We study the propagation of polarized light in turbid media as a random walk of vector photons. Both propagation and polarization directions of light are found to isotropize, following a power law of the number of scattering events. The characteristic length scale governing light isotropization and linear depolarization, the isotropization length $l_p$, is derived using the exact Mie scattering for spherical particles. A simple relation $l_p/l_t\simeq 2.8-2.5g$ is obtained for Rayleigh-Gans scatterers where $l_t$ is the transport mean free path and $g$ is the mean cosine of scattering angles.

It has been suggested that the equilibrium-range properties of high-Reynolds number turbulence are more readily observed in spectral space, using $E(k)$ or $T(k)$, than in real space, using second- or third-order structure functions. For example, the $-5/3$ law is usually easier to see in experimental data than the equivalent $2/3$ law. We argue that this is not an implicit feature of a real-space description of turbulence. Rather, it is because the second-order structure function mixes small and large-scale information. To remedy this problem we adopt a real-space function, the signature function, which plays the role of an energy density, somewhat analogous to $E(k)$. In this Letter we determine the form of the signature function in a variety of turbulent flows. We find that dissipation-range phenomena, such as the so-called bottleneck effect, are evident in the signature function, while absent in the structure function.

The state of polarization of an optical field provides detailed information concerning both the radiation emission processes and the intricate interaction between light and matter. We report here a novel approach for characterizing the polarization properties of electromagnetic fields for which the electric field vector at a point may fluctuate in three dimensions. Using probes which couple all three components of the field, we were able to extract the polarized and unpolarized components of such fields. Our results constitute the proof of concept for what could be called three-dimensional optical polarimetry.

Direct simulations of large populations of confined hydrodynamically interacting swimming particles at low Reynolds number are performed. Hydrodynamic coupling between the swimmers leads to large-scale coherent vortex motions in the flow and regimes of anomalous diffusion that are consistent with experimental observations. At low concentrations, swimmers propelled from behind (like spermatazoa) strongly migrate toward solid surfaces in agreement with simple theoretical considerations; at higher concentrations this localization is disrupted by the large-scale coherent motions.

The single-mode Richtmyer-Meshkov hydrodynamic instability at light/heavy ($\mathrm{\text{air}}/\mathrm{S}{\mathrm{F}}_6$ and $\mathrm{\text{air}}/\mathrm{C}{\mathrm{O}}_2$), close density ($\mathrm{\text{air}}/{\mathrm{N}}_2$), and heavy/light (air/He) interfaces has been experimentally studied for a low incident shock wave Mach number. Two identical 2D half sinusoidal initial perturbations, with a relatively high initial amplitude, were considered in order to rapidly reach the nonlinear regime and check the reduction of the initial growth rate compared to that predicted by the small-amplitude theory. The growth rate measurements for the $\mathrm{\text{air}}/\mathrm{S}{\mathrm{F}}_6$ and $\mathrm{\text{air}}/\mathrm{C}{\mathrm{O}}_2$ cases are in excellent agreement with the nonlinear model of Sadot et al. coupled with a reduction factor suggested by Rikanati et al. In the $\mathrm{\text{air}}/{\mathrm{N}}_2$ case, the reversal phase can be precisely described by the linear theory. Finally, the heavy/light experiment is well described by the Vandenboomgaerde model also coupled with a smaller reduction factor.

We show that in integro-differential delayed dynamical systems, a hybrid state of simultaneous fast-scale chaos and slow-scale periodicity can emerge subsequently to a sequence of Hopf bifurcations. The resulting time trace thereby consists in chaotic oscillations “breathing” periodically at a significantly lower frequency. Experimental evidence of this type of dynamics in delayed dynamical systems is achieved with a Mach-Zehnder modulator optically fed by a semiconductor laser and is subjected to a delayed nonlinear electro-optical feedback. We also propose a theoretical understanding of the phenomenon.

We introduce a novel class of spatially localized self-trapped ringlike singular optical beams in nonlinear media, the so-called azimuthons, which appear due to a continuous azimuthal deformation of vortex solitons. We demonstrate that the azimuthons are characterized by two independent integer indices, the topological charge $m$ and the number $N$ of the intensity peaks along the ring. Each soliton family includes azimuthons with negative, positive, and zero angular velocity.

