We studied the propagation of an electromagnetic (EM) wave in a piezoelectric superlattice. Because of the piezoelectric effect, a transverse polarization can be induced by a longitudinal wave which couples strongly to the EM wave in some particular frequency regions, resulting in the creation of a new type of polariton that does not exist in ionic crystals. The forbidden band associated with the polariton is not due to the Bragg reflection, but rather to the coupling.

We experimentally investigate the formation of a vector polarization pattern from an isotropic microcavity laser. It is found that the orthogonal components of the observed pattern are localized on the geometrical rays. The connection between eigenfunctions and geometrical rays is analytically constructed by using the SU(2) coherent states. With the analytical function form, the observed vector pattern is completely reconstructed and the vector vortex lattice is apparent.

We investigate numerically the Navier-Stokes dynamics of reconnecting vortex rings at small Reynolds number for a variety of configurations. We find that reconnections are dissipative due to the smoothing of vorticity gradients at reconnection kinks and to the formation of secondary structures of stretched antiparallel vorticity which transfer kinetic energy to small scales where it is subsequently dissipated efficiently. In addition, the relaxation of the reconnection kinks excites Kelvin waves which due to strong damping are of low wave number and affect directly only large scale properties of the flow.

We show that unlike the bright solitons, the parametrically driven kinks are immune from instabilities for all dampings and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of stable kinks and their complexes can travel with nonzero velocities.

This Letter presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to populations of any size and functional form in the region of coherence. It requires linear variation or a narrow distribution for the dispersed parameter. Although an approximation, the method allows us to quantitatively study the transitions among the collective regimes as bifurcations of the effective macroscopic degrees of freedom. To illustrate, the phenomenon of oscillator death and the route to full locking are examined for chaotic oscillators with time scale mismatch.

We experimentally and numerically investigate the quantum accelerator mode dynamics of an atom optical realization of the quantum $\delta$-kicked accelerator, whose classical dynamics are chaotic. Using a Ramsey-type experiment, we observe interference, demonstrating that quantum accelerator modes are formed coherently. We construct a link between the behavior of the evolution’s fidelity and the phase space structure of a recently proposed pseudoclassical map, and thus account for the observed interference visibilities.

We demonstrate an efficient intracavity nonlinear interaction of laser modes in a specially adapted quantum cascade laser. A two-wavelength quantum cascade laser structure emitting at wavelengths of 7.1 and $9.5\mu \mathrm{m}$ included cascaded resonant optical intersubband transitions in an intracavity configuration leading to resonantly enhanced sum-frequency and second-harmonic generation at wavelengths of 4.1, 3.6, and $4.7\mu \mathrm{m}$, respectively. Laser peak optical powers of 60 and 80 mW resulted in 30 nW of sum-frequency signal and 10–15 nW of second-harmonic signal, both in good agreement with theoretical calculations.

The nonlinear vibrational properties of a periodic micromechanical oscillator array have been measured. For sufficiently large amplitude of the driver, the optic mode of the di-element cantilever array becomes unstable and breaks up into excitations ranging over only a few cells. A driver-induced locking effect is observed to eternalize some of these intrinsic localized modes so that their amplitudes become fixed and the modes become spatially pinned.

We investigate Rayleigh scattering in dissipative optical lattices. In particular, following recent proposals [S. Guibal et al., Phys. Rev. Lett. 78, 4709 (1997); C. Jurczak et al., Phys. Rev. Lett. 77, 1727 (1996)], we study whether the Rayleigh resonance originates from the diffraction on a density grating and is therefore a probe of transport of atoms in optical lattices. It turns out that this is not the case: the Rayleigh line is instead a measure of the cooling rate, while spatial diffusion contributes to the scattering spectrum with a much broader resonance.

Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects and on the grain/fluid density ratio $r$. In gas ($r\gg 1$ and $\mathrm{S}\mathrm{t}>1$, e.g., the dry case), the amplitude and time duration of avalanches do not depend on any fluid effect. In liquids ($r\sim 1$), for decreasing St, the amplitude decreases and the time duration increases, exploring an inertial regime and a viscous regime. These three regimes are described by the analysis of the elementary motion of one grain.

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated. We also describe the classical analogs of this behavior.

We develop a method to detect the presence of integrals of the motion in symplectic rational maps, by representing these maps over finite fields and examining their orbit structure. We find markedly different orbit statistics depending upon whether the map is integrable or not.

The ultimate regime of thermal convection, the so-called Kraichnan regime [R. H. Kraichnan, Phys. Fluids 5, 1374 (1962)], hitherto has been elusive. Here numerical evidence for that regime is presented by performing simulations of the bulk of turbulence only, eliminating the thermal and kinetic boundary layers and replacing them with periodic boundary conditions.

A microwave experiment has been realized to measure the phase difference of the oscillating electric field at two points inside the cavity. The technique has been applied to a dissipative resonator which exhibits a singularity—called exceptional point—in its eigenvalue and eigenvector spectrum. At the singularity, two modes coalesce with a phase difference of $\pi /2$. We conclude that the state excited at the singularity has a definitive chirality.

We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions where mixing is less efficient. We examine two situations. The first is of a spatially homogeneous stationary turbulent flow with both viscous and inertial scales present. It is shown that at large times scalar fluctuations decay algebraically in time at all spatial scales. The second example explains chaotic stationary flow in a disk/pipe. The boundary region of the flow controls the long-time decay, which is algebraic at some transient times, but becomes exponential, with the decay rate dependent on the scalar diffusion coefficient, at longer times.

We show that the distortionless tunneling of electromagnetic pulses through a barrier is a quasistatic process in which the slowly varying envelope of the incident pulse modulates the amplitude of a standing wave. For pulses longer than the barrier width, the barrier acts as a lumped element with respect to the pulse envelope. The envelopes of the transmitted and reflected fields can adiabatically follow the incident pulse with only a small delay that originates from energy storage. The theory presented here provides a physical explanation of the tunneling process and resolves the mystery of apparent superluminality.

We report the first experimental observation of discrete solitons in an array of optically induced waveguides. The waveguide lattice is induced in real time by illuminating a photorefractive crystal with a pair of interfering plane waves. We demonstrate two types of bright discrete solitons: in-phase self-localized states and the staggered ($\pi$ out-of-phase) soliton family. This experiment is the first observation of bright staggered solitons in any physical system. Our scheme paves the way for reconfigurable focusing and defocusing photonic lattices where low-power (mW) discrete solitons can be thoroughly investigated.

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to steplike contraction, and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur.

Kinematic simulations of turbulent pair diffusion in planar turbulence with a $k^{-5/3}$ energy spectrum reproduce the laboratory results of Jullien et al. [Phys. Rev. Lett. 82, 2872 (1999)], in particular the stretched exponential form of the probability density function of pair separations and their correlation functions. The root mean square separation is found to be strongly dependent on initial conditions for very long stretches of time. This dependence is consistent with the topological picture where pairs initially close enough travel together for long stretches of time and separate violently when they meet straining regions around hyperbolic points. A new argument based on the divergence of accelerations is given to support this picture.

The spatial and temporal persistence, or first-return distributions are measured for slow-combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on the front dynamics, which asymptotically belongs to the Kardar-Parisi-Zhang universality class. The stationary short-range and the transient behavior of the fronts are non-Markovian, and the observed persistence properties thus do not agree with the predictions based on Markovian theory. This deviation is a consequence of additional time and length scales, related to the crossovers to the asymptotic coarse-grained behavior.