We report on the observation of a discrete family of spatial dissipative solitons in a simple optical pattern forming system, which is based on a modified single-mirror feedback arrangement. After a pitchfork bifurcation the system possesses two (nearly) equivalent coexisting states of different polarizations. The spatial solitons correspond to excursions from one of the two states serving as a background state towards the other one. The members of the soliton family differ in the number of high-amplitude radial oscillations. The observations are in good agreement with numerical simulations and general expectations for dissipative solitons.

Dynamic cracks in rubber can spontaneously oscillate under certain biaxial strain conditions [R. D. Deegan et al., Phys. Rev. Lett. 88, 014304 (2002)]. We have found that this unusual phenomenon can be understood from the unique mechanical properties of rubber: hyperelasticity, viscoelasticity, and nonlocal elasticity. While all these are important, the decisive role of nonlocality needs to be particularly emphasized. Through numerical simulations with a lattice model, we have quantitatively reproduced the experimental results.

We measure the fundamental phase conjugation of a light field arising from enhanced backscattering in a multiple scattering medium. The measurements employ a two-window, time-resolved heterodyne method to suppress specularly reflected light and to determine the transverse Wigner function of the field, yielding joint amplitude and phase information. Using this method, a light field backscattered from an aqueous suspension of polystyrene spheres is found to reverse curvature relative to that of the incident field.

We propose a simple method for generation and detection of photons with nonzero angular momentum. The method utilizes high-quality factor ring resonators that transform a plane electromagnetic wave into a wave with nonzero angular momentum, and vice versa. We show that the method is especially promising for studying high-order Bessel beams, unreachable by other techniques.

We show the standard two-level continuous-time model of loss-modulated ${\mathrm{CO}}_2$ lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. Our results suggest that the two-parameter space of class $B$ laser models and that of a certain class of discrete mappings could be isomorphic.

We present the first study of the dynamic scaling or multiscaling of passive-scalar turbulence. For the Kraichnan version of passive-scalar turbulence we show analytically, in both Eulerian and quasi-Lagrangian frameworks, that simple dynamic scaling is obtained but with different dynamic exponents. By developing the multifractal model we show that dynamic multiscaling occurs in passive-scalar turbulence only if the advecting velocity field is itself multifractal. We substantiate our results by detailed numerical simulations in shell models of passive-scalar advection.

A bound state of temporal solitons in optical fibers is predicted numerically and demonstrated experimentally. It is appropriately described as a pair of bright solitons, bound together by a dark soliton. This structure exists only in dispersion-managed fiber and is different from bound solitons in fiber lasers.

A simple and transparent example of a nonautonomous flow system with a hyperbolic strange attractor is suggested. The system is constructed on the basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and the parameters controlling generation in both oscillators undergo a slow periodic counterphase variation in time. In terms of stroboscopic Poincaré sections, the respective 4D mapping has a hyperbolic strange attractor of the Smale-Williams type. Qualitative reasoning and quantitative data of numerical computations are presented and discussed, e.g., Lyapunov exponents and their parameter dependencies. A special test for hyperbolicity based on analysis of distributions of angles between stable and unstable subspaces of a chaotic trajectory is performed.

We theoretically demonstrate a mechanism for reduction of mode volume in high index contrast optical microcavities to below a cubic half wavelength. We show that by using dielectric discontinuities with subwavelength dimensions as a means of local field enhancement, the effective mode volume ($V_{\mathrm{eff}}$) becomes wavelength independent. Cavities with $V_{\mathrm{eff}}$ on the order of ${10}^{-2}(\lambda /2n{)}^{-3}$ can be achieved using such discontinuities, with a corresponding increase in the Purcell factor of nearly 2 orders of magnitude relative to previously demonstrated high index photonic crystal cavities.

