Using a retarded-motion expansion to describe the polymer stress, we derive a low-dimensional model to understand the effects of polymer elasticity on the self-sustaining process that maintains the coherent wavy streamwise vortical structures underlying wall-bounded turbulence. Our analysis shows that at small Weissenberg numbers, Wi, elasticity enhances the coherent structures. At higher Wi, however, polymer stresses suppress the streamwise vortices (rolls) by calming down the instability of the streaks that regenerates the rolls. We show that this behavior can be attributed to the nonmonotonic dependence of the biaxial extensional viscosity on Wi, and identify it as the key rheological property controlling drag reduction.

We demonstrate that propagation direction and velocity of optical pulses can be controlled independently in the structures with multiscale modulation of the refractive index in transverse and longitudinal directions. We reveal that, in arrays of waveguides with phase-shifted Bragg gratings, the refraction angle does not depend on the speed of light, allowing for efficient spatial steering of slow light. In this system, both spatial diffraction and temporal dispersion can be designed independently, and we identify the possibility for self-collimation of slow light when spatial diffraction is suppressed for certain propagation directions. We also show that broadening of pulses in space and time can be eliminated in nonlinear media, supporting the formation of slow-light optical bullets that remain localized irrespective of propagation direction.

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green’s function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green’s function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green’s function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in “remote sensing without a source.”

We study the energy propagation in subwavelength waveguides and demonstrate that the mechanism of material gain, previously suggested for loss compensation, is also a powerful tool to manipulate dispersion and propagation characteristics of electromagnetic pulses at the nanoscale. We show theoretically that the group velocity in lossy nanowaveguides can be controlled from slow to superluminal values by the material gain and waveguide geometry and develop an analytical description of the relevant physics. We utilize the developed formalism to show that gain-assisted dispersion management can be used to control the transition between “photonic-funnel” and “photonic-compressor” regimes in tapered nanowaveguides. The phenomenon of strong modulation of group velocity in subwavelength structures can be realized in waveguides with different geometries and is present for both volume and surface modes.

Spatially extended chaotic systems with power-law decaying interactions are considered. Two coupled replicas of such systems synchronize to a common spatiotemporal chaotic state above a certain coupling strength. The synchronization transition is studied as a nonequilibrium phase transition and its critical properties are analyzed at varying the interaction range. The transition is found to be always continuous, while the critical indexes vary with continuity with the power-law exponent characterizing the interaction. Strong numerical evidences indicate that the transition belongs to the anomalous directed percolation family of universality classes found for Lévy-flight spreading of epidemic processes.

We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of classical fluctuations. We apply the method to the case where the incident wave experiences many small angle scattering events during propagation, but the total angle change remains small. In many aspects our results for this case are different from results previously known in the literature. The correlation function of the wave intensity at two points separated by a distance $r$, has a long-range character. It decays as a power of $r$ and changes sign. We also consider sensitivities of the speckles to changes of external parameters, such as the wave frequency and the incidence angle.

We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond random matrix theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on a generalization of Berry’s random wave model, combined with a consistent semiclassical representation of spatial two-point correlations. We derive closed expressions for arbitrary wave-function averages in terms of universal coefficients and sums over classical paths, which contain, besides the supersymmetry results, novel oscillatory contributions. Their physical relevance is demonstrated in the context of Coulomb blockade physics.

We observed self-formations of multiple lasing channels and two-dimensional lasing patterns consisting of composite local modes having different lasing frequencies in a laser-diode-pumped wide-aperture thin-slice solid-state laser with imperfect reflective end surfaces. Global patterns resembling higher-order Hermite-Gaussian modes or possessing $N$-fold rotational symmetries were experimentally shown to appear due to the standard polished surface roughness of closely spaced reflective ends and nonlinear modal interactions.

All-optical noninvasive control of a multisection semiconductor laser by means of time-delayed feedback from an external Fabry-Perot cavity is realized experimentally. A theoretical analysis, in both a generic model as well as a device-specific simulation, points out the role of the optical phase. Using phase-dependent feedback we demonstrate stabilization of the continuous-wave laser output and noninvasive suppression of intensity pulsations.

We investigate how a droplet of a complex liquid is modified by its internal nanoscale structure. As the liquid passes from an isotropic disordered state to an anisotropic layered morphology, the droplet shape switches from a smooth spherical cap to a terraced hyperbolic profile, which can be modeled as a stack of thin concentric circular disks with a repulsion between adjacent disk edges. Our ability to resolve the detailed shape of these defect-free droplets offers a unique opportunity to explore the underlying physics.

