Consistent experimental and numerical simulation studies of the propagation of a one-dimensional Gaussian beam in optically active BSO crystal in the presence of an alternating external field are presented. We have observed three forms of the beam evolution: (i) polarization-dependent self-bending, in which the crystal acts as a nonlinear polarization beam splitter; (ii) spatially nonuniform self-modulation of the state of polarization; (iii) formation of narrow inclined waveguides within the Gaussian beam. The effects of optical activity and the crystal orientation are discussed.

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. We track the time evolution of the drop near snap-off in the experiments and then compare with a scaling theory developed for $\lambda =1\mathrm{}$. The theory is in excellent agreement with both the experiments and the previous simulations of Lister and Stone. Finally, we also investigate the $\lambda$ dependence of the drop shape and breaking rate, and develop a simple theory for the latter.

Self-similar profiles associated with capillary instability of a fluid thread of viscosity $\lambda \eta$ in surrounding fluid of viscosity $\eta$ are obtained for $\frac{1}{16}\le \lambda \le 16$ via a simplified numerical scheme. Universal similarity scaling is preserved despite an asymptotically large velocity in the pinching neck driven by nonlocal dynamics. The numerical results agree well with experimental measurements by Cohen et al. [preceding Letter, Phys. Rev. Lett. 83, 1147 (1999)]. For all $\lambda$, the self-similar profile is asymmetric and conical far from the minimum. The steep cone slope increases monotonically with $\lambda$; the shallow cone slope is maximized around $\lambda =\frac{1}{4}$.

We propose to use periodically spaced, curved optical waveguides for observation of optical Bloch oscillations. The refractive index distribution in this system is equivalent to the sum of a periodic term resulting from the equal spacing of the waveguides and a linear ramp, created by the curvature. We demonstrate numerically that light propagation in this geometry exhibits spatial Bloch oscillations with the period depending on the radius of the curvature and the wavelength.

We demonstrate that when an optically birefringent nematic liquid crystal is infiltrated into the void regions of an inverse opal, photonic-band-gap (PBG) material, the resulting composite material exhibits a completely tunable PBG. In particular, the three-dimensional PBG can be completely opened or closed by applying an electric field which rotates the axis of the nematic molecules relative to the inverse opal backbone. Tunable light localization effects may be realized by controlling the orientational disorder in the nematic.

A system of first-order differential-difference equations with time lag describes the formation of density waves, called quasisolitons, for dissipative systems in this paper. For comoving density waves, the system reduces to some exactly solvable lattice models. We construct a shock-wave solution as well as one-quasi-soliton solution, and argue that there are pseudoconserved quantities which characterize the formation of the comoving waves. The simplest nontrivial one is given to discuss the presence of a cascade phenomenon in a relaxation process toward pattern formation.

Coherent growth of high-order harmonic radiation has been extended to propagation lengths comparable to the XUV absorption length at wavelengths as short as 10 nm range for the first time. Absorption-limited production of high harmonics of sub-10-fs near-infrared laser pulses in gas jets gives rise to a harmonic conversion efficiency of $(3–4)\times {10}^{-8\mathrm{}}$ in the range of 10–13 nm in neon and some 2 orders of magnitude higher at about 30 nm in argon. This kHz-repetition-rate ultrafast soft-x-ray source emits approximately ${10}^{10}$ photons per sec within a 0.9-nm bandwidth of a typical Mo:Si mirror at 13.4 nm in a near-diffraction-limited beam and opens up the way to soft-x-ray nonlinear optics and the measurement of sub-fs soft-x-ray pulses.

The low-frequency eigenmodes of a fractal drum are studied through experimental observation of the acoustical resonances of a fractal-shaped liquid crystal film. The resonance frequencies agree with the numerical predictions for the Laplacian eigenvalues in the fractal domain with Dirichlet boundary conditions. The amplitude distribution of the modes is detected by scanning the excitation position. Several modes are found to be localized in agreement with numerical predictions. Two types of localization related to “strong” and “weak” localization mechanisms are observed in this system. This Letter presents the first direct experimental study of localized modes in fractal geometries.

