We present a novel optical device based on an integrated system of microlenses and single-mode optical fibers. It allows us to collect and direct into many modes two photons generated by spontaneous parametric down-conversion. By this device multiqubit entangled states and/or multilevel qudit states of two photons, encoded in the longitudinal momentum degree of freedom, are created. The multipath photon entanglement realized by this device is expected to find important applications in modern quantum information technology.

A theory of self-propelled particles is developed in such a way that the particles can be deformed from a circular shape when the propagating velocity is finite. A coupled set of equations in terms of the velocity and a tensor variable is introduced to represent the motion of a deformed particle. It is shown that there is a bifurcation from a straight motion to a circular motion by increasing the propagating velocity. The dynamics of assembly of the particles is studied numerically in two dimensions imposing a global interaction such that the elongated particles tend to undergo an orientational order.

We discuss how to engineer the phase and amplitude of a complex order parameter using localized dissipative perturbations. Our results are applied to generate and control various types of atomic nonlinear matter waves (solitons) by means of localized dissipative defects.

We study the angle and frequency dependence of sound transmission through water-immersed perforated aluminum plates. Three types of resonances are found to govern the acoustic properties of the plates: lattice resonances in periodic arrays, Fabry-Perot modes of the hole cavities, and elastic Lamb modes. The last two of them are still present in random arrays and have no parallel in optical transmission through holes. These modes are identified by comparing experiment with various levels of theoretical analysis, including full solution of the elasto-acoustic wave equations. We observe strong mixture of different transmission mechanisms, giving rise to unique acoustic behavior and opening new perspectives for exotic wave phenomena.

We simulate the evolution of the steady-state interface in the selective withdrawal regime. Selective withdrawal ends when the upward pull exerted by the viscous flow in the withdrawing liquid layer overcomes the downward force due to surface tension. The lower-layer dynamics are unimportant. The dominant contribution to the surface-tension force comes from the large area where the interface is weakly deflected, instead of the small area where the surface is most distorted. A scaling estimate based on this idea yields results that agree quantitatively with both simulations and previous experiments.

Here we report the formation of void (hole) structures when concentrated colloidal solutions of magnetic nanocrystals are subjected to a magnetic field during slow evaporation. This presents a new type of solid mesostructure obtained by self-assembly of nanocrystals. The voids are characterized by a cylindrical shape with either circular or elliptical base. We show that the morphology of these patterns is essentially controlled by the fraction of the volume occupied by the magnetic phase to the total volume of the film. Monte Carlo simulations carried out using a Stockmayer fluid model agree remarkably well with the experiments for the formation of void structures in the range of considered volume fractions.

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the von Kármán sodium experiment, also provides a simple explanation of the reversals of Earth’s magnetic field, despite strong differences between both systems. The validity of the model relies on the smallness of the magnetic Prandtl number.

An electromagnetic nondiffractive Bessel-like beam from a subwavelength aperture is generated by placing a metallic circular gratinglike structure in front of the aperture. When the incident wave is linearly polarized, the beam is axially asymmetric. The beam possesses fluctuating, but approximately uniform, intensity distribution along its longitudinal axis. The full width at half maximum of the beam remains less than two wavelengths over nearly ten wavelengths. Our experimental results are in good agreement with the simulation results and analytical results.

We numerically study the topology of optical vortex lines (nodal lines) in volumes of optical speckle, modeled as superpositions of random plane waves. It is known that the vortex lines may be infinitely long, or form closed loops. Loops are occasionally threaded by infinite lines, or linked with other loops. We find the probability of a loop not being threaded decays exponentially with the length of the loop. This behavior has a similarity to scaling laws studied in superfluid turbulence, and polymers modeled as random walks.

Shear-induced vertical mixing in a stratified flow is a key ingredient of thermohaline circulation. We experimentally determine the vertical flux of momentum and density of a forced gravity current using high-resolution velocity and density measurements. A constant eddy-viscosity model provides a poor description of the physics of mixing, but a Prandtl mixing length model relating momentum and density fluxes to mean velocity and density gradients works well. For the average gradient Richardson number ${\mathrm{Ri}}_g\approx 0.08$ and a Taylor Reynolds number ${\mathrm{Re}}_{\lambda }\approx 100$, the mixing lengths are fairly constant, about the same magnitude, comparable to the turbulent shear length.

We describe a dynamical model that predicts the zigzag motion of disks and oblate spheroids moving freely in a viscous liquid over a continuous range of aspect ratios and Reynolds numbers. This model combines the generalized Kirchhoff equations to describe the linear and angular momentum balances for the fluid-body system with a dynamical model for the wake-induced force and torque that incorporates the main characteristics of the wake dynamics deduced from previous experimental observations. The resulting model is shown to be able to reproduce quantitatively the oscillatory paths measured experimentally.

