By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time ($\mathcal{P}\mathcal{T}$-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrödinger equation with dissipation and gain, we show that the equivalence of the underlying linear spectra does not imply similarity of the structure or stability of the nonlinear modes in the arrays. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the $\mathcal{P}\mathcal{T}$ symmetry of a newly obtained system. In addition, the stability is not directly related to the $\mathcal{P}\mathcal{T}$ symmetry: stable nonlinear modes exist even when the spectrum of the linear array is not purely real. We use a graph representation of $\mathcal{P}\mathcal{T}$-symmetric networks allowing for a simple illustration of linearly equivalent networks and indicating their possible experimental design.

We present an efficient approach to realize the spatial power combination for omnidirectional radiation via metamaterials in the two-dimensional case. We propose a radially anisotropic zero-index metamaterial which can always produce ominidirectional radiation, independent of the number and position of the sources inside the metamaterial. When the radial component of the permeability tensor is approaching zero and the wave impedance is equal to that of free space, waves emitted from all sources inside the metamaterial are transformed into perfectly cylindrical waves without any reflection, and powers from different sources can be combined together to enhance the omnidirectional radiation. We have designed and fabricated such a radially anisotropic metamaterial, and both numerical and experimental results demonstrate the spatial power combination with high efficiency. The proposed idea can be extended to the three-dimensional case to generate perfectly coherent isotropic radiation in nature, which does not exist now. Metamaterial is a unique approach to obtain such a high-efficiency spatial power combination for omnidirectional radiation and isotropic radiation.

Defects due to growth fluctuations in broad-area semiconductor lasers induce pinning and frequency shifts of spatial laser solitons. The effects of defects on the interaction of two solitons are considered in lasers with frequency-selective feedback both theoretically and experimentally. We demonstrate frequency and phase synchronization of paired laser solitons as their detuning is varied. In both theory and experiment the locking behavior is well described by the Adler model for the synchronization of coupled oscillators.

Synchronization in large laser networks with both homogeneous and heterogeneous coupling delay times is examined. The number of synchronized clusters of lasers is established to equal the greatest common divisor of network loops. We experimentally demonstrate up to 16 multicluster phase synchronization scenarios within unidirectional coupled laser networks, whereby synchronization in heterogeneous networks is deduced by mapping to an equivalent homogeneous network. The synchronization in large laser networks is controlled by means of tunable coupling and self-coupling.

It is experimentally shown that the nonclassical high Reynolds number energy dissipation behavior, $C_{\epsilon }\equiv \epsilon L/u^3=f({\mathrm{Re}}_M)/{\mathrm{Re}}_L$, observed during the decay of fractal square grid-generated turbulence (where ${\mathrm{Re}}_M$ is a global inlet Reynolds number and ${\mathrm{Re}}_L$ is a local turbulence Reynolds number) is also manifested in decaying turbulence originating from various regular grids. For sufficiently high values of the global Reynolds numbers ${\mathrm{Re}}_M$, $f({\mathrm{Re}}_M)\sim {\mathrm{Re}}_M$.

We propose a method to separate enantiomers in microfluidic or nanofluidic channels. It requires flow profiles that break chiral symmetry and have regions with high local shear. Such profiles can be generated in channels confined by walls with different hydrodynamic boundary conditions (e.g., slip lengths). Because of a nonlinear hydrodynamic effect, particles with different chirality migrate at different speeds and can be separated. The mechanism is demonstrated by computer simulations. We investigate the influence of thermal fluctuations (i.e., the Péclet number) and show that the effect disappears in the linear response regime. The details of the microscopic flow are important and determine which volume forces are necessary to achieve separation.

We introduce the concept of an indirect photonic transition and demonstrate its use in a dynamic delay line to alter the group velocity of an optical pulse. Operating on an ultrafast time scale, we show continuously tunable delays of up to 20 ps, using a slow light photonic crystal waveguide only $300\mu \mathrm{m}$ in length. Our approach is flexible, in that individual pulses in a pulse stream can be controlled independently, which we demonstrate by operating on pulses separated by just 30 ps. The two-step indirect transition is demonstrated here with a 30% conversion efficiency.

We experimentally demonstrate the direct generation of polarization-entangled photon pairs in an optical fiber at room temperature by exploiting type-II phase-matched spontaneous parametric down-conversion. A second-order nonlinearity is artificially induced in the 17-cm-long weakly birefringent step-index fiber through the process of thermal poling, and quasi-phase-matching allows for the generation of entangled photons in the 1.5-micron telecom band when the fiber is pumped at 775 nm. A greater-than $80:1$ coincidence-to-accidental ratio is achieved, limited mainly by multiphoton pair generation. Without the need to subtract accidentals or to compensate for walk-off, the raw two-photon interference visibility is found to be better than $95\%$, and violation of Bell’s inequality is observed by more than 18 standard deviations. This makes for a truly alignment-free, plug-and-play source of polarization-entangled photon pairs.

Highly ordered, close packed granular systems present a nonlinear dynamic behavior stemming from the Hertzian contact interaction between particles. We investigated the propagation of elastic stress waves in an uncompressed, centered square array of spherical and cylindrical particles. We show, via experiments and numerical simulations, that systematic variations of the mass and stiffness ratios of the spherical and cylindrical particles lead to large variations in the characteristics of the propagating stress wave fronts traveling through the system. The ability to control the stress wave front properties in these granular systems may allow for the development of new wave-tailoring materials including systems capable of redirecting impact energy.