We present a general method for the design of 2-dimensional nonlinear photonic quasicrystals that can be utilized for the simultaneous phase matching of arbitrary optical frequency-conversion processes. The proposed scheme—based on the generalized dual-grid method that is used for constructing tiling models of quasicrystals—gives complete design flexibility, removing any constraints imposed by previous approaches. As an example we demonstrate the design of a color fan—a nonlinear photonic quasicrystal whose input is a single wave at frequency $\omega$ and whose output consists of the second, third, and fourth harmonics of $\omega$, each in a different spatial direction.

We study the linear stability of planar shear banded flow with respect to perturbations with wave vector in the plane of the banding interface, within the nonlocal Johnson-Segalman model. We find that perturbations grow in time, over a range of wave vectors, rendering the interface linearly unstable. Results for the unstable eigenfunction are used to discuss the nature of the instability. We also comment on the stability of phase separated domains to shear flow in model $H$.

Analysis indicates that certain types of optically active media are capable of producing negative refraction and focusing of circularly polarized waves. It is established that a slab of such material acts just as Veselago’s hypothetical left-handed media lens, providing subwavelength resolution as Sir Pendry’s ideal lens, but for circularly polarized waves.

We report on the observation of coherence resonance for a semiconductor laser with short optical feedback close to Hopf bifurcations. Noise-induced self-pulsations are documented by distinct Lorentzian-like features in the power spectrum. The character of coherence is critically related to the type of the bifurcation. In the supercritical case, spectral width and height of the peak are monotonic functions of the noise level. In contrast, for the subcritical bifurcation, the width exhibits a minimum, translating into resonance behavior of the correlation time in the pulsation transients. A theoretical analysis based on the generic model of a self-sustained oscillator demonstrates that these observations are of general nature and are related to the fact that the damping depends qualitatively different on the noise intensity for the subcritical and supercritical case.

We study the influence of surface roughness on the adhesion between elastic solids. We present experimental data for the force necessary to pull off rubber balls from hard rough substrates. We show that the effective adhesion (or the pull-off force) can be calculated accurately from the surface roughness power spectra obtained from the measured surface height profile.

We study the stability of cylindrical Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields, and show that adding an azimuthal field profoundly alters the previous results for purely axial fields. For small magnetic Prandtl numbers Pm, the critical Reynolds number ${\mathrm{Re}}_c$ for the onset of the magnetorotational instability becomes independent of Pm, whereas for purely axial fields it scales as ${\mathrm{Pm}}^{-1}$. For typical liquid metals, ${\mathrm{Re}}_c$ is then reduced by several orders of magnitude, enough that this new design should succeed in realizing this instability in the laboratory.

Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of finite order. We establish on theoretical grounds a “transmutation pass rule” determining the conditions for this phenomenon to occur and numerically analyze it in the context of two-dimensional optical lattices. An analogous approach is applicable to the problems of Bose-Einstein condensates in periodic potentials.

We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general “charge rule” using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing on the case of Bessel lattices allows us to derive also an overall stability rule for the allowed vortex solitons.

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discover that the nonlocality of the nonlinear response can profoundly affect the soliton mobility, hence all the related phenomena. Such behavior manifests itself in significant reductions of the Peierls-Nabarro potential with an increase in the degree of nonlocality, a result that opens the rare possibility in nature of almost radiationless propagation of highly localized solitons across the lattice.

We study crack propagation in rubberlike materials and show that the nonuniform temperature distribution which occurs in the vicinity of the crack tip has a profound influence on the crack propagation, and may strongly enhance the crack propagation energy $G(v)$ for high crack velocities $v$. At very low crack-tip velocities, the heat produced at the crack tip can diffuse away, but already at moderate crack-tip velocities a very large temperature increase occurs close to the crack tip resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt and may result in unstable crack motion, e.g., stick-slip motion or catastrophic failure.

We consider the dynamics of small excitable systems, ubiquitous in physics, chemistry, and biology. Spontaneous excitation rates induced by system-size fluctuations exhibit sharp maxima at multiple, small system sizes at which also the system’s response to external perturbations is strongly enhanced. This novel effect is traced back to algebraic features of small integers and thus generic.