We report on the generation of pure rotational stimulated Raman scattering in a hydrogen gas hollow-core photonic crystal fiber. Using the special properties of this low-loss fiber, the normally dominant vibrational stimulated Raman scattering is suppressed, permitting pure conversion to the rotational Stokes frequency in a single-pass configuration pumped by a microchip laser. We report 92% quantum conversion efficiency (40 nJ pulses in 2.9 m fiber) and threshold energies (3 nJ in 35 m) more than $1\times {10}^6$ times lower than previously reported. The control of the output spectral components by varying only the pump polarization is also shown. The results point to a new generation of highly engineerable and compact laser sources.

Field spectra are analyzed to yield the time-resolved statistics of pulsed transmission through quasi-one-dimensional dielectric media with static disorder. The normalized intensity correlation function with displacement and polarization rotation for an incident pulse of linewidth $\sigma$ at delay time $t$ is a function only of the field correlation function, which is identical to that found for steady-state excitation, and of ${\kappa }_{\sigma }(t)$, the residual degree of intensity correlation at points at which the field correlation function vanishes. The dynamic probability distribution of normalized intensity depends only upon ${\kappa }_{\sigma }(t)$. Steady-state statistics are recovered in the limit $\sigma \to 0$, in which ${\kappa }_{\sigma =0}$ is the steady-state degree of correlation.

We present a scheme to extract the velocity of buoyant structures in turbulent thermal convection from simultaneous local velocity and temperature measurements. Applying this scheme to measurements taken at positions within the convection cell where the buoyant structures are dominated by plumes, we obtain the temperature dependence of the plume velocity and understand our results using the equations of motion. We further obtain the scaling behavior of the average local heat flux in the vertical direction at the cell center with the Rayleigh number and find that the scaling exponent is different from that measured for the Nusselt number. This difference leads to the conclusion that heat cannot be mainly transported through the central region of the convection cell.

The breakdown into turbulent spots is the least understood stage of the laminar-turbulent transition process. With cellular-automaton stochastic simulations and stability analysis, we show that the pattern of breakdown in boundary-layer flow bears a connection to laminar instability and may be reconstructed using macroscopic properties of the transition zone, such as persistence times and transitional intermittency. We propose experimental tests of our ideas.

Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.

The photoinduced isotropic state of liquid crystalline azobenzenes exhibits one of the strongest nonlinear optical refraction known for isotropic materials. The optical nonlinearity of these materials is large in a wide band of the visible spectrum and is accompanied with high, over $90\%$, transmission for red wavelengths.

Discrete solitons with two frequency components mutually locked by a quadratic nonlinearity have been observed for the first time. Optical experiments have been performed in arrays of coupled channel waveguides with tunable cascaded quadratic nonlinearity. The tunability was the prerequisite that soliton species with different topology could be identified in the same array. Moreover, soliton stability has been experimentally probed. Good agreement with theoretical predictions was found.

We consider a ring of identical or near-identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.

We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times. This allows us to explain in a simple way the mechanism behind the phenomenon of anticipating synchronization in excitable systems.

The size dependence of whispering gallery modes in dielectric resonators with hexagonal cross section has been observed within the visible spectral range for cavity diameters comparable to the light wavelength. As a model system single, tapered, high aspect ratio zinc oxide nanoneedles were analyzed. They enable systematic investigations as a function of the resonator diameter down to the nanometer regime. A simple plane wave interference model without free parameter describes the spectral positions and the linewidths of the modes in good agreement with the experiment.

We predict a new type of instability induced by shear flow in chemical systems. A homogeneous steady state solution of a reaction-diffusion system loses stability in a Poiseuille flow. The instability appears as the speed of the flow increases beyond a certain threshold. This results in a steady pattern moving with the average fluid velocity. The chemical reaction consists of two species (activator and inhibitor) moving with identical velocities. Contrary to Turing's instability, the pattern arises when the activator has a higher diffusivity than the inhibitor.

We propose a method of optical waveguiding, which relies on Bragg diffractions from a 1D grating that gives rise to waveguiding in the direction normal to the grating wave vector. The waveguide structure consists of a shallow 1D grating that has a bell- or trough-shaped amplitude in the confinement direction. Finally, we provide an experimental proof of the concept for this mechanism.

Air-cored, photonic band-gap crystal fibers exhibiting low nonlinearity and anomalous chromatic dispersion in spectral ranges inaccessible to conventional fibers can be used in the realization of all-fiber-format pulse compressors with unprecedented peak powers and wavelength diversity. Linear compression of inherently chirped and prestretched pulses by factors ranging from 20 to 80 around 1.0 and $1.5\mu \mathrm{m}$ have allowed generation of pulses as short as 163 fs. The results show that totally integrated femtosecond fiber laser sources can be realized throughout the visible and near-infrared and point to the possibility of megawatt peak and tens of watt average in-fiber power levels.

Self-sustained oscillators may turn non-self-oscillatory as a result of some kind of deterioration, which we call aging for simplicity. We discuss the effect of aging on the behavior of globally and diffusively coupled oscillators which are either all periodic or chaotic. It is shown that at a certain level of aging, macroscopic oscillation stops in a way which depends on the coupling strength. A universal scaling function to describe it is analytically derived and numerically verified.

Large-scale molecular dynamics (MD) simulations on two-phase immiscible flows show that, associated with the moving contact line, there is a very large $1/x$ partial-slip region where $x$ denotes the distance from the contact line. This power-law partial-slip region is verified in large-scale adaptive continuum calculations based on a local, continuum hydrodynamic formulation, which has proved successful in reproducing MD results at the nanoscale. Both MD simulations and numerical solutions of continuum equations indicate the existence of a universal slip profile in the Stokes-flow regime.

We report our investigation of Kerr nonlinear beam interactions in discrete systems. The influence of power and the relative phase between two Gaussian shaped beams was investigated in detail by performing numerical simulations of the discrete nonlinear Schrödinger equation and comparing the results with experiments done in AlGaAs waveguide arrays. Good agreement between theory and experiment was obtained.

We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media. We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, in addition to the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.

A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath. In the latter, dewetting case, a critical speed exists above which a three-phase contact line is no longer sustainable and the solid can no longer remain dry. Instead, a liquid film is being deposited on the solid. Demonstrating this transition from a dry to a wetted solid to be of hydrodynamic origin, we provide the first theoretical explanation of a classical prediction due to Derjaguin and Levi: instability occurs when the outer, static meniscus approaches the shape corresponding to a perfectly wetting fluid. Our analysis investigates the conditions under which the highly curved contact line region can be matched to the static profile far away from it.

Interference measurements of a polychromatic partially coherent light source verify the existence of a temporal correlation vortex. Topological dispersion is found to destabilize this singularity.

We isolate spatial shifts and Wigner delays for reflection at the same interface and demonstrate that they can carry different information. The spatial shifts associated with Wood anomalies on gratings can be either positive or negative, while the corresponding delays are both positive. In the standard case of total reflection at a glass-air interface, a differential two-photon absorption correlation technique allows us to measure for the first time a delay of up to 35 fs in agreement with the associated $10.5\mu \mathrm{m}$ spatial shift. The method also allows us to isolate giant Wigner delays. The existence of similar delays in different areas of physics is discussed.