We have directly observed the Anderson localized wave functions in three dimensions in a new class of photonic band gap systems. Such systems are networks made of one-dimensional waveguides. By adopting a simple scattering geometry in a unit cell, we are able to obtain large photonic band gaps. In the presence of defects or randomness, we have systematically studied the structures of transmission and the localized wave functions inside a gap. The effects due to absorption are investigated. Excellent quantitative agreements between theory and experiments have been obtained.

We demonstrate that the main features of high harmonic generation by ultrashort laser pulses can be explained in terms of the intensity dependent phase of the atomic polarization. Focusing conditions and chirped driving fields may be used to control the harmonic spectrum, while temporal compression provides a unique way to tailor the time profile.

We present time-resolved measurements of photoinduced birefringence in liquid crystalline polyester films. After excitation with a single nanosecond pulse, the induced birefringence is monitored on time scales ranging from nanoseconds up to minutes. The maximum birefringence is attained in a dark reaction after excitation. Subsequently, most of the induced birefringence is lost due to relaxation processes involving up to four different time constants. We observed that at high pulse energies the relaxation characteristics are strongly influenced by thermal effects.

Controlling turbulence in the complex Ginzburg-Landau equation (CGLE) is investigated. The CGLE is generalized to include gradient force. Local injections (pinnings) are applied for turbulence control. It is found that local injections are effective in eliminating turbulence. In particular, for large gradient force, it is possible to suppress fully developed turbulence by adding a few injections much less in number than the number of positive Lyapunov exponents of the system. The high efficiency of controlling is heuristically explained, based on the spatial correlation length and space-time-variable transformation.

In the study of chaos, Lyapunov exponents have been successfully used in describing the expansion and contraction rates of various modes. In this Letter, generalized winding numbers are defined in association with the corresponding Lyapunov exponents to characterize the rotation behavior of these modes during the evolution. A Hopf bifurcation from chaos, namely, a blowout bifurcation with certain finite typical frequency, is revealed. The frequency of the motion after the bifurcation is justified to be equal to the generalized winding number of the critical transverse mode, for which the Lyapunov exponent crosses zero at the bifurcation.

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the phase-locking state, simultaneous phase slips of all oscillators and quantized phase shifts in these phase slips are observed. By increasing the coupling, a bifurcation tree from high-dimensional quasiperiodicity to chaos to quasiperiodicity and periodicity is found. Different orders of phase synchronizations of chaotic oscillators and chaotic clusters play the key role for constructing this tree structure.

We report the first room temperature observation of an emission pattern from a single fluorescent molecule signifying that the emission dipole is aligned along the optic $\left(z\right)$ axis of a microscopic imaging system. This technique takes advantage of the $x$, $y$, and $z$-polarized evanescent fields generated in total internal reflection and the usually nettlesome aberrations commonly encountered when imaging biological samples with high numerical aperture oil-immersion objectives. For both $z$-oriented and transverse-oriented individual molecules of the carbocyanine dye ${\mathrm{DiIC}}_{18}$ embedded in polymethyl-methacrylate (PMMA), calculated images accurately model the main features of observed emission patterns.

The first femtosecond three-pulse photon echo experiment of a vibrational transition is presented. A mode of the azide ion ${\mathrm{N}}_3^{-}$ at $2043{\mathrm{cm}}^{-1\mathrm{}}$ is used to probe the impulsively excited vibrational energy distribution and hence the dynamics of the water around the ion. The vibrational frequency correlations decay on time scales of about 80 fs and 1.3 ps, while a small part remains for longer than about 10 ps. The 1.3 ps decay is the residence time for hydrogen bonds to the ion. Major differences between vibrational and optical three-pulse echoes are addressed.

We analyze turbulent velocity signals in the atmospheric surface layer, obtained by pairs of probes separated by inertial-range distances parallel to the ground and (nominally) orthogonal to the mean wind. The Taylor microscale Reynolds number ranges up to 20 000. Choosing a suitable coordinate system with respect to the mean wind, we derive theoretical forms for second order structure functions and fit them to experimental data. The effect of flow anisotropy is small for the longitudinal component but significant for the transverse component. The data provide an estimate for a universal exponent from among a hierarchy that governs the decay of flow anisotropy with the scale size.

For Rayleigh-Bénard convection of a fluid with Prandtl number $\sigma =1.4\mathrm{}$, we report experimental and theoretical results on a pattern selection mechanism for cell-filling, giant, rotating spirals. We show that the pattern selection in a certain limit can be explained quantitatively by a phase-diffusion mechanism. This mechanism for pattern selection is very different from that for spirals in excitable media.

We propose the viscous Camassa-Holm equations as a closure approximation for the Reynolds-averaged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel and pipe flows with steady mean. Analytical solutions for the mean velocity and the Reynolds shear stress are consistent with experiments in most of the flow region.

We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for 3 degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.

We study spin glass clusters (“shards”) in a random transverse magnetic field, and determine the regime where quantum chaos and random matrix level statistics emerge from the integrable limits of weak and strong fields. Relations with quantum phase transition are also discussed.

We show that optical vortices and $J_0$ Bessel-like beams can be generated via traveling-wave linear parametric amplification of the quantum noise, in the absence of external seeding or resonator feedback. The shot-to-shot fluctuations in the topological charge of the amplified signal are driven by the quantum-noise seed.

We present two methods for approximating the mapping between two systems exhibiting generalized synchronization. If the equations of motion are known then an analytic approximation to the mapping can be found. If time series data are used then a numerical approximation can be found.

It is shown that two-degree-of-freedom Hamiltonian systems of the billiard type are equivalent to adiabatically varying one-degree-of-freedom Hamiltonian systems for solutions staying near the boundary. Under some nondegeneracy conditions such systems possess a large set of quasiperiodic solutions filling out two-dimensional invariant tori. The latter separate the extended phase space into layers providing stability for all time. The result is illustrated on a few examples.

We have investigated level statistics in constant-scaled-energy spectra of the diamagnetic helium atom. In a transversely laser-cooled beam metastable triplet atoms are excited to Rydberg states in the presence of a magnetic field, resolving all resonances. In the regime of regular classical motion level distributions obeying Poisson statistics are observed. Small deviations are attributed to scattering at the nonhydrogenic $\mathrm{He}{}^{+}$ core as inferred from closed-orbit theory. The nearest-neighbor spacings in spectra in the chaotic regime demonstrate a clear shift towards Wigner statistics.

Two superconducting microwave billiards have been electromagnetically coupled in a variable way. The spectrum of the entire system has been measured and the spectral statistics analyzed as a function of the coupling strength. It is shown that the results can be understood in terms of a random matrix model of quantum mechanical symmetry breaking—as, e.g., the violation of parity or isospin in nuclear physics.

We show that an azimuthally periodically modulated bright ring “necklace” beam can self-trap in self-focusing Kerr media and can exhibit stable propagation for very large distances. These are the first bright $(2+1)\mathrm{D}$ beams to exhibit stable self-trapping in a system described by the cubic $(2+1)\mathrm{D}$ nonlinear Schrödinger equation.

The bottleneck pileup in the energy spectrum is investigated for several two-dimensional (2D) turbulence systems by numerical simulation using high-order diffusion terms to amplify the effect, which is weak for normal diffusion. For 2D magnetohydrodynamic (MHD) turbulence, 2D electron MHD (EMHD) turbulence, and 2D thermal convection, which all exhibit direct energy cascades, a nonlocal behavior is found resulting in a logarithmic enhancement of the spectrum.