorganization. It is generic for all networks having such hierarchical construction rules. We introduce a “geometrical charge,” analogous to Euler’s topological charge, as the difference from four of the number of sides of a domain. It is preserved during the pattern formation of the crack pattern.

We present an experimental and theoretical study of the optical transmission of a thin metal screen perforated by two subwavelength slits, separated by many optical wavelengths. The total intensity of the far-field double-slit pattern is shown to be reduced or enhanced as a function of the wavelength of the incident light beam. This modulation is attributed to an interference phenomenon at each of the slits, instead of at the detector. The interference arises as a consequence of the excitation of surface plasmons propagating from one slit to the other.

Homoclinic motion plays a key role in the organization of classical chaos in Hamiltonian systems. In this Letter, we show that it also imprints a clear signature in the corresponding quantum spectra. By numerically studying the fluctuations of the widths of wave functions localized along periodic orbits we reveal the existence of an oscillatory behavior that is explained solely in terms of the primary homoclinic motion. Furthermore, our results indicate that it survives the semiclassical limit.

We introduce a criterion for the existence of regular states in systems with a mixed phase space. If this condition is not fulfilled chaotic eigenstates substantially extend into a regular island. Wave packets started in the chaotic sea progressively flood the island. The extent of flooding by eigenstates and wave packets increases logarithmically with the size of the chaotic sea and the time, respectively. This new effect is observed for the example of island chains with just ten islands.

We present a dynamic van der Waals theory. It is useful to study phase separation when the temperature varies in space. We show that, if heat flow is applied to liquid suspending a gas droplet at zero gravity, a convective flow occurs such that the temperature gradient within the droplet nearly vanishes. As the heat flux is increased, the droplet becomes attached to the heated wall that is wetted by liquid in equilibrium. In one case corresponding to partial wetting by gas, an apparent contact angle can be defined. In the other case with larger heat flux, the droplet completely wets the heated wall expelling liquid.

Dynamics of two-sign point vortices in two-dimensional circular boundary is examined by numerical simulations with MDGRAPE-2. The vortex system is characterized by the inverse temperature $\beta$ as determined from the density of states of the microcanonical ensemble of numerically generated ${10}^7$ states. The massive simulation shows that different configurations appear in the time-asymptotic state depending on the sign of $\beta$. Condensation of the same-sign vortices is observed when $\beta <0$, while the both-sign vortices tend to be uniformly neutralized when $\beta >0$. During the condensation, a part of the vortices gains energy to form clumps (patches), and the other part of the vortices loses energy to keep the total energy constant and mixes with vortices of the other sign. This observation demonstrates a characteristic feature of negative $\beta$ states that the system energy concentrates into the clumps of the same-sign vortices.

Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.