We study the discrete nonlinear Schrödinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective nonrigid pendulum Hamiltonian. The different regimes include the complete reflection and refocusing of the initial wave, solitonic structures, and a superfluid state. In the superfluid regime, which occurs above a critical value of nonlinearity, a plane wave travels coherently through the randomly distributed defects. This superfluidity criterion for the DNLS is analogous to (yet very different from) the Landau superfluidity criteria in translationally invariant systems. Experimental implications for the physics of Bose-Einstein condensate gases trapped in optical potentials and of arrays of optical fibers are discussed.

Single clusters in a vibro-fluidized granular gas in $N$ connected compartments become unstable at strong shaking. They are experimentally shown to collapse very abruptly. The observed cluster lifetime (as a function of the driving intensity) is analytically calculated within a flux model, making use of the self-similarity of the process. After collapse, the cluster diffuses out into the uniform distribution in a self-similar way, with an anomalous diffusion exponent $1/3$.

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.

Pinch-off and scaling during drop formation are studied using high-accuracy computation and ultrafast, high-resolution imaging. The interface of a water drop (viscosity $\mu \approx 1\mathrm{cP}$) is shown to overturn prior to breakup for the first time in experiments, well before the dynamics transitions from the potential flow (PF) to the inertial-viscous (IV) regime. A drop of $83\%$ glycerol-water solution $\left(\mu \approx 85\mathrm{cP}\right)$ is shown to exhibit a transition from the PF to the IV regime both computationally and experimentally. The computed value of the minimum neck radius in the latter case follows Eggers’s universal solution until it becomes unstable.

We report on an experimental study of supercontinuum generation in photonic crystal fibers with low-intensity femtosecond pulses, which provides evidence for a novel spectral broadening mechanism. The observed results agree with our theoretical calculations carried out without making the slowly varying envelope approximation. Peculiarities of the measured spectra and their theoretical explanation demonstrate that the reason for the white-light generation in photonic crystal fibers is fission of higher-order solitons into redshifted fundamental solitons and blueshifted nonsolitonic radiation.

We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplicity, extremely fast calculation, robustness, and invariance with respect to nonlinear monotonous transformations.

We demonstrate the influence of vectorial coupling on the synchronization behavior of complex systems. We study two semiconductor lasers subject to delayed optical feedback which are unidirectionally coherently coupled via their optical fields. Our experimental and numerical results demonstrate a characteristic synchronization scenario in dependence on the relative feedback phase leading cyclically from chaos synchronization to almost uncorrelated states, and back to chaos synchronization. Finally, we reveal the influence of the feedback phase on the dynamics of the solitary delay system.

We report spots of excited molecules of 33 nm width created with focused light of $\lambda =760\mathrm{}\mathrm{nm}$ wavelength and conventional optics along the optic axis. This is accomplished by exciting the molecules with a femtosecond pulse and subsequent depletion of their excited state with red-shifted, picosecond-pulsed, counterpropagating, coherent light fields. The $\lambda /23\mathrm{}$ ratio constitutes what is to our knowledge the sharpest spatial definition attained with freely propagating electromagnetic radiation. The sub-diffraction spots enable for the first time far-field fluorescence microscopy with resolution at the tens of nanometer scale, as demonstrated in images of membranes of bacillus megaterium.

Evaporating drops provide a means of organizing particles suspended within them. Here, the manner in which surfactants alter these patterns is studied as a function of the surface state of an insoluble monolayer at the drop interface. The surface state is visualized throughout the drop evolution using fluorescence microscopy. A regime of surfactant coverage is identified that creates conditions that enhance the Marangoni-Bénard instability. This result was not anticipated in prior studies, in which surfactants are predicted to prevent this instability. These data demonstrate that, by tuning the liquid-gas boundary condition, the patterns formed from an evaporating drop can be controlled.

A novel class of nonlinear optical processes is described in which radiation at the nth harmonic is generated through the use of a $(2n+1)$-order nonlinearity. Utilizing an odd-order nonlinearity, this process allows for the generation and amplification of both odd- and even-order harmonics in isotropic materials. Additionally, this process can always be phase matched in normal-dispersion materials without the use of birefringence. Experimental results are presented in which conical third-harmonic emission is generated from a sapphire sample.

We study an analog of the classical Arnol’d diffusion in a quantum system of two coupled nonlinear oscillators one of which is governed by an external periodic force with two frequencies. In a classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance and leads to an increase of the total energy of the system. We show that quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol’d diffusion. This specific diffusion represents a new type of quantum dynamics and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.

