An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.

The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized $\alpha$ effect, which includes both the usual $\alpha$ effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that this generalized $\alpha$ effect scales as $O(R{m}^{-1})$, suggesting the takeover of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.

The motion of a large, neutrally buoyant, particle freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity, provides evidence of a lift force acting on the particle.

A revisited realization of the Young’s double slit experiment is introduced to directly probe the photonic mode symmetry by photoluminescence experiments. We experimentally measure the far field angular emission pattern of quantum dots embedded in photonic molecules. The experimental data well agree with predictions from Young’s interference and numerical simulations. Moreover, the vectorial nature of photonic eigenmodes results in a rather complicated parity property for different polarizations, a feature which has no counterpart in quantum mechanics.

We demonstrate ultrafast dephasing in the random transport of light through a layer consisting of strongly scattering GaP nanowires. Dephasing results in a nonlinear intensity modulation of individual pseudomodes which is 100 times larger than that of bulk GaP. Different contributions to the nonlinear response are separated by using total transmission, white-light frequency correlation, and statistical pseudomode analysis. A dephasing time of $1.2\pm 0.2\mathrm{ps}$ is found. Quantitative agreement is obtained with numerical model calculations which include photoinduced absorption and deformation of individual scatterers. Nonlinear dephasing of photonic eigenmodes opens up avenues for ultrafast control of random lasers, nanophotonic switches, and photon localization.

Whispering-gallery resonators (WGR’s), based on total internal reflection, possess high quality factors in a broad spectral range. Thus, nonlinear-optical processes in such cavities are ideally suited for the generation of broadband or tunable electromagnetic radiation. Experimentally and theoretically, we investigate the tunability of optical parametric oscillation in a radially structured WGR made of lithium niobate. With a $1.04\mu \mathrm{m}$ pump wave, the signal and idler waves are tuned from 1.78 to $2.5\mu \mathrm{m}$—including the point of degeneracy—by varying the temperature between 20 and $62°\mathrm{C}$. A weak off centering of the radial domain structure extends considerably the tuning capabilities. The oscillation threshold lies in the mW-power range.

We present boundary-integral simulations of the evolution of critically charged droplets. For such droplets, small perturbations are unstable and eventually lead to the formation of a lemon-shaped drop with very sharp tips. For perfectly conducting drops, the tip forms a self-similar cone shape with a subtended angle identical to that of a Taylor cone, and quantities such as pressure and velocity diverge in time with power-law scaling. In contrast, when charge transport is described by a finite conductivity, we find that small progeny drops are formed at the tips, whose size decreases as the conductivity is increased. These small progeny drops are of nearly critical charge, and are precursors to the emission of a sustained flow of liquid from the tips as observed in experiments of isolated charged drops.

We predict and confirm experimentally the regime of complete synchronization between lateral modes in a quantum cascade laser, when frequency combs belonging to different lateral modes merge into a single comb. The synchronization occurs through the transition from multistability to a single stable state and is accompanied by phase locking and beam steering effects.

Plasmonic systems are known for their distinct nonlinear optical properties when compared to purely dielectric materials. Although it is well accepted that the enhanced nonlinear processes in plasmonic-dielectric compounds are related to the excitation of localized plasmon resonances, their exact origin is concealed by the local field enhancement in the surrounding material and the nonlinearity in the metal. Here, we show that the origin of third-harmonic generation in hybrid plasmonic-dielectric compounds can be unambiguously identified from the shape of the nonlinear spectrum.

We show both theoretically and experimentally that a collapsing ($2+1$)-dimensional wave packet in a medium with cubic nonlinearity and a two-dimensional dispersion of an order higher than parabolic irradiates untrapped dispersive waves. The studies are performed for a spin-wave bullet propagating in an in-plane magnetized ferrimagnetic film. An induced uniaxial anisotropy in such a medium leads to the formation of narrow spin-wave caustic beams whose angles to the bullet’s propagation direction are modified by the motion of the source.

In this Letter we present results from particle tracking velocimetry and direct numerical simulation that are congruent with the existence of a laminar superlayer, as proposed in the pioneering work of Corrsin and Kistler (NACA, Technical Report No. 1244, 1955). We find that the local superlayer velocity is dominated by a viscous component and its magnitude is comparable to the characteristic velocity of the smallest scales of motion. This slow viscous process involves a large surface area so that the global rate of turbulence spreading is set by the largest scales of motion. These findings are important for a better understanding of mixing of mass and momentum in a variety of flows where thin layers of shear exist. Examples are boundary layers, clouds, planetary atmospheres, and oceans.

