Parity-time ($\mathcal{P}\mathcal{T}$) symmetric periodic structures, near the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking point, can act as unidirectional invisible media. In this regime, the reflection from one end is diminished while it is enhanced from the other. Furthermore, the transmission coefficient and phase are indistinguishable from those expected in the absence of a grating. The phenomenon is robust even in the presence of Kerr nonlinearities, and it can also effectively suppress optical bistabilities.

We demonstrate, theoretically and experimentally, nonbroadening optical beams propagating along any arbitrarily chosen convex trajectory in space. We present a general method to construct such beams, and demonstrate it by generating beams following polynomial and exponential trajectories. We find that all such beams, accelerating along any convex trajectory, display the same universal intensity cross section, irrespective of their acceleration. The universal features of these beams are explored using catastrophe theory.

The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology. We identify cases where the commonly used annealed approximation is valid and others where it breaks down. Broader links between BN and general Boolean formulas are highlighted.

The phase inversion that undergoes an emulsion while being sheared is a sudden phenomenon that is still puzzling. In this Letter, we report an experimental investigation on propagative coalescence by using a microfluidic device where a calibrated two-dimensional emulsion is created and destabilized. The velocity of propagation and the probability of the coalescence are reported as a function of the size and the spatial distribution of the drops, respectively. We then discuss the efficiency of this novel scenario of phase inversion and suggest that inversion can be favored by the existence of a drop size distribution.

Direct real-time visualization and measurement of laser-driven shock generation, propagation, and 2D focusing in a sample are demonstrated. A substantial increase of the pressure at the convergence of the cylindrical acoustic shock front is observed experimentally and simulated numerically. Single-shot acquisitions using a streak camera reveal that at the convergence of the shock wave in water the supersonic speed reaches Mach 6, corresponding to the multiple gigapascal pressure range $\sim 30\mathrm{GPa}$.

We demonstrate and quantify a highly effective drag reduction technique that exploits the Leidenfrost effect to create a continuous and robust lubricating vapor layer on the surface of a heated solid sphere moving in a liquid. Using high-speed video, we show that such vapor layers can reduce the hydrodynamic drag by over 85%. These results appear to approach the ultimate limit of drag reduction possible by different methods based on gas-layer lubrication and can stimulate the development of related energy saving technologies.

We report a phenomenon that an optical beam transmits in a negative direction when passing through a single array of high-refractive-index dielectric nanorods. The mechanism of the negative directional transmission is believed to be due to the symmetry of resonant modes in the dielectric nanoparticles. It is expected to find applications in designing compact optical components to achieve the on-chip beam steering in photonic circuits.

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal stiffness rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughness, system size, and Poisson ratio can be collapsed using Persson’s contact theory for continuous elastic media. The compliance due to atomic-scale motion at the interface between solids has little effect on the area and normal stiffness, but can reduce the total transverse stiffness by orders of magnitude. The scaling of this effect with system size is discussed.

We present results of a hybrid experimental and theoretical investigation of the fracture scaling in scratch tests and show that scratching is a fracture dominated process. Validated for paraffin wax, cement paste, Jurassic limestone and steel, we derive a model that provides a quantitative means to relate quantities measured in scratch tests to fracture properties of materials at multiple scales. The scalability of scratching for different probes and depths opens new venues towards miniaturization of our technique, to extract fracture properties of materials at even smaller length scales.

We examine turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-Löwner evolution (SLE) curves. The data stem from a run with ${1536}^3$ grid points, with Reynolds and Rossby numbers of, respectively, 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation and examine the resulting $⟨{\omega }_z{⟩}_z$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $\kappa =3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales and to the partial bidimensionalization of the flow because of rotation. We recover the value of $\kappa$ with a heuristic argument and show that this is consistent with several nontrivial SLE predictions.

Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of $\sim 3(\lambda /n{)}^3$. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical vacuum coupling rate using a frequency calibration technique. The highest measured values exceed 80 kHz, demonstrating high coupling of optical and mechanical modes in such structures.

We report on the spectral broadening of $\sim 1\mu \mathrm{J}$ 30 fs pulses propagating in an Ar-filled hollow-core photonic crystal fiber. In contrast with supercontinuum generation in a solid-core photonic crystal fiber, the absence of Raman and unique pressure-controlled dispersion results in efficient emission of dispersive waves in the deep-UV region. The UV light emerges in the single-lobed fundamental mode and is tunable from 200 to 320 nm by varying the pulse energy and gas pressure. The setup is extremely simple, involving $<1\mathrm{m}$ of a gas-filled photonic crystal fiber, and the UV signal is stable and bright, with experimental IR to deep-UV conversion efficiencies as high as 8%. The source is of immediate interest in applications demanding high spatial coherence, such as laser lithography or confocal microscopy.

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. We find good agreement between a simple fluctuating hydrodynamics theory and particle and finite-volume simulations. The enhancement of the diffusive transport depends on the system size $L$ and grows as $\ln (L/L_0)$ in quasi-two-dimensional systems, while in three dimensions it scales as $L_0^{-1}-L^{-1}$, where $L_0$ is a reference length. Our results demonstrate that fluctuations play an important role in the hydrodynamics of small-scale systems.

The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schrödinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It is localized in both space and time, thus describing a unique wave event. Until now, experiments specifically designed for observation of breather states in the evolution of deep water waves have never been made in this double limit. In the present work, we present the first experimental results with observations of the Peregrine soliton in a water wave tank.

We study, experimentally and numerically, amorphous photonic lattices and the existence of band gaps therein. Our amorphous system comprises 2D waveguides distributed randomly according to a liquidlike model responsible for the absence of Bragg peaks, as opposed to ordered lattices with disorder which always exhibit Bragg peaks. In amorphous lattices the bands comprise localized states, but we find that defect states residing in the gap are more localized than the localization length of states within the band. Finally, we show how the concept of effective mass carries over to amorphous photonic lattices.

The smallest structures that conventional lenses are able to optically resolve are of the order of 200 nm. We introduce a new type of lens that exploits multiple scattering of light to generate a scanning nanosized optical focus. With an experimental realization of this lens in gallium phosphide we imaged gold nanoparticles at 97 nm optical resolution. Our work is the first lens that provides a resolution better than 100 nm at visible wavelengths.

We realize experimentally a true reflectionless potential, which facilitates nonresonant unity transmission for all incident waves and at the same time supports localized modes. We utilize arrays of evanescently coupled optical waveguides, where a particular modulation of the transverse waveguide separations provides a physical realization of reflectionless Ablowitz-Ladik soliton potentials.

Mixing efficiency at low Reynolds numbers can be enhanced by exploiting hydrodynamic instabilities that induce heterogeneity and disorder in the flow. The unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid-fluid interfacial area and enhance mixing. Here we describe the dissipative structure of miscible viscous fingering, and propose a two-equation model for the scalar variance and its dissipation rate. Our analysis predicts the optimum range of viscosity contrasts that, for a given Péclet number, maximizes interfacial area and minimizes mixing time. In the spirit of turbulence modeling, the proposed two-equation model permits upscaling dissipation due to fingering at unresolved scales.

We show that for pulse-coupled oscillators a class of phase response curves with both excitation and inhibition exhibit robust convergence to synchrony on arbitrary aperiodic connected graphs with delays. We describe the basins of convergence and give explicit bounds on the convergence times. These results provide new and more robust methods for synchronization of sensor nets and also have biological implications.

We investigate the interaction between two cracks propagating quasistatically in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. A single tear propagates in a straight line independently of its position in the sheet. In contrast, we find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.