We have calculated and measured the properties of X-band microwaves propagating in a 2D array of low-loss high-dielectric-constant cylinders. Transmission bands and photonic band gaps are conclusively identified in excellent agreement with the theoretical predictions. Detailed data on the properties of isolated defect states are also presented. We conclude that studies of this model scattering system allow the quantitative evaluation and testing of ideas regarding wave propagation and localization in strongly scattering media.

Stimulated backscattered harmonic radiation generated by the interaction of an intense pump-laser field with an electron beam or plasma is analyzed using a fully nonlinear, relativistic, fluid theory valid to all orders in the pump-laser amplitude. The backscattered radiation occurs at odd harmonics of the Doppler-shifted incident laser frequency. The growth rates, saturation levels (efficiencies), and thermal limitations are calculated for the backscattered harmonic radiation. This mechanism may provide a practical method for producing coherent radiation in the XUV regime.

We have obtained high-resolution spectra of hyperfine transitions in an excited state ${(}^1$${\mathit{D}}_2$) of ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_3$ using a novel four-wave-mixing technique. Subkilohertz resolution is obtained. The hyperfine transition line shapes are determined unambiguously, revealing an interesting effect of mutual-flip interaction between the Im=±1/2> hyperfine states of the Pr ions and the host nuclear spins. The necessary conditions for obtaining laser-jitter-independent resolution in inhomogeneously broadened samples are discussed.

We present a Lagrangian calculation of the area of isothermal (or isoconcentration) surfaces in a medium of fluid turbulence. We argue that such surfaces appear fractal above some inner scale which depends on the Reynolds number. The fractal dimension is estimated theoretically. The theory is compared to experiments in which a dye is used as a passive scalar in various turbulent flows. We find excellent agreement in many details.

We have measured gain profiles by light-beating techniques for an argon-ion laser operated above threshold. The observed behavior is interpreted by developing a theory which incorporates four-wave mixing of signal and image frequencies. The gain shows the typical characteristics of a second-order phase transition. We also discuss the implications for fundamental laser noise, and predict strong correlations between the noise contributions from either side of the laser frequency.

Modulation of the beam current has been observed during ion-focused-regime (IFR) transport of a high-power relativistic electron beam propagating through a low-density background plasma. In this experiment, a 1.7-MeV, 1-kA, rise-time-sharpened electron beam is transported in a KrF-excimer-laser–produced IFR channel in trimethylamine gas. The IFR channel is immersed in a low-density plasma-filled transport tube. We present experimental measurements and computer simulations demonstrating modulation of this high-current relativistic electron beam near the low-density background plasma frequency.

Molecular-dynamics simulations of noncohesive granular assemblies under shear are described. At low shear rate γ̇, the assembly is unstable to uniform motion and exhibits stick-slip dynamics involving periodic dilatancy transitions and gravitational compactification. Steady-state motion occurs at larger γ̇ where 6–12 layers of grains flow over a compact, static assembly. A phase boundary, characterized by a discontinuity in γ̇ and an enhanced normal stress, separates the static and flowing regions. In the steady-state regime, dilatancy leads to a shear stress that is independent of γ̇.

${\mathrm{C}}_{60}$Buckminsterfullerene exhibits a large ultrafast third-order nonlinear optical response. Degenerate four-wave-mixing measurements in ${\mathrm{C}}_{60}$-benzene solutions were performed using 50-psec pulses at 1.064 μm. The magnitude of the nonlinear susceptibility per ${\mathrm{C}}_{60}$ molecule is ‖γ‖=1.5×${10}^{\mathrm{-}42}$ ${\mathrm{m}}^5$ ${\mathrm{V}}^{\mathrm{-}2}$ and of the same size as that observed in polydiacetylene. In contrast to conjugated polymers, however, a dominant positive real part of the nonlinearity is found, 3 times larger than the imaginary component. The nonlinear response can be described within the model of a free electron in a spherical box, confirming the complete delocalization of electrons on the ${\mathrm{C}}_{60}$ molecule.

We address the problem of identifying the dynamical variables representing the phase of a quantum field by analyzing what is measured in two simple homodyne experiments. This leads us to identify operators C${\mathrm{^}}_{\mathit{M}}$,S${\mathrm{^}}_{\mathit{M}}$ corresponding to the measured cosine and sine of the phase difference. The predictions of the theory are tested in an experiment in which the input fields are derived from a highly stable He:Ne laser. Photon-counting measurements extending from mean photon numbers 30 down to ${10}^{\mathrm{-}2}$ show good agreement between theory and experiment. The implications for identifying the ‘‘correct’’ phase operator are briefly discussed.

The evolution of fluid interfaces in parallel flow in Hele-Shaw cells is studied theoretically and experimentally in the limit of large capillary number. It is shown that such interfaces support wave motion, the amplitude of which for long waves is governed by a set of Korteweg–de Vries and Airy equations. Experiments conducted in a long Hele-Shaw cell validate the theory in the symmetric case.

