We present a simple and unified classification of macroscopic electromagnetic resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D structures situated in free space. By observing the complex-plane dynamics of the spatial spectrum of the volume integral operator as a function of angular frequency and constitutive parameters, we identify and generalize all the usual resonances, including complex plasmons, real laser resonances in media with gain, and real quasistatic resonances in media with negative permittivity and gain.

We demonstrate theoretically and experimentally a novel type of localized beam supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.

The quantum dynamics of atoms subjected to pairs of closely spaced $\delta$ kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the single $\delta$-kick system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L\sim {\hslash }^{-0.75}$ and obtain a regime of near-linear spectral variances which approximate the “critical statistics” relation ${\Sigma }_2(L)\simeq \chi L\approx \frac{1}{2}(1-\nu )L$, where $\nu \approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $\nu \approx 0.75$ exponent is analyzed.

We show through rigorous derivation and experimental support that the dynamic effective mass density of an inhomogeneous mixture, used in the prediction of wave velocities in the long wavelength limit, can differ from the static version—the volume average of the component mass densities. The physical reason for this difference is explained. The dynamic mass density expression, first derived by Berryman more than two decades ago, is shown to give a closer correspondence between the acoustic and electromagnetic metamaterials by allowing for negative mass densities at frequencies around resonances.

We report measurements of the Lagrangian velocity structure functions of orders 1 through 10 in a high Reynolds number (Taylor microscale Reynolds numbers of up to $R_{\lambda }=815$) turbulence experiment. Passive tracer particles are tracked optically in three dimensions and in time, and velocities are calculated from the particle tracks. The structure function anomalous scaling exponents are measured both directly and using extended self-similarity and are found to be more intermittent than their Eulerian counterparts. Classical Kolmogorov inertial range scaling is also found for all structure function orders at times that trend downward as the order increases. The temporal shift of this classical scaling behavior is observed to saturate as the structure function order increases at times shorter than the Kolmogorov time scale.

We experimentally investigate photonic Zener tunneling between the bands of a waveguide array by directly monitoring the propagating light inside this structure. For strong transverse index gradients we observe Zener breakdown as regular outbursts of radiation escaping from the Bloch oscillations. Tunneling to higher order photonic bands and Bloch oscillations in different bands have been detected.

By transforming the optical fiber span into an ultralong cavity laser, we experimentally demonstrate quasilossless transmission over long (up to 75 km) distances and virtually zero signal power variation over shorter (up to 20 km) spans, opening the way for the practical implementation of integrable nonlinear systems in optical fiber. As a by-product of our technique, the longest ever laser (to the best of our knowledge) has been implemented, with a cavity length of 75 km. A simple theory of the lossless fiber span, in excellent agreement with the observed results, is presented.

We study a four-level atomic system with electromagnetically induced transparency with giant ${\chi }^{(3)}$ and ${\chi }^{(5)}$ susceptibilities of opposite signs. This system will allow us to obtain multidimensional solitons and light condensates with surface tension properties analogous to those of usual liquids.

The effects of chaotic advection and diffusion on fast chemical reactions in two-dimensional fluid flows are investigated using experimentally measured stretching fields and fluorescent monitoring of the local concentration. Flow symmetry, Reynolds number, and mean path length affect the spatial distribution and time dependence of the reaction product. A single parameter $\overline{\lambda }N$, where $\overline{\lambda }$ is the mean Lyapunov exponent and $N$ is the number of mixing cycles, can be used to predict the time-dependent total product for flows having different dynamical features.

We investigate the effect of dilute polymers on driven two-dimensional turbulence in a soap film. Transitions from strong to weak turbulence are identified by independently varying the polymer concentration $\varphi$ and the energy injection rate ${\epsilon }_{\mathrm{inj}}$. Studies of velocity structures in small scales reveal that strong saddles are suppressed, whereas weak ones become more populated. Interestingly, this redistribution of saddle points in turbulent flows strongly correlates with the quenching of velocity fluctuations on large scales, suggesting that this hydrodynamic structure may play a role in transferring energy from scale to scale.

The spatiotemporal synchronization between two plasma instabilities of autonomous glow discharge tubes is observed experimentally. For this purpose, two tubes are placed separately and two chaotic waves interact with each other through a coupler. When the coupling strength is changed, the coupled oscillators exhibit synchronization in time and space. This is the first experimental evidence of spatiotemporal synchronization by mutual chaotic wave interaction in plasma.

