By different methods we show that for dynamical chaos in the standard map with critical golden curve, the Poincaré recurrences $P\left(\tau \right)$ and correlations $C\left(\tau \right)$ decay asymptotically in time as $P\propto C/\tau \propto 1/{\tau }^3$. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent $p=3\mathrm{}$ should be also valid for a general chaos border.

Motivated by numerical bifurcation detection, we present a methodology for the direct location of bifurcation points in nonlinear dynamic laboratory experiments. The procedure involves active, adaptive use of the bifurcation parameter(s) as control variable(s), coupled with the on-line identification of low-order nonlinear dynamic models from experimental time-series data. Application of the procedure to such “hard” transitions as saddle-node and subcritical Hopf bifurcations is demonstrated through simulated experiments of lumped as well as spatially distributed systems.

We report a quantum ringlike toroidal cavity naturally formed in a vertical-cavity-like active microdisk plane due to Rayleigh's band of whispering gallery modes. The $\sqrt{T}$-dependent redshift and a square-law property of microampere-range threshold currents down to $2\mu \mathrm{A}$ are consistent with a photonic quantum wire view, due to whispering gallery mode-induced dimensional reduction.

We investigate theoretically and experimentally the three dimensional propagation and interaction of mutually incoherent screening spatial solitons in an SBN crystal. We show that the interaction of solitons results in complex trajectories which typically show partial mutual spiraling, followed by damped oscillations and the fusion of solitons. This nontrivial behavior is caused by the anisotropy of the nonlinear refractive index change in the crystal.

The question of spiraling or no spiraling of incoherent screening spatial solitons in photorefractive crystals is addressed by a careful numerical analysis. We find that the interaction of solitons typically results in an initial mutual rotation of their trajectories, followed by damped oscillations and the fusion of solitons. The rotation can be propelled to prolonged spiraling by the skewed launching of beams. This behavior is caused by the anisotropy of the refractive index change in the crystal.

We investigate the properties of photonic band gap structures of finite size and arbitrary geometry using the density of states deduced from scattering calculations. We first demonstrate this procedure on a finite 2D array of cylinders and then study at optical frequencies a system formed by a finite array of finite height cylinders positioned on a substrate and illuminated with an evanescent field.

We consider observer-based synchronization of chaotic systems. In this scheme, for a given chaotic drive system, response system is chosen in observer form. We show by examples that many response systems proposed in the literature are of this form. We give a necessary condition for synchronization and a selection criterion for appropriate synchronization signal in this case. We apply this idea to synchronization of well-known hyperchaotic Rössler system.

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: Periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory explains earlier observations and provides a number of predictions which are verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controlled by the degree of mutual initial coherence.

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyze how it may occur for dark solitons of the discrete nonlinear Schrödinger and generalized Ablowitz-Ladik equations.

We show that special types of orbits, which are nonperiodic and complex “saddle orbits” (SOs), describe accurately the quantal and experimental current oscillations in the resonant tunneling diode in tilted fields. The SOs solve the puzzle of broad regions of experimental oscillations where we find no real or complex periodic orbit (PO) that can explain the data. The SOs succeed in regimes involving several nonisolated POs, where PO formulas fail. We show that their contribution can, unexpectedly, decay very slowly in the classical limit.

We observed that laser light, multiply scattered through small samples of optically dense colloidal suspensions, builds up anomalous long range correlations in the transmission speckle pattern. The dynamic autocorrelation function of angular integrated light intensity has two contributions, $C_2\left(t\right)$ and $C_3\left(t\right)$, which decay on very different time scales. $C_2$ and $C_3$ are explained by onefold and twofold crossing, respectively, of multiple scattering paths, in quantitative agreement with theory. Our $C_3$ data provide the first evidence for the classical wave analog of universal electronic conductance fluctuations and pinpoint their physical origin as a macroscopic quantum-wave interference effect.

We report the first demonstration of a high average power tabletop soft x-ray laser. An average laser output power of $\approx 1\mathrm{mW}$ $(>2\mathrm{}\times {10}^{14}\mathrm{photons}/\mathrm{s})$ was generated at 46.9 nm in Ne-like Ar using a very compact tabletop discharge. The spatially coherent average power emitted by this 26.5 eV laser is comparable to that generated at this photon energy in a similar bandwidth $(\Delta \lambda /\lambda {=10\mathrm{}}^{-4\mathrm{}})$ by a third-generation synchrotron beam line. Lasing was obtained at a repetition rate of 7 Hz with an average output energy of $135\mu \mathrm{J}/\mathrm{pulse}$ by exciting a plasma column in a ceramic capillary with a fast current pulse. This very compact high-repetition-rate laser source makes intense short-wavelength coherent radiation accessible to a wide variety of new applications.

Solitary waves originating from quantum noise in stimulated Raman forward scattering are interferometrically investigated. The experimental data obtained proves the existence of solitary waves of different character. This finding is also supported by numerical calculations. The observed solitary pulses are interpreted as either a solitary wave, an antisolitary wave, or a breather.

We present the first experimental observation of phase conjugate (PC) second sound (SS) waves in superfluid helium. The main feature of a PC wave is that its phase is complex conjugate to the incident wave phase. It is generated and amplified as a result of nonlinear interaction between an incident SS wave and a first sound (FS) pumping wave. At FS amplitudes larger than the threshold value, a parametric instability, i.e., spontaneous decay of a FS wave into two SS waves, takes place. Three main, theoretically predicted, features of phase conjugate waves were verified experimentally.

A Comment on the Letter by Mark Mineev-Weinstein, Phys. Rev. Lett. 80, 2113 (1998). The authors of the Letter offer a Reply.

A Comment on the Letter by Mark Mineev-Weinstein, Phys. Rev. Lett. 80, 2113 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by J. Casademunt and F. X. Magdaleno, and also the Comment by Robert F. Almgren.

Translating the dynamics of the Hénon-Heiles Hamiltonian as a geodesic flow on a Finsler manifold, we obtain a local and synthetic geometric indicator of chaos (GIC), which represents a link between local quantities and asymptotic behavior of orbits and gives a strikingly evident, one-to-one, correspondence between geometry and instability. Going beyond the results attained using the customary dynamical approach and improving also on the global criteria established within the Riemannian framework, the GIC is able to discriminate between regular and stochastic orbits on a given energy surface, simply on the basis of the value it assumes along a relatively small piece of the trajectory, without long integrations of the dynamics and without any reference to a perturbation.

We measure the temporal evolution of the intensity of an edge emitting semiconductor laser with delayed optical feedback for time spans ranging from 4.5 to 65 ns with a time resolution from 16 to 230 ps, respectively. Spectrally resolved streak camera measurements show that the fast pulsing of the total intensity is a consequence of the time delay and multimode operation of the laser. We experimentally observe that the instabilities at low frequency are generated by the interaction among different modes of the laser.