A new class of amplitude instabilities severely restricts the stability domain of the transverse patterns in a laser that takes the form of a continuum of waves traveling transverse to the laser axis. Linear stability analyses and numerical solution of the laser equations reveal that one of the instabilities, which should be manifest in a broad range of contexts for which traveling waves are the preferred pattern, results in the death of the traveling wave and its replacement by a wave traveling in the opposite direction which exhibits novel transient and asymptotic behavior.

We propose and analyze a nonlinear optical amplifier that is phase insensitive but has no additive noise. When the input field is in a coherent state, the noise figure is -6 dB when the gain is high. However, unlike conventional linear amplifiers with -3 dB noise figures, the detectibility of the amplified signal is not degraded. The amplifier is constructed simply, in principle, by the same type of nonlinear interferometer used in photon number quantum nondemolition measurements.

We present an alternative approach to statistical analysis of an intermittent ideal magnetohydrodynamics fluid in two dimensions, based on the hydrodynamic discrete vortex model applied to the Elsasser variables. The model contains negative temperature states which predict the formation of magnetic islands, but also includes a natural limit under which the equilibrium states revert to the familiar twin-vortex states predicted by hydrodynamic turbulence theories. Numerical dynamical calculations yield equilibrium spectra in agreement with the theoretical predictions.

When a chemical wave encounters a boundary between two media with different wave speeds, refraction and reflection can occur. We demonstrate experimentally that the refraction of chemical waves obeys Snell’s law. Reflection of chemical waves has been observed for the first time. The waves do not show specular reflection, but rather exhibit a single reflection angle, equal to the critical angle.

Since Berry introduced topological phases to describe the adiabatic transport of the spin of particles in parameter space, they have become a practical and descriptive concept for understanding interference phenomena in many quantum mechanical systems. For the photon two different applications of this concept were found in crystal optics: (1) the optical activity of helically wound optical fibers and (2) the development of the state of polarization on the Poincaré sphere. We present a remarkable optical ‘‘nonlinearity’’ of certain polarizing interferometers, which we discovered by using the concept of the topological phase on the Poincaré sphere and we demonstrate it with a simple experiment.

Coherent transfer of energy (CTE) gives rise to a new peak and dip in the probe gain spectrum that move proportionally with the intracavity injected power showing that stimulated emission and absorption significantly speed up the semiconductor response. Gain modification is seen in two nondegenerate, cross-polarized modes of a microcavity laser when light is injected into only one mode, giving strong evidence for the CTE origin of the gain asymmetry.

Turing patterns involve regions of different chemical compositions which lead to density gradients that, in liquids, are potentially unstable hydrodynamically. Nonlinear hydrodynamics coupled with a model of Turing pattern formation show that convection modifies and coexists with some Turing patterns and excludes others, and thereby plays a significant role in pattern selection.

The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Bénard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution.

We report a new phenomenon observed along a crisis locus when two control parameters of physical models are varied simultaneously: the existence of one or several vertices. The occurrence of a vertex (loss of differentiability) on a crisis locus implies the existence of simultaneous sudden changes in the structure of both the chaotic attractor and of its basin boundary. Vertices correspond to degenerate tangencies between manifolds of the unstable periodic orbits accessible from the basin of the chaotic attractor. Physically, small parameter perturbations (noise) about such vertices induce drastic changes in the dynamics.

We have found experimentally that the flow of sand in an hour glass is oscillatory in a certain range of parameters. The oscillatory motion results from a coupling between the flow of sand and convection of air through the sand matrix. The period of the oscillation is remarkably insensitive to the grain size, while the mass of the sand contained in one period strongly depends on it.

The Landau-Ginzburg equations used to describe periodic spatial patterns in two dimensions are extended to a set of spatiotemporal equations. The extension is determined by the requirement that the equations of motion commute with translations, reflections, and rotations in the plane. This simple model produces a variety of complex structures similar to those observed in chemical reactions, ferrofluids, Rayleigh-Bénard convection, and magnetic bubble materials.