The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and for observing quantum behavior. Here, we demonstrate a technique to push the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen or trap a particular motional mode. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly lossless optical potential, thereby strongly diluting the effect of material dissipation. By placing a 130 nm thick ${\mathrm{SiO}}_2$ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of $Q=5.8(1.1)\times {10}^5$, representing more than an order of magnitude improvement over the conventional limits of ${\mathrm{SiO}}_2$ for this geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems.

Utilizing a multilayered composite approach, we have designed and constructed a new class of artificial materials for thermal conduction. We show that an engineered material can be utilized to control the diffusive heat flow in ways inconceivable with naturally occurring materials. By shielding, concentrating, and inverting heat current, we experimentally demonstrate the unique potential and the utility of guiding heat flux.

We present a comprehensive description of vector chromatography (VC) that includes deterministic and stochastic transport in one-dimensional periodic free-energy landscapes, with both energetic and entropic contributions, and identifies the parameters governing the deflection angle. We also investigate the dependence of the deflection angle on the shape of the free-energy landscape by varying the width of the linear transitions in an otherwise dichotomous potential. Finally, we present experimental results obtained in a microfluidic system in which gravity drives the suspended particles and, in combination with a bottom surface patterned with shallow rectangular grooves, creates a periodic landscape of (potential) energy barriers. The experiments validate the model and demonstrate that a simple, passive microdevice can lead to VC of colloidal particles based on both size and density. More generally, other fields, e.g., electric, dielectrophoretic, or magnetic, can play or enhance the role of gravity, potentially leading to a versatile technique.

Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border.

The entrainment of air by advancing contact lines is studied by plunging a solid plate into a very viscous liquid. Above a threshold velocity, we observe the formation of an extended air film, typically 10 microns thick, which subsequently decays into air bubbles. Exploring a large range of viscous liquids, we find an unexpectedly weak dependence of entrainment speed on liquid viscosity, pointing towards a crucial role of the flow inside the air film. This induces a striking asymmetry between wetting and dewetting: while the breakup of the air film strongly resembles the dewetting of a liquid film, the wetting speeds are larger by orders of magnitude.

We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective modes of long wavelengths. We use this approach to study spatial phase profiles of cellular oscillators in the segmentation clock, a dynamic patterning system of vertebrate embryos. Collective wave patterns result from the interplay of coupling delays and moving boundary conditions. We show that the phase profiles of collective modes depend on coupling delays.

In this Letter, we introduce the concept of spatial pinning control for a network of mobile chaotic agents. In a planar space, $N$ agents move as random walkers and interact according to a time-varying $r$-disk proximity graph. A control input is applied only to those agents which enter a given area, called control region. The control is effective in driving all the agents to a reference evolution and has better performance than pinning control on a fixed set of agents. We derive analytical conditions on the relative size of the control region and the agent density for the global convergence of the system to the reference evolution and study the system under different regimes inherited by the velocity.

We report a surprising new result for wave turbulence which may have broader ramifications for general turbulence theories. Spatial homogeneity, the symmetry property that all statistical moments are functions only of the relative geometry of any configuration of points, can be spontaneously broken by the instability of the finite flux Kolmogorov-Zakharov spectrum in certain (usually one dimensional) situations. As a result, the nature of the statistical attractor changes dramatically, from a sea of resonantly interacting dispersive waves to an ensemble of coherent radiating pulses.

Contrary to conventional wisdom that light bends away from the normal when it passes from high to low refractive index media, here we demonstrate an exotic phenomenon that the direction of electromagnetic power can bend toward the normal when light is incident from an arbitrary high refractive index medium (or air) to a $ϵ$-near-zero (ENZ) metamaterial. Moreover, the direction of the transmission is close to the normal for all angles of incidence. This anti-Snell’s law refraction results from the interplay between ENZ and material loss. The loss can increase the transmission at the air-ENZ interface and collimate the beam inside the ENZ medium. Furthermore, in an ideal loss configuration, the propagation loss in anisotropic ENZ materials can approach zero when the material loss goes to infinity.

We consider linear waves in compressible fluids in a uniform potential field, such as a gravity field, and demonstrate that a particular type of wave motion, in which pressure remains constant in each fluid parcel, is supported by inhomogeneous fluids occupying bounded or unbounded domains. We present elementary, exact solutions of linearized hydrodynamics equations, which describe the new type of waves in the coupled ocean-atmosphere system. The solutions provide an extension of surface gravity waves in an incompressible fluid half-space with a free boundary to waves in compressible, three-dimensionally inhomogeneous, rotating fluids.

High-order harmonic generation in the presence of a chirped THz pulse is investigated numerically with a complete 3D nonadiabatic model. The assisting THz pulse illuminates the high-order harmonic generation gas cell laterally inducing quasi-phase-matching. We demonstrate that it is possible to compensate the phase mismatch during propagation and extend the macroscopic cutoff of a propagated strong IR pulse to the single-dipole cutoff. We obtain 2 orders of magnitude increase in the harmonic efficiency of cutoff harmonics ($\approx 170\mathrm{eV}$) using a THz pulse of constant wavelength, and a further factor of 3 enhancement when a chirped THz pulse is used.