We report observations of stabilized traveling-wave (TW) convection in a regime in which the uncontrolled system exhibits repeated, erratic growth and abrupt decay of spatially localized bursts of TW. By applying as feedback a spatially varying Rayleigh-number profile computed from the measured convection pattern, we suppress this behavior and stabilize states of unidirectional TW with spatially uniform amplitude on the unstable branch of the subcritical bifurcation to convection. This allows us to measure the nonlinear coefficients of the corresponding quintic complex Ginzburg-Landau equation.

The existence of the “ $-1\mathrm{}$” spectral law in wall turbulence is explained by the effect of superposition of Kolmogorov's eddy cascades generated at all possible distances from the wall, within an equilibrium layer. This concept is justified using only the well-known properties of wall-bounded flows. The presence of coherent structures appears to be not essential for the inverse-power law. The model predicts the $-1\mathrm{}$ scaling for the range $(1/H)\le k\le (1/z)$, which agrees very well with the measurements ( $k$ is the wave number, $H$ is the external scale of the flow, and $z$ is the distance from the wall).

We report the synchronization of two nonidentical spatially extended fields, ruled by one-dimensional complex Ginzburg-Landau equations, both in the phase and in the amplitude turbulence regimes. In the case of small parameter mismatches, the coupling induces a transition to a completely synchronized state. For large parameter mismatches, the transition is mediated by phase synchronization. In the former case, the synchronized state is not qualitatively different from the unsynchronized one, while in the latter case the synchronized state may substantially differ from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects.

We report the numerical observation of edge-type phase defects which occur during the self-focusing of ultrashort pulses. We identified two distinct kinds of defects, formed at the temporal or spatial edges of the pulse. We show the effect of phase defect creation on the dynamics and the eventual arrest of the self-focusing process. Phase defects often lead to the inversion of the phase fronts curvature, transforming contracting pulses into expanding pulses.

We demonstrated that optical subcycle pulses can be generated in dense media of two-level systems due to pulse splitting and reshaping of pulses of a few optical-cycles time duration. Novel features in the spectral signatures of the pulses are predicted, a large blueshift in the transmitted and a large redshift in the reflected pulse, which are explained by intrapulse four-wave mixing. Solitary propagation phenomena in the full Maxwell-Bloch equations beyond the limits of slowly varying envelope and rotating-wave approximations are observed, e.g., the formation of solitary half-cycle pulses and two-soliton pulses.

We generate an observable which relates the interspike time statistics in a noise driven excitable system with its phase space global properties. Experimental results from a semiconductor laser with optical feedback are analyzed within this framework.

We demonstrate that, in contrast with what was previously believed, multihump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves governed by incoherent beam interaction in a saturable medium, providing a theoretical background for the stability of the experimental results reported by Mitchell, Segev, and Christodoulides [Phys. Rev. Lett. 80, 4657 (1998)].

We report observations of the optical stop band of periodic planar arrays of submicron silica spheres, and of macroporous polymers grown from these silica templates. The stop-band width and peak attenuation depend on the number of layers and on the dielectric contrast between the spheres and the interstitial regions, both of which are experimentally controlled. The results are compared to the predictions of the scalar wave approximation. This is the first systematic study of the thickness dependence of the stop band in colloidal photonic band gap structures.

We study the phenomenon of internal avalanching within the context of recently proposed “Tetris” lattice models for granular media. We define a recycling dynamics under which the system reaches a steady state which is self-structured, i.e., it shows a complex interplay between textured internal structures and critical avalanche behavior. Furthermore, we develop a general mean-field theory for this class of systems and discuss possible scenarios for the breakdown of universality.

We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external drive preempts the usual subharmonic Faraday instability. Close to the bicriticality, the nonlinear wave interaction gives rise to a variety of novel surface states: sharply localized islands of hexagons or superlattices and hexagons or superlattices coexisting with line patterns of a different spatial periodicity length. Theoretical stability calculations on the basis of the rheometric viscosity data and qualitative resonance arguments support the experimental observations.

The dynamics of a “kicked” quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic. The diffusion coefficient is explicitly computed for a large class of Hamiltonians and compared to the classical case.

We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all $n$-point correlation functions in the complex plane. As a by-product, we establish the Ginibre-like statistics of resonances for many open channels. Our method is a combination of Itzykson-Zuber integration and a variant of nonlinear $\sigma$ model and can be applied when the use of orthogonal polynomials is problematic.