The phase dynamics of wavy vortex flow is studied by applying a forced modulation to the upper boundary of a large-aspect-ratio concentric cylinders system. The experimental results are consistent with a model based on coupled phase equations. We find that the perturbations propagate as traveling waves parallel with the axis of the system when there is a strong coupling between the axial and azimuthal phase variables, and diffusively for weak coupling. The propagating wave speed is measured for a range of Reynolds numbers.

I demonstrate a very large degree of quenching of spontaneous emission noise in different laser systems that work on mechanisms other than the population inversion between the bare states of the atom. Such laser systems have much narrower linewidths. I give explicit results for phase diffusion for four different model systems.

Cavitation in a liquid seeded with bubbles is used as a new visualization technique to single out the regions of very low pressure of a fully developed turbulent flow. By this means, the sudden appearance of high vorticity filaments is observed. These structures are very thin and short lived and display a high degree of temporal as well as spatial intermittency. They contribute to the flow organization: In particular their disintegration corresponds to the formation of large eddies.

The first experimental demonstration of a harmonic free-electron-laser amplifier utilizing a periodic position instability is described for a planar wiggler configuration. The interaction occurs at the even harmonics of the fundamental. A maximum gain of 7 dB was observed over a frequency band ranging from 14 to 15 GHz. The experimental results are compared with predictions from the three-dimensional simulation code wigglin with excellent agreement. Improvements due to a tapered wiggler for this interaction are discussed.

Current continuum models based on the theory of plasticity have failed to describe the observed gravitational flow patterns of granular particles in a confined geometry. We propose a random-walk model that correctly predicts the shape of the free surface of the granular media and the solid stream lines with and without obstacles. We present simulation results that qualitatively exhibit many of the unique features of granular flows. The simulation results are also compared with experimental data.

The coupling between different oscillation branches of a waveguide-mode free-electron laser has been studied. It is observed that the wave form of the upper branch of a waveguide-mode free-electron laser is modulated at the rate of the period of the mode-locked oscillation of the lower branch for a wide range of experiment parameters. This phenomenon is explained as the temporally periodic modulation of the gain of the upper-branch oscillation by the electromagnetic radiation of the lower-branch oscillation through the periodic bunching of the electron beam.

It is shown that the frequency-temperature spectrum recently observed by Wu et al. in developed convective turbulence, ${\mathit{F}}_{\mathit{T}\mathit{T}}$(ω)∝${\mathrm{\omega }}^{\mathrm{-}1.4}$, follows from the condition that the entropy flux in $ k — space is constant, just as the Kolmogorov-Obukhov spectrum of barotropic turbulence, ${\mathit{F}}_{\mathit{V}\mathit{V}}$(k)≃(ɛ/ρ${)}^{2/3}$${\mathit{k}}^{\mathrm{-}11/3}$, follows from the condition kinetic-energy flux ɛ(k)=ɛ. On the contrary, for convective turbulence ɛ(k) changes as ${\mathit{k}}^{\mathrm{-}4/5}$ because of conversion of kinetic energy into a potential energy, which leads to a stronger k dependence of the double velocity moment [${\mathit{F}}_{\mathit{V}\mathit{V}}$(k)∝${\mathit{k}}^{\mathrm{-}21/5}$] than that for barotropic turbulence.

We present experiments and computer simulations of slow drainage in a two-dimensional porous medium. The effect of gravity is systematically varied by tilting the system from the horizontal position. The width σ of the front between the fluids is found to scale with the dimensionless Bond number Bo (ratio between gravitational and capillary forces) as σ∼${\mathrm{Bo}}^{\mathrm{-}0.57}$, as predicted by theory. The external perimeter of the invaded structure is shown to be fractal with the fractal dimension ${\mathit{D}}_{\mathit{e}}$≃1.34 for length scales smaller than the front width.

Magnetically confined columns of electrons are excellent experimental realizations of extended two-dimensional vortices in an inviscid fluid. Here, we consider two nearly identical vortices orbiting around one another inside a cylindrical wall. The vortices merge symmetrically, in a time which varies from less than 1 to about ${10}^4$ orbit periods as the vortex separation is increased by 30%. We have obtained images of the vorticity distribution during this merger process, and observe filamentary tails and mixing. These experimental results are consistent with analytic models and numerical simulations.

The inverse scattering transform for the periodic Korteweg–de Vries equation is used to analyze surface-wave data obtained in the Adriatic Sea and a robust solition spectrum is found. While the solitons are not observable in the data due to the presence of energetic radiation modes, a new nonlinear filtering technique renders the solitons visible. Numerical simulations support the existence of solitons in the measurements and suggest that, as a wave train propagates into shallow water, the solitons grow at the expense of the radiation.