Bubbles confined in microchannels self-organize without directly contacting one another when excited by an external acoustic field. The bubbles tend to form periodic “crystal”-like lattices with a finite interbubble distance. This equilibrium distance can be adjusted by simply tuning the acoustic frequency. This new type of crystal is purely mediated by acoustic surface waves emitted by the pulsating bubbles. Because these waves are reflected at the channel boundaries, the bubbles interact with their own images across the boundary.

We determine the initial condition on the laminar-turbulent boundary closest to the laminar state using nonlinear optimization for plane Couette flow. Resorting to the general evolution criterion of nonequilibrium systems we optimize the route to the statistically steady turbulent state, i.e., the state characterized by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimization procedure. We demonstrate that the optimal initial condition is localized in space for realistic flow domains.

We utilize the interaction of tightly focused ultrashort pulses with transparent media to imprint their local polarization in the focal region. In particular, we demonstrate that this technique allows for a subwavelength resolution diagnostic of complex polarization states including the presence of the longitudinal component of the electric field. Moreover, we demonstrate the first ever material ablation with the longitudinal electric field of femtosecond pulses.

Extraordinary optical transmission through metallic gratings is a well established effect based on the collective resonance of corrugated screens. Being based on plasmonic resonances, its bandwidth is inherently narrow, in particular, for thick screens and narrow apertures. We introduce here a different mechanism to achieve total transmission through an otherwise opaque screen, based on an ultrabroadband tunneling that can span from dc to the visible range at a given incidence angle. This phenomenon effectively represents the equivalent of Brewster transmission for plasmonic and opaque screens.

In certain ($2+1$)-dimensional dynamical systems, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen classification theorem. Periodic orbits generated by the dynamics can behave as physical obstructions that “stir” the surrounding domain and serve as the basis for this topological analysis. We provide evidence that, even in the absence of periodic orbits, almost-cyclic regions identified using a transfer operator approach can reveal an underlying structure that enables topological analysis of chaos in the domain.

Nonlinear straining and random sweeping spatiotemporal decorrelation properties, originally introduced as the main processes for turbulent fluctuations decorrelation in usual fluid flows, have been observed experimentally in anisotropic electroconvective turbulence generated in a nematic liquid crystal under the action of an external oscillating electric field. A transition between both processes occurs when the instability is driven toward states of increasing complexity, thus showing that decorrelation mechanisms in turbulent media are more universal than naively expected. A model for both decorrelation mechanisms is introduced, its comparison with experimental results providing an estimate of the characteristic sweeping velocity.

Optical parametric down-conversion has proven to be a valuable source of nonclassical light. The process is inherently able to produce twin-beam correlations along with individual intensity squeezing of either parametric beam, when pumped far above threshold. Here, we present for the first time the direct observation of intensity squeezing of $-1.2\mathrm{dB}$ of each of the individual parametric beams in parametric down-conversion by use of a high quality whispering-gallery-mode disk resonator. In addition, we observed twin-beam quantum correlations of $-2.7\mathrm{dB}$ with this cavity. Such resonators feature strong optical confinement and offer tunable coupling to an external optical field. This work exemplifies the potential of crystalline whispering-gallery-mode resonators for the generation of quantum light. The simplicity of this device makes the application of quantum light in various fields highly feasible.

Using an electrical method and high-speed imaging, we probe drop coalescence down to 10 ns after the drops touch. By varying the liquid viscosity over two decades, we conclude that, at a sufficiently low approach velocity where deformation is not present, the drops coalesce with an unexpectedly late crossover time between a regime dominated by viscous and one dominated by inertial effects. We argue that the late crossover, not accounted for in the theory, can be explained by an appropriate choice of length scales present in the flow geometry.

Nature provides impressive examples of chiral photonic crystals, with the notable example of the cubic so-called srs network (the label for the chiral degree-three network modeled on $\mathrm{SrS}{\mathrm{i}}_2$) or gyroid structure realized in wing scales of several butterfly species. By a circular polarization analysis of the band structure of such networks, we demonstrate strong circular dichroism effects: The butterfly srs microstructure, of cubic $I{4}_{1}32$ symmetry, shows significant circular dichroism for blue to ultraviolet light, that warrants a search for biological receptors sensitive to circular polarization. A derived synthetic structure based on four like-handed silicon srs nets exhibits a large circular polarization stop band of a width exceeding 30%. These findings offer design principles for chiral photonic devices.