We measure the field transmission matrix $t$ for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance $g$ and the individual eigenvalues ${\tau }_n$ of the transmission matrix $t{t}^{†}$ whose sum equals $g$. In diffusive samples, the highest eigenvalue, ${\tau }_1$, is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of ${\tau }_1$, is nearly equal to $g$. We find that the spacing between average values of $\ln {\tau }_n$ is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.

We report a new all-optical approach to measuring the phase and amplitude of high-harmonic emission from aligned molecules. We combine the transient grating technique with a continuous rotation of the molecular alignment axis and develop an analytical model that enables the simultaneous determination of phases and amplitudes. Measurements in $N_2$ molecules are shown to be in qualitative agreement with the results of ab initio quantum scattering calculations.

We show that ripples on the surface of deep water which are driven parametrically by monochromatic vertical vibration represent ensembles of oscillating solitons, or quasiparticles, rather than waves. The horizontal mobility of oscillons determines the broadening of spectral lines and transitions from chaos to regular patterns. It is found that microscopic additions of proteins to water dramatically affect the oscillon mobility and drive transitions from chaos to order. The shape of the oscillons in physical space determines the shape of the frequency spectra of the surface ripple.

The instabilities arising in a one-dimensional beam sustained by the diffusive photorefractive nonlinearity in out-of-equilibrium ferroelectrics are theoretically and numerically investigated. In the “scale-free model,” in striking contrast with the well-known spatial modulational instability, two different beam instabilities dominate: a defocusing and a fragmenting process. Both are independent of the beam power and are not associated with any specific periodic pattern.

We demonstrate, by theory and experiment, the ultrafast tilting of the dispersion curve of a photonic-crystal waveguide following the absorption of a femtosecond pump pulse. By shaping the pump-beam cross section with a nanometric shadow mask, different waveguide eigenmodes acquire different spatial overlap with the perturbing pump, leading to a local flattening of the dispersion by up to 11%. We find that such partial mode perturbation can be used to adiabatically compress the spectrum of a light pulse traveling through the waveguide.

Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain poorly understood. In this Letter, we focus on the transport of a finite number of particles in one-dimensional loop networks. By combining numerical, theoretical, and experimental efforts, we evidence that this collective process offers a unique example of Hamiltonian dynamics for hydrodynamically interacting particles. In addition, we show that the asymptotic trajectories are necessarily reciprocal despite the microscopic traffic rules explicitly break the time-reversal symmetry. We exploit these two remarkable properties to account for the salient features of the effective three-particle interaction induced by the exploration of fluidic loops.

A generic nonparaxial model for pulse envelopes is presented. Classic Schrödinger-type descriptions of wave propagation have their origins in slowly-varying envelopes combined with a Galilean boost to the local time frame. By abandoning these two simplifications, a picture of pulse evolution emerges in which frame-of-reference considerations and space-time transformations take center stage. A wide range of effects, analogous to those in special relativity, then follows for both linear and nonlinear systems. Explicit demonstration is presented through exact bright and dark soliton pulse solutions.

Metallic structures with sharp corners harvest the energy of incident light through plasmonic resonances, concentrating it in the corners and greatly increasing the local energy density. Despite its wide array of applications, this effect is normally strongly dependent on how sharp the corners are, presenting problems for fabrication. In this Letter, an analytical approach is proposed, based on transformation optics, to investigate a general class of plasmonic nanostructures with blunt edges or corners. Comprehensive discussions are provided on how the geometry affects the local field enhancement as well as the frequency and energy of each plasmonic resonance. Remarkably, our results evidence the possibility of designing broadband light harvesting devices with an absorption property insensitive to the geometry bluntness.

We demonstrate the presence of parity-time ($\mathcal{P}\mathcal{T}$) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its $\mathcal{P}\mathcal{T}$ symmetry. Spontaneous symmetry breaking occurs at the EP.

The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to ${\mathrm{Re}}_i=2\times {10}^6$ of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers ${\mathrm{Re}}_w$ of the turbulent Taylor-vortex flow is found to scale as ${\mathrm{Re}}_w\propto {\mathrm{Ta}}^{1/2}$, exactly as predicted by Grossmann and Lohse [Phys. Fluids 23, 045108 (2011).] for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of ${\mathrm{Nu}}_{\omega }\propto {\mathrm{Ta}}^{0.38}$, also in correspondence with turbulence in the ultimate regime. The scaling of ${\mathrm{Nu}}_{\omega }$ is confirmed by local angular velocity flux measurements extracted from high-speed PIV measurements: though the flux shows huge fluctuations, its spatial and temporal average nicely agrees with the result from the global torque measurements.

