We present results for the operation of a three-level solid-state laser both with normal and with completely suppressed spontaneous emission between the lasing levels. The output power difference in these two cases drops as the pump rate is increased above threshold and is not greatly different at higher powers. The threshold pump power, although typically reduced by an order of magnitude, is not zero and our results thus throw further light on the concept of “thresholdless” lasing. The theory is also applicable to light-emitting diodes and amplifiers which function on the same principles as a laser.

We propose systems with structures defined by self-assembled triply periodic minimal surfaces (STPMS) as candidates for photonic band gap materials. To support our proposal we have calculated the photonic bands for different STPMS and we have found that, at least, the double diamond and gyroid structures present full photonic band gaps. Given the great variety of systems which crystallize in these structures, the diversity of possible materials that form them, and the range of lattice constants they present, the construction of photonic band gap materials with gaps in the visible range may be presently within reach.

We propose an alternative formulation of structure functions for the velocity field in fully developed turbulence. Instead of averaging moments of the velocity differences as a function of the distance, we suggest to average moments of the distances as a function of the velocity difference. This is like an “inverted” structure function, with a different statistics. On the basis of shell model calculations we obtain a new multiscaling spectrum.

Experimental investigation of the wake of a sphere is reported, namely, the change from steady to periodic flow in the Reynolds number range [100, 360]. First, visualizations have been carried out in a water channel to make precise the geometry of downstream bubble and shedding vortices behind the sphere. Thereafter, measurements have been performed in a wind tunnel and results have been compared successfully to the predictions of the Landau model.

The family of solenoidal solutions of the Navier-Stokes equation, satisfying the dynamic boundary conditions typical for flows above the Ekman layer, is discussed. Three velocity components of this helical flow which we call the spin flow are expressed in terms of a single stream function governed by the 2D vorticity equation. The inverse energy cascade found in spin flows has a different power exponent from the case of 2D turbulence.

We have studied experimentally the formation and evolution of sand ripples under water shear flow in a narrow annular channel. The amplitude of the sediment ripples vanishes at a critical value of the shear rate. Near this onset, a band of Fourier modes can be described by exponential growth functions. The growth rates vary linearly with the shear rate. On longer times the sand ripples display complex dynamics.

The quantum resonances of classically chaotic $n$-disk geometries were studied experimentally utilizing thin 2D microwave geometries. The experiments yield the frequencies and widths of low-lying resonances, which are compared with semiclassical calculations. The long time or small energy behavior of the wave-vector autocorrelation gives information about the quantum decay rate, which is in good agreement with that obtained from classical scattering theory. The intermediate energy behavior shows nonuniversal oscillations determined by periodic orbits.

Tunneling from a chaotic potential well is explained in terms of a set of complex periodic orbits which contain information about the real dynamics inside the well, as well as the complex dynamics under the confining barrier. These orbits are associated with trajectories which are homoclinic to a real trajectory emerging from the optimal tunneling path. The theory is verified by considering a model double-well problem.

Experiments on a slowly sheared 2D granular material show a continuous transition as the packing fraction $\gamma$ passes through ${\gamma }_c\simeq 0.776$. The mean stress, $\overline{\sigma }$, plays the role of an order parameter. As $\gamma \to {\gamma }_c$ from above, (1) the compressibility becomes large, (2) a slowing down of the mean velocity occurs, (3) the force distributions change, and (4) the network of stress chains changes from intermittent long radial chains near ${\gamma }_c$ to a tangled dense network for larger $\gamma$.

We formulate an extension of the lattice Boltzmann equation to irregular lattices. It is demonstrated that the recovery of isothermal Navier-Stokes equations is possible by a construction of the local equilibrium subject to an extended list of moment constraints which take into account the lattice geometry. A particular version of the local equilibrium is discussed in some detail.

We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to correlate the variations of the friction factor for different porosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to nonlinear behavior which is typical of experiments. We find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system.