We observe the (r,θ) drift motion of two nearly identical magnetized electron columns bounded by a cylindrical wall. In the 2D E×B drift approximation, these columns are vortices evolving according to the Euler equation. We observe stable and unstable equilibria in which the vortices orbit about the center of the cylinder. The equilibrium positions, oscillation frequencies, and instability rates for these spatially extended vortices agree well with the predictions of integrable point vortex theory, apparently because surface waves and shape distortions do not couple to the center-of-mass motion.

A useful physical model for superfluid turbulence considers the flow to consist of a dense tangle of vortex lines which evolve and interact. It has been suggested that these vortex lines can dynamically reconnect upon close approach. Here, we consider the nonlinear Schrödinger equation model of superfluid quantum mechanics, and use numerical simulation to study this topology changing core-scale process. Our results support the idea that vortex reconnection will occur whenever filaments come within a few core lengths of one another.

It is suggested that solitary wave solutions exist in the gap region of photonic band gap materials with a Kerr nonlinearity. Using a variational trial function we estimate the amplitude, size scale, and the nature of phase modulation of these nonlinear waves. In two dimensions, we predict the occurrence of a variety of finite energy solitary waves associated with the different symmetry points of the crystalline Brillouin zone. Solutions which preserve the symmetry of the crystal exist for both positive and negative Kerr coefficient whereas solutions which break the symmetry occur only for positive nonlinearity. These states are relevant to the bistable switching properties of photonic band gap materials.

Zakharov and L’vov long ago invoked a Kolmogorov cascade hypothesis to describe the modal transfer of energy for surface gravity waves in deep water. Within this context the cascade hypothesis requires the existence of dynamical time scales in the evolution of the mode amplitudes which scale with wave number. The purpose of this Letter is to study the temporal evolution of individual modes, with the aim of identifying these dynamical time scales. The main result reported here is that mode-dependent time scales τ(k)∼${\mathit{k}}^{\mathrm{-}\mathrm{\beta }}$ can indeed be identified, with exponent β related to the exponent α which describes the spectrum of the waveheight autocorrelation function.

Based on our theoretical results of dynamical behaviors of light transmission in optical superlattices, we show that there is a new type of optical bistable mechanism, i.e., the index-modulation mechanism, existing in a two-dimensional superlattice that contains dielectric nonlinearity of the Kerr form. This bistable mechanism is not exhibited in one-dimensional superlattices.

Depolarized hyper Rayleigh scattering of para-nitroaniline (${\mathit{C}}_{2\mathit{v}}$ symmetry) and nitrocalix[4]arene (${\mathit{C}}_{4\mathit{v}}$ symmetry) in solution has been measured. Using linearly and circularly polarized fundamental radiation information about the ratios between the several hyperpolarizability tensor components, including their sign, was obtained. Results are consistent with the theory developed for both symmetry groups. Comparison between experimental depolarization ratios and ratios obtained from ab initio calculated hyperpolarizability tensor components shows good agreement.

We reexamine the multiple-time-scale method as applied to ergodic adiabatic Hamiltonian systems. Solving for the evolution of the phase space density to first order in the slowness parameter, we find a term previously overlooked. The inclusion of this term resolves a standing discrepancy between the multiple-time-scale approach to this problem, and an approach using a Fokker-Planck equation. We apply our solution to the dynamics of a ‘‘slow’’ system coupled to an ensemble of ‘‘fast’’ systems following chaotic trajectories.

In this Letter, we show that coherent structures are related to folds of horseshoes which are present in chaotic systems. We develop techniques that allow us to construct coherent structures by manipulating folds in three prototypical problems: a 1D chaotic map, a 2D chaotic map, and a chaotically advected fluid. The ability to construct such structures is of practical importance for the control of chaotic or turbulent extended systems such as fluids, plasmas, and coupled oscillator arrays.

We present a model for a Saffman-Taylor finger advancing into a viscoelastic medium, along with solutions for the dynamics of the top of the finger coupled to a ‘‘fractured zone.’’ The fractured zone is defined as a region of the medium which the finger can penetrate, and ahead of which stress build up, eventually leading to fracture of the medium. The model predicts a self-sustained oscillation in the tip velocity arising via a Hopf bifurcation.