Measurements of the Nusselt number Nu and of a Reynolds number ${\mathrm{Re}}_{\mathrm{eff}}$ for Rayleigh-Bénard convection (RBC) over the Rayleigh-number range ${10}^{12}\lesssim \mathrm{Ra}\lesssim {10}^{15}$ and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio $\Gamma \equiv D/L$ of a cylindrical sample was 0.50. For $\mathrm{Ra}\lesssim {10}^{13}$ the data yielded $\mathrm{Nu}\propto {\mathrm{Ra}}^{{\gamma }_{\mathrm{eff}}}$ with ${\gamma }_{\mathrm{eff}}\simeq 0.31$ and ${\mathrm{Re}}_{\mathrm{eff}}\propto {\mathrm{Ra}}^{{\zeta }_{\mathrm{eff}}}$ with ${\zeta }_{\mathrm{eff}}\simeq 0.43$, consistent with classical turbulent RBC. After a transition region for ${10}^{13}\lesssim \mathrm{Ra}\lesssim 5\times {10}^{14}$, where multistability occurred, we found ${\gamma }_{\mathrm{eff}}\simeq 0.38$ and ${\zeta }_{\mathrm{eff}}=\zeta \simeq 0.50$, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.

Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous; i.e., the mode amplitude $X$ scales with departure from onset $\mu$ as $⟨X⟩\propto {\mu }^{\beta }$ with an exponent $\beta$ different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability, and our results provide a possible explanation for recent experimental observations.

Following a theoretical proposal [M. Farhat et al., Phys. Rev. Lett. 103, 024301 (2009)], we design, fabricate, and characterize a cloaking structure for elastic waves in 1 mm thin structured polymer plates. The cloak consists of 20 concentric rings of 16 different metamaterials, each being a tailored composite of polyvinyl chloride and polydimethylsiloxane. By using stroboscopic imaging with a camera from the direction normal to the plate, we record movies of the elastic waves for monochromatic plane-wave excitation. We observe good cloaking behavior for carrier frequencies in the range from 200 to 400 Hz (one octave), in good agreement with a complete continuum-mechanics numerical treatment. This system is thus ideally suited for demonstration experiments conveying the ideas of transformation optics.

Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.

We study the collision probability $p$ of particles advected by open flows with chaotic advection. We show that $p$ scales with the particle size (or, alternatively, reaction distance) $\delta$ as a power law whose coefficient is determined by the fractal dimensions of the invariant sets defined by the advection dynamics. We also argue that this same scaling also holds for the reaction rate of active particles in the low-density regime. These analytical results are compared to numerical simulations, and they are found to agree very well.

We use the Richtmyer-Meshkov instability (RMI) at a metal-gas interface to infer the metal’s yield stress ($Y$) under shock loading and release. We first model how $Y$ stabilizes the RMI using hydrodynamics simulations with a perfectly plastic constitutive relation for copper (Cu). The model is then tested with molecular dynamics (MD) of crystalline Cu by comparing the inferred $Y$ from RMI simulations with direct stress-strain calculations, both with MD at the same conditions. Finally, new RMI experiments with solid Cu validate our simulation-based model and infer $Y\sim 0.47\mathrm{GPa}$ for a 36 GPa shock.

We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The decomposition of the time-reversal operator is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization, and selective excitation of nanoparticles.

Dissipative localized structures exhibit intricate bifurcation diagrams. An adequate theory has been developed in one space dimension; however, discrepancies arise with the experiments. Based on an optical feedback with spatially modulated input beam, we set up a 1D forced configuration in a nematic liquid crystal layer. We characterize experimentally and theoretically the homoclinic snaking diagram of localized patterns, providing a reconciliation between theory and experiments.

Writing with ink involves the supply of liquid from a pen onto a porous hydrophilic solid surface, paper. The resulting linewidth depends on the pen speed and the physicochemical properties of the ink and paper. Here we quantify the dynamics of this process using a combination of experiment and theory. Our experiments are carried out using a minimal pen, a long narrow tube that serves as a reservoir of liquid, which can write on a model of paper, a hydrophilic micropillar array. A minimal theory for the rate of wicking or spreading of the liquid is given by balancing the capillary force that drives the liquid flow and the resistance associated with flow through the porous substrate. This allows us to predict the shape of the front and the width of the line laid out by the pen, with results that are corroborated by our experiments.

We demonstrate a method for performing nonlinear microspectroscopy that provides an intuitive and unified description of the various signal contributions, and allows the direct extraction of the vibrational response. Three optical fields create a pair of Stokes Raman pathways that interfere in the same vibrational state. Frequency modulating one of the fields leads to amplitude modulations on all of the fields. This vibrational molecular interferometry technique allows imaging at high speed free of nonresonant background, and is able to distinguish between electronic and vibrational contributions to the total signal.