We used interferometry to measure the electric-field-induced (i.e., “electrostrictive”) increase of the density of sulfur hexafluoride near its critical point. The results at the temperatures $T_c+5\mathrm{}\mathrm{mK}$, $T_c+10\mathrm{}\mathrm{mK}$, and $T_c+30\mathrm{}\mathrm{mK}$, with $T_c=319\mathrm{}\mathrm{K}$, agree with a calculation based on the Clausius-Mossotti relation and the restricted cubic model equation of state. These measurements were performed in microgravity so that the electrostrictive density changes ( $\le 3.5\%$ in this work) would not be complicated by stratification of the fluid's density induced by the Earth's gravity.

We address scaling in inhomogeneous and anisotropic turbulent flows by decomposing structure functions into their irreducible representation of the SO(3) symmetry group which are designated by $j,m$ indices. Employing simulations of channel flows with ${\mathrm{Re}}_{\lambda }\approx 70$ we demonstrate that different components characterized by different $j$ display different scaling exponents, but for a given $j$ these remain the same at different distances from the wall. The $j=0\mathrm{}$ exponent agrees extremely well with high Re measurements of the scaling exponents, demonstrating the vitality of the SO(3) decomposition.

We present a study of intermittency in a turbulent channel flow. Scaling exponents of longitudinal streamwise structure functions, ${\zeta }_p/{\zeta }_3$, are used as quantitative indicators of intermittency. We find that near the center of the channel the values of ${\zeta }_p/{\zeta }_3$ up to $p=7\mathrm{}$ are consistent with the assumption of homogeneous and isotropic turbulence. Moving towards the boundaries, we observe a growth of intermittency which appears to be related to an intensified presence of ordered vortical structures. We argue that the clear transition in the nature of intermittency appearing in the region close to the wall is related to a new length scale which becomes the relevant one for scaling in high shear flows.

Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations.

The transverse spatial coherence of an optical beam alters as the light traverses a dense, multiple-scattering, random dielectric medium. Results of measurements show the predicted initial increase of the decoherence (or decorrelation) rate with spatial separation, followed by saturation at large separation. This behavior can be modeled by using a Boltzmann-like transport equation for the Wigner function of the wave field, whereas the standard model for decoherence (developed for quantum wave fields), which is based on the Fokker-Planck phase-space diffusion equation, contains no saturation and fails at all separations to describe the observed behavior.

A novel class of optical materials, microcavities doped with nanostructured fractal aggregates, was studied. Fractal aggregate optical excitations may be concentrated in regions smaller than the diffraction limit of conventional optics, resulting in large local fields. Seeding the aggregates into microcavities further increases the local fields because of light trapping by microcavity resonance modes. These microcomposites possess unique optical properties, including very large probabilities of radiative processes. In our experiments, lasing at extremely low pump intensities, below 1 mW, and strongly enhanced Raman scattering was observed in fractal-microcavity-dye composites.

We report stochastic polarization switching in vertical-cavity semiconductor lasers, with residence times that vary by 8 orders of magnitude for a single such laser by changing its switch current with a hot-spot technique. In spite of the potentially complicated polarization dynamics of these lasers, the experimental results agree with Kramers hopping in a 1D double-well potential initiated by quantum fluctuations. We confirm the validity of this surprisingly simple theoretical model by independent measurements of the potential barrier between the wells and the spontaneous emission noise strength.

Clustering of granular gases is caused by the dissipation occurring in particle collisions. We use the generalized dimension, a measure for the inhomogeneity of a spatial distribution of particles to characterize the structural evolution. Furthermore, we quantify the typical length scale of the clusters obtained by 3D simulations using the index of dispersion, a measure for the deviation of the particle density from a Poissonian. We then derive an expression for the expected length scales of cluster formation from a stability analysis in the hydrodynamical approximation. We find a good agreement between our theoretical prediction and numerical experiments.

We investigate the coupled lateral-normal response to a lateral external drive in a nanoscale molecular system confined between two atomically smooth solid surfaces. We discuss the effects of shear induced dilatancy, which results from the coupling, on the energy dissipation, and therefore on the frictional properties. It is demonstrated that measurements of response in the normal direction provide additional information on the mechanisms of friction and that manipulating the dilatancy opens new possibilities to control the motion in the lateral direction. The dilatancy leads to a novel memory effect which is amenable to experimental verification.