An approach based on a lattice version of the Boltzmann kinetic equation for describing multiphase flows in nano- and microcorrugated devices is proposed. We specialize it to describe the wetting-dewetting transition of fluids in the presence of nanoscopic grooves etched on the boundaries. This approach permits us to retain the essential supramolecular details of fluid-solid interactions without surrendering—actually boosting—the computational efficiency of continuum methods. The method is used to analyze the importance of conspiring effects between hydrophobicity and roughness on the global mass flow rate of the microchannel. In particular we show that smart surfaces can be tailored to yield very different mass throughput by changing the bulk pressure. The mesoscopic method is also validated quantitatively against the molecular dynamics results of [Cottin-Bizonne et al., Nat. Mater. 2, 237 (2003)].

Pinning and depinning of driven drops on heterogeneous substrates is studied as a function of the driving and heterogeneity amplitude. Two types of heterogeneity are considered: a “hydrophobic” defect that blocks the drop in front and a “hydrophilic” one that holds it at the back. Two different types of depinning leading to sliding motion are identified, and the resulting stick-slip motion is studied numerically.

We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrates that quantum-classical correspondence at the microscopic level does not require coupling to a large number of external degrees of freedom.

We show that the inclusion of nonlocality in the constitutive relations in photonic structures has important repercussions in their eigenmode configuration and distribution. In the case of optical activity, the primary manifestation of nonlocality, these features are traced to a photospin-orbit interaction analogous to the electron spin-orbit interaction in asymmetric semiconducting compounds; its impact can be assimilated to that of a magnetic field whose magnitude and direction follow that of the photon quasimomentum, with implications in photospin transport and photospintronics.

The nonlinear Schrödinger equation $i{\partial }_{z}A(z,x,t)+{\nabla }_{x,t}^{2}A+[1+m(\kappa x)]|A{|}^{2}A=0$ models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate $x$, and also the evolution of 2D Bose-Einstein condensates in which the scattering length varies in one dimension. Stability of bound states depends on the value of $\kappa =\mathrm{\text{beamwidth}}/\mathrm{\text{lattice period}}$. Wide ($\kappa \gg 1$) and $\kappa =O(1)$ bound states centered at a maximum of $m(x)$ are unstable, as they violate the slope condition. Bound states centered at a minimum of $m(x)$ violate the spectral condition, resulting in a drift instability. Thus, a nonlinear lattice can only stabilize narrow bound states centered at a maximum of $m(x)$. Even in that case, the stability region is so small that these bound states are “mathematically stable” but “physically unstable.”

A generalized scheme for phase-conjugate resonant $2n$-wave mixing, which has a high efficiency and is easy for phase matching, is proposed. As a new type of coherent laser spectroscopy this approach can be employed for studying highly excited atomic states or states with a high angular momentum. To demonstrate its feasibility we have studied the doubly excited autoionizing Rydberg states of Ba by phase-conjugate six-wave mixing, and have furthermore achieved eight-wave mixing in Na. This method may find wide application in related areas such as coherent transient spectroscopy, Autler-Townes spectroscopy and electromagnetically induced transparency. In particular, it may provide new insights into the nature of highly excited states.

Fermi acceleration in a Fermi-Ulam model, consisting of an ensemble of particles bouncing between two, infinitely heavy, stochastically oscillating hard walls, is investigated. It is shown that the widely used approximation, neglecting the displacement of the walls (static wall approximation), leads to a systematic underestimation of particle acceleration. An improved approximative map is introduced, which takes into account the effect of the wall displacement, and in addition allows the analytical estimation of the long term behavior of the particle mean velocity as well as the corresponding probability distribution, in complete agreement with the numerical results of the exact dynamics. This effect accounting for the increased particle acceleration—Fermi hyperacceleration—is also present in higher-dimensional systems, such as the driven Lorentz gas.

We study experimentally the interactions between normal solitons and tilted beams in glass waveguide arrays. We find that as a tilted beam, traversing away from a normally propagating soliton, coincides with the self-defocusing regime of the array, it can be refocused and routed back into any of the intermediate sites due to the interaction, as a function of the initial phase difference. Numerically, distinct parameter regimes exhibiting this behavior of the interaction are identified.

We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity. These findings show that intrinsic diversity might have a constructive role and suggest that natural systems might profit from their diversity in order to optimize the response to an external stimulus.

Periodic heterogeneity is introduced in experiments with thin solution layers where downward propagating planar autocatalytic fronts are hydrodynamically unstable and cellular patterns develop. The evolution of fingers is greatly affected by the spatial heterogeneity when the wave number associated with it falls in the vicinity of the most unstable mode of the reference system with uniform thickness. The imposed heterogeneity will drive the instability by amplifying the modes with the matching wave numbers as indicated by the experimentally constructed dispersion curves.