Inspired by the concept of complementary media, we experimentally demonstrate that an engineered metamaterial made of alternating, stripe layers of negatively refracting (photonic crystals) and positively refracting (air) materials strongly collimates a beam of near-infrared light. This quasi-zero-average-index metamaterial fully preserves the beam spot size throughout the sample for a light beam traveling through the metamaterial a distance of 2 mm—more than 1000 times the input wavelength $\lambda =1.55\mu \mathrm{m}$. These results demonstrate the first explicit experimental verification of optical antimatter as proposed by Pendry and Ramakrishna [J. Pendry and S. Ramakrishna, J. Phys. Condens. Matter 15, 6345 (2003)], using two complementary media in which each $n_{\mathrm{eff}}=-1$ layer appears to annihilate an equal thickness layer of air.

Surface soliton formation and lattice soliton dynamics at an interface between two inhomogeneous periodic media are studied in terms of an effective particle approach. The global reflection, transmission, and trapping characteristics are obtained in direct analogy to linear Snell’s laws for homogeneous media. Interesting dynamics related to soliton power-dependent formation of potential barriers and wells suggest a spatial filtering functionality of the respective structures.

The breakup of spatial bright optical solitons due to oscillatory neck instability is experimentally studied by propagating a laser beam in normally dispersive and self-focusing Kerr media. This intriguing and unusual phenomenon, recently predicted for solitons of the $(2+1)$-dimensional hyperbolic nonlinear Schrödinger (NLS) equation, is observed in the spatially resolved temporal spectrum. The snake instability that is known to occur in hyperbolic systems is also demonstrated to validate our experimental approach. Our results not only apply to photonics but also to other fields of physics, such as hydrodynamics or plasma physics, in which the hyperbolic NLS equation is used as a canonical model.

We report on a new nonlinear dynamics occurring in a confined cylindrical column filled with fluid (liquid bridge) and heated from above. We demonstrate and analyze the novel oscillatory flow state created by the interaction of two hydrothermal waves of different origins: one propagates vertically from the cold towards the hot side ($m=0$) and another is traveling in the azimuthal direction ($m=1$). Their interaction leads to an exotic flow structure: during a part of the oscillation period the resulting wave propagates in a given azimuthal direction, whereas during the rest of the period it moves in the opposite direction. A new bimodal flow regime is found to exist over a parameter range where these modes have comparable influence. The phase diagrams, obtained by three-dimensional nonlinear simulations, are reported. They shed light on the instability mechanism and criteria of the existence of novel states.

In spatiotemporal systems with advection, suppression of noise-sustained structures involves questions that are outside of the framework of deterministic dynamical systems control (such as Ott-Grebogi-Yorke-type methods). Here we propose and test an alternate strategy where a nonlocal additive feedback is applied, with the objective to create a new deterministic solution that becomes robust to noise. As a remarkable fact—though the needed parameter perturbations required have essentially a finite size—they turn out to be extraordinarily small in principle: ${10}^{-8}$ in the free-electron laser experiment presented here.

A high velocity impact between a liquid droplet and a solid surface produces a splash. Classical work traced the origin of the splash to a thin sheet of fluid ejected near the impact point. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. We demonstrate that, neglecting intermolecular forces between the liquid and the solid, the liquid does not contact the solid, and instead spreads on a very thin air film. The interface of the droplet develops a high curvature and emits capillary waves.

Light propagation in all-dielectric rod-type metamaterials is studied theoretically. The electric and magnetic dipole moments of the rods are derived analytically in the long-wavelength limit. The effective permittivity and permeability of a square lattice of rods are calculated by homogenizing the corresponding array of dipoles. The role of dipole resonances in the optical properties of the rod array is interpreted. This structure is found to exhibit a true left-handed behavior, confirming previous experiments [L. Peng et al., Phys. Rev. Lett. 98, 157403 (2007)]. A scaling analysis shows that this effect holds at optical frequencies and can be obtained by using rods made, for example, of silicon.

We demonstrate spatial Rabi oscillations in optical waveguide arrays. Adiabatic transitions between extended Floquet-Bloch modes associated with different bands are stimulated by periodic modulation of the photonic lattice in the propagation direction. When the stimulating modulation also carries transverse momentum, the transition becomes indirect, equivalent to phonon-assisted Rabi oscillations. In solid state physics such indirect Rabi oscillations necessitate coherent phonons and hence they have never been observed. Our experiments suggest that phonon-assisted Rabi oscillations are observable also with Bose-Einstein condensates, as well as with other wave systems—where coherence can be maintained for at least one period of the Rabi oscillation.

We study the hydrodynamic phenomenon of waves blocking by a countercurrent with the tools of dynamical systems theory. We show that, for a uniform background velocity and within the small wavelength approximation, the stopping of gravity waves is described by a stationary saddle-node bifurcation due to the spatial resonance of an incident wave with the converted “blueshifted” wave. We explain why the classical regularization effect of interferences avoids the height singularity in complete analogy with the intensity of light close to the principal arc of a rainbow. The application to the behavior of light near a gravitational horizon is discussed.