The real part of the refractive index $n\left(\omega \right)$ of a nearly transparent and passive medium is usually taken to have only positive values. Through an analysis of a current source radiating into a 1D “left-handed” material (LHM)—where the permittivity and permeability are simultaneously less than zero—we determine the analytic structure of $n\left(\omega \right)$, demonstrating frequency regions where the sign of $\mathrm{Re}\left[n\right(\omega \left)\right]$ must, in fact, be negative. The regime of negative index, made relevant by a recent demonstration of an effective LHM, leads to unusual electromagnetic wave propagation and merits further exploration.

We present three novel pulsating solutions of the cubic-quintic complex Ginzburg-Landau equation. They describe some complicated pulsating behavior of solitons in dissipative systems. We study their main features and the regions of parameter space where they exist.

It is shown that $m$-fold symmetric vortex waves in two dimensions ( $V$ states) preserve their functional form in a weak straining flow having appropriate symmetry, but arbitrary time dependence. This phenomenon is used in driving the $V$ states into a highly nonlinear excitation by subjecting a circular vortex patch to rotation and strain with oscillating strain rate and varying the rotation angular velocity. The effect is due to autoresonance in the system as the excited vortex state boundary self-adjusts its aspect ratio to synchronize with the external flow.

Quantum and classical correlations are studied experimentally in model $n$-disk microwave billiards. The wave vector $\kappa$ autocorrelation $C\left(\kappa \right)$ of the quantum spectrum displays nonuniversal oscillations for large $\kappa$, comparable to the universal random matrix theory behavior observed for small $\kappa$. The nonuniversal behavior is shown to be completely determined by the classical Ruelle-Pollicott resonances, arising from the complex eigenvalues of the Perron-Frobenius operator, and calculated using periodic orbit theory. This work establishes a fundamental connection between the quantum and classical correlations of an open system.

This paper presents the first experimental evidence of the transition from dynamical localization to delocalization under the influence of a quasiperiodic driving on a quantum system. A quantum kicked rotator is realized by placing cold atoms in a pulsed, far-detuned, standing wave. If the standing wave is periodically pulsed, one observes the suppression of the classical chaotic diffusion, i.e., dynamical localization. If the standing wave is pulsed quasiperiodically, dynamical localization is observed or not, depending on the driving frequencies being commensurable or incommensurable. One can thus study the transition from the localized to the delocalized case as a function of the effective dimensionality of the system.

The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular, and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. In this Letter, the first direct experimental verification of this effect, known as resonance trapping, is presented. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.

We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a two-dimensional microwave resonator are analyzed as a function of an experimentally determined time-reversal symmetry-breaking parameter. We test four theories of one-point eigenfunction statistics and introduce a new theory relating the one-point and two-point statistical properties in the crossover regime. We also find a universal correlation between the one-point and two-point statistical parameters for the crossover eigenfunctions.

The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that if $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics is not changed by the perturbation. This is done first within the random matrix model. Then it is shown by semiclassical techniques that the result is due to a cancellation between diagonal diffractive and off-diagonal periodic-diffractive contributions. The compensation is a very general phenomenon encoding the semiclassical content of the optical theorem.

A chaotic attractor containing unstable periodic orbits with different numbers of unstable directions is said to exhibit unstable dimension variability (UDV). We present general mechanisms for the progressive development of UDV in uni- and bidirectionally coupled systems of chaotic elements. Our results are applicable to systems of dissimilar elements without invariant manifolds. We also quantify the severity of UDV to identify coupling ranges where the shadowability and modelability of such systems are significantly compromised.

Harmonic radiation generated in a neon gas jet by sub-10-fs laser pulses was investigated both experimentally and theoretically. The spectral profile of the harmonics with respect to the order, their intensity and relative spectral shifts were measured as a function of the position of the gas jet. The results point out spectral features typical of the quasi-single-cycle excitation regime. A nonadiabatic three-dimensional numerical model was developed, which provides harmonic spectra in remarkable agreement with the experiments.

We have created a one- (rather than two-) dimensional quasi-steady-state photorefractive spatial soliton induced by a laser beam instead of an applied electric field. The formation of this type of spatial soliton depends on the intensity of the self-trapped beam, which is different from quasi-steady-state spatial solitons reported in the literature. The optically induced spatial soliton can be exploited in all optical switching applications.

We investigate electromagnetic localization in a nonlinear photonic crystal, i.e., a structure with a stop band in its nonlinear spectral response. Taking a one-dimensional model of degenerate two-wave interaction we introduce the concept of parametric nonlinear-gap solitons, that is, strongly localized two-color locked envelopes arising from interplay of two nonlinear effects, which propagate slowly. We discuss the observable signature of these novel localized structures.

Experimental studies were performed on the buoyancy-driven instability of an autocatalytic reaction front in a quasi-2D cell. The unstable density stratification at an ascending front leads to convection that results in a fingerlike front deformation. The growth rates of the spatial modes of the instability are determined at the initial stage. A stabilization is found at higher wave numbers, while the system is unstable against low wave number perturbations. Whereas comparison with a reported model governed by Hele-Shaw flow fails, a two-dimensional Navier-Stokes model yields more satisfactory results. Still, present deviations suggest the presence of an additional mechanism that suppresses the growth.

A Comment on the Letter by M. Palus and D. Novotna, Phys. Rev. Lett. 83, 3406 (1999). The authors of the Letter offer a Reply.

A Reply to the Comment by J. Timmer.

A technique to forecast spatiotemporal time series is presented. It uses a proper orthogonal or Karhunen-Loève decomposition to encode large spatiotemporal data sets in a few time series, and genetic algorithms to efficiently extract dynamical rules from the data. The method works very well for confined systems displaying spatiotemporal chaos, as exemplified here by forecasting the evolution of the one-dimensional complex Ginzburg-Landau equation in a finite domain.

We studied the mechanism behind the connection between the transition to chaos of random dynamical systems and the synchronization of chaotic maps driven by external common noises. Near the chaotic transition, the spatial size of random dynamical systems shows an extreme intermittent behavior. By calculating the scaling exponents, we have found that the origin of this intermittent behavior is on-off intermittency. This led us to conclude that chaotic transitions through on-off intermittency can be regarded as a route for random dynamical systems. To clarify this argument, a two-dimensional random dynamical system and two coupled logistic maps driven by external common noises were analyzed.

We report an experiment of type 2 parametric image amplification in a phase sensitive configuration. In the spatial frequency domain, the parametric gain corresponds to amplification or deamplification, depending on the relative phase of the input image with respect to the pump wave and on the spatial frequencies of the input image.

The energy-optimal entraining of the dynamics of a periodically driven oscillator, moving it from a chaotic attractor to a coexisting stable limit cycle, is investigated via analysis of fluctuational transitions between the two states. The deterministic optimal control function is identified with the corresponding optimal fluctuational force, which is found by numerical and analog simulations.

We show that the diffraction of a shocking optical pulse formed in a nonlinear transparent dielectric creates an optical missile, or localized radiation field whose amplitude and energy decays are slower than $1/R$ and ${1/R}^2$, respectively, far from the aperture. Dispersion does not eliminate, but limits missile behavior to a finite range. Experimental techniques for optical missile generation are suggested.