We report the occurrence of spontaneous synchronizing events between two semiconductor lasers, when the emission of a frequency- and intensity-chaotic driving laser is unidirectionally coupled into a second stable response laser. The driving laser is driven chaotic by delayed optical feedback, the response laser is a device-identical solitary laser. We demonstrate the onset of an episodic synchronization regime when the two lasers are spectrally detuned with respect to each other. By a joint experimental and modeling analysis we can attribute the onset and the duration of the episodes to properties of spectral overlap of both lasers. This effect can even give rise to seemingly anticorrelated intensity behavior. We expect episodic synchronization to be a generic scenario for the loss of synchronization of chaotic oscillators exhibiting frequency cycles.

We show that a conservative system of a pair of coupled incoherent nonlinear waves exhibits huge oscillations of coherence, which are characterized by a recurrent transfer of noise fluctuations between the coupled waves. This sustained oscillatory behavior is in contradiction with the expected irreversible evolution towards equilibrium. As a consequence, the process of coherence transfer is characterized by a reduction of nonequilibrium entropy, which violates the $H$ theorem of entropy growth inherent to the kinetic theory.

The generation and nonlinear dynamics of multidimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the $(D+1)$-dimensional complex cubic-quintic Ginzburg-Landau equation ($D=1,2,3$). A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative solitons.

We predict that coherent electromagnetic radiation in the 1–100 THz frequency range can be generated in crystalline materials when subject to a shock wave or solitonlike propagating excitation. To our knowledge, this phenomenon represents a fundamentally new form of coherent optical radiation source that is distinct from lasers and free-electron lasers. The radiation is generated by the synchronized motion of large numbers of atoms when a shock wave propagates through a crystal. General analytical theory and NaCl molecular dynamics simulations demonstrate coherence lengths on the order of mm (around 20 THz) and potentially greater. The emission frequencies are determined by the shock speed and the lattice constants of the crystal and can potentially be used to determine atomic-scale properties of the shocked material.

Here we consider a simple weakly nonlinear model that describes the interaction of two-wave systems in deep water with two different directions of propagation. Under the hypothesis that both sea systems are narrow banded, we derive from the Zakharov equation two coupled nonlinear Schrödinger equations. Given a single unstable plane wave, here we show that the introduction of a second plane wave, propagating in a different direction, can result in an increase of the instability growth rates and enlargement of the instability region. We discuss these results in the context of the formation of rogue waves.

Acoustic negative refractions with backward-wave (BW) effects were both theoretically and experimentally established in the second band of a two-dimensional (2D) triangular sonic crystal (SC). Intense Bragg scatterings result in the extreme deformation of the second band equifrequency surface (EFS) into two classes: one around the $K$ point and the other around the $\Gamma$ point of the reduced Brillouin zone. The two classes can lead to BW negative refractions (BWNRs) but with reverse negative refraction dependences on frequencies and incident angles. Not only BWNR but BW positive refraction can be present at EFSs around the $K$ point, so it is possible to enhance the resolution of acoustic waves with a subdiffraction limit regardless of refractions, which is no analogy in both left-handed material and SCs’ first band. These abundant characters make refractions in the second band distinguished.

According to the traditional view of synchronization, a weak periodic input is able to lock a nonlinear oscillator at a frequency close to that of the input ($1:1$ zone). If the forcing increases, it is possible to achieve synchronization at subharmonic bands also. Using a competitive dynamical system we show the inverse phenomenon: with a weak signal the $1:1$ zone is narrow, but the synchronization of ultrasubharmonics is dominant. In the system’s phase space, there exists a heteroclinic contour in the autonomous regime, which is the image of sequential dynamics. Under the action of a weak periodic forcing, in the vicinity of the contour a stable limit cycle with long period appears. This results in the locking of very low-frequency oscillations with the finite frequency of the forcing. We hypothesize that this phenomenon can be the origin for the synchronization of slow and fast brain rhythms.

Molecules that only differ by their chirality, so-called enantiomers, often possess different properties with respect to their biological function. Therefore, the separation of enantiomers presents a prominent challenge in molecular biology and has long been a main pursuit of organic chemistry. We suggest a new separation technique for chiral molecules that is based on the transport properties in a microfluidic flow with spatially variable vorticity. Because of their size the thermal fluctuating motion of the molecules must be taken into account. These fluctuations play a decisive role in the proposed separation mechanism.

We introduce a background-free real-time detection scheme capable of recognizing low-index nanoparticles such as single viruses in water. The method is based on interferometrically measuring the electromagnetic field amplitude of the scattered light. A split detector is used to generate a background-free signal that renders unprecedented sensitivity for small particles. In its current configuration the sensor is capable of detecting low-index particles in water down to 10 nm in radius or single gold particles as small as 5 nm. We demonstrate the detection of such small particles in a microfluidic system with a time resolution of 1 ms and we discuss the theoretical limits of this novel detection scheme.