The degree of interfacial structuring of $n$-hexadecane and octamethylcyclotetrasiloxane (OMCTS) was measured within a nanometer boundary regime to silicon surfaces. Boundary-layer effects on lubricating sliding (in terms of a thermodynamic stress activation parameter) and the layer thickness were determined by scanning force microscopy. A $2.0\pm 0.3\mathrm{nm}$ thick, entropically cooled layer was found for $n$-hexadecane. Measurements on spherically shaped OMCTS molecules exhibited only an interfacial “monolayer,” and identified the molecular shape of $n$-hexadecane responsible for augmented interfacial structuring. Interfacial liquid structuring was found to reduce friction.

A simple theoretical analysis and direct numerical simulations on ${512}^3$ grid points suggest that the velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow at high Reynolds number is given by a simple form that is an anisotropic function of the wave vector. The tensor is determined by the rate of the strain tensor of the mean flow, the rate of energy dissipation per unit mass, the wave vector, and two nondimensional constants.

Results of extensive and accurate numerical studies on heat transfer in a system of particles with unequal masses, interacting through hard-point potentials with two types of symmetry, are reported. The particles are confined in a one-dimensional box with fixed ends coupled to heat reservoirs at different temperatures. The study aims to throw light upon recent controversial results on thermal conductivity in one-dimensional systems. When the particles interact through elastic hard-point collisions (a standard asymmetric case), the system is shown to have always infinite (anomalous) thermal conductivity as follows from the Prosen-Campbell theorem.

The output of a dynamical system in a regime of homoclinic chaos transforms from a continuous train of irregularly spaced spikes to clusters of regularly spaced spikes with quiescent periods in between (bursting), provided a low frequency portion of the output is fed back. We provide experimental evidence of such an autonomous bursting by a ${\mathrm{CO}}_2$ laser with feedback. The phenomena here presented are extremely robust against noise and display qualitative analogies with bursting phenomena in neurons.

The correlations between waves transmitted through random media are analyzed by use of a random-matrix approach and numerical simulations of rough waveguides. Although the intensity and conductance fluctuations are practically independent of the sample length, the correlations present a strong dependence on the length of the disordered region. In waveguide geometries the long-range correlations $C^{\left(2\right)}$ and $C^{\left(3\right)}$, usually associated to intensity and conductance fluctuations, respectively, become negative as the length of the system decreases. Our results provide a new interpretation of recent optical experiments on disordered slab geometries.

We show that by strongly modifying the dispersion properties of a four-level system, nonexisting wave mixing channels can be opened and significantly enhanced. Specifically, we show that coherent optical four-wave mixing with a pump wave mediated by electromagnetically induced transparency (thereby propagating with an extremely slow group velocity) will lead to many orders of magnitude enhancement in the amplitude of the generated wave. Contrary to common belief, a large transparency window, which causes a large propagation velocity, actually diminishes efficient mixing wave production.

We observed for the first time a strong angle-independent modification of spontaneous emission spectra from laser dyes in photonic crystals, made of inverse opals in titania. Comparison with spectra from such crystals with much smaller lattice spacing, for which emission is in the long wavelength limit, reveals inhibition of emission up to a factor $\sim 5$ over a large bandwidth of $13\%$ of the first order Bragg resonance frequency. The center frequency and bandwidth of the inhibition agree with calculated total density of states, while the measured inhibition of vacuum fluctuations is much larger. Because of the specific location of the dye molecules, we likely probe the strongly modulated local photonic density of states.

We report on the theoretical derivation and experimental observation of spatiotemporal modulation instability (MI) of a coherent light beam in noninstantaneous nonlinear media. We obtain analytically the MI growth rate as a function of the spatial and temporal frequencies of the perturbation and the material response time. In the experiment, we observe that the varying speed of the MI patterns increases with the decreased material response time. We also observe that increasing the material response time can arrest the MI, agreeing with our theoretical derivation.

We report the first direct observation of Brillouin-like propagation modes in a dissipative periodic optical lattice. This has been done by observing a resonant behavior of the spatial diffusion coefficient in the direction corresponding to the propagation mode with the phase velocity of the moving intensity modulation used to excite these propagation modes. Furthermore, we show theoretically that the amplitude of the Brillouin mode is a nonmonotonic function of the strength of the noise corresponding to the optical pumping, and discuss this behavior in terms of nonconventional stochastic resonance.