Arrays of gold split rings with a 50-nm minimum feature size and with an $LC$ resonance at 200 THz frequency ($1.5\mu \mathrm{m}$ wavelength) are fabricated. For normal-incidence conditions, they exhibit a pronounced fundamental magnetic mode, arising from a coupling via the electric component of the incident light. For oblique incidence, a coupling via the magnetic component is demonstrated as well. Moreover, we identify a novel higher-order magnetic resonance at around 370 THz (800 nm wavelength) that evolves out of the Mie resonance for oblique incidence. Comparison with theory delivers good agreement and also shows that the structures allow for a negative magnetic permeability.

The spectra of ${\chi }^{(2)}$ spatial solitons are measured close to the soliton-formation threshold and show the presence of sidebands, shifted by 39 THz from the laser line. By comparing with the predictions of a quantum optical field model, solved numerically in the full ($3+1$)-dimensional space, it is claimed that the observed temporal instability of the spatial soliton is seeded by vacuum state fluctuations of the electromagnetic field.

We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions. Owing to complete integrability of the soliton equations, only pairwise soliton interactions contribute to the solution, and the evolution reduces to a transport of the eigenvalues of the associated spectral problem with the corresponding soliton velocities modified by the collisions. The proposed general procedure of the derivation of the kinetic equation is illustrated by the examples of the Korteweg–de Vries and nonlinear Schrödinger (NLS) equations. As a simple physical example, we construct an explicit solution for the case of interaction of two cold NLS soliton gases.

We propose and demonstrate the feasibility of a new microscopic technique, which is based on variable coherence illumination. By manipulating the spatial coherence properties of an incident evanescent field, subwavelength resolution is achieved over a large field of view from far-field intensity measurements.

Drag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log law, estimated experimentally by Virk as $V^{+}(y^{+})\approx 11.7\log y^{+}-17$. Here $V^{+}(y)$ and $y^{+}$ are the mean streamwise velocity and the distance from the wall in “wall” units. In this Letter we propose that this MDR profile is an edge solution of the Navier-Stokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab initio calculation of the parameters in this law without any viscoelastic experimental input.

Experimental measurements of pair separation statistics in two-dimensional turbulence are reported for an electromagnetically forced stratified-layer system with simultaneous ranges of direct-enstrophy and inverse-energy transfer separated by a well-defined spatial injection scale. Data for pair separation as a function of time are analyzed to determine the dependence of separation statistics in both regimes. Using doubling-time statistics, we show how the measured scalings of the mean quantities are consistent with exponential behavior in the enstrophy range and power-law behavior in the inverse-energy range. Exponential scaling of the doubling-time probability distribution function agrees well with theoretical predictions. Finite size effects are shown to play an important role in the interpretation of the data.

Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic band gap. It is believed that modulation of the refractive index in all three spatial dimensions is required to open a complete band gap and prevent the propagation of electromagnetic waves in all directions. Here we reveal that, in sharp contrast to what was known before and contrary to the accepted physical intuition, a one-dimensional periodic structure containing the layers of transparent left-handed (or negative-index) metamaterial can trap light in three-dimensional space due to the existence of a complete band gap.

We demonstrate a novel technique for direct measurement of the oscillation frequency in an optical-tweezers trap. The technique uses the phenomenon of parametric resonance in an oscillator when the stiffness of the trapping potential is modulated. The trapped particle is a strongly damped oscillator; hence, the signature of parametric resonance is not an increase in the amplitude but an increase in the size of Brownian fluctuations. The trap frequency is measured with an accuracy of 0.1%, which is better than previous techniques and thus opens up new possibilities in experiments with optical tweezers.

We report the first experimental investigation of quantum chaotic scattering in an atomic system: ${}^{85}\mathrm{Rb}$ in strong crossed magnetic and electric fields in an energy regime beyond the ionization threshold, where the classical dynamics is an example of chaotic scattering. We find Ericson fluctuations in the spectra for photo excitation into this regime. This result constitutes the first observation of Ericson fluctuations in atomic and molecular physics. Furthermore, we confirm the prediction that chaotic scattering in the underlying classical dynamics implies Ericson fluctuations.

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, $r_n$, decreases as $\tau \propto r_n^2\sqrt{-\ln r_n^2}$, where $\tau$ is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a $r_n\propto {\tau }^{1/3}$ power law. These findings are verified experimentally.

We examine the robustness of ultrashort optical vortices propagating freely in the atmosphere. We first approximate the stability regions of femtosecond spinning pulses as a function of their topological charge. Next, we numerically demonstrate that atmospheric optical vortices are capable of conveying high power levels in air over hundreds of meters before they break up into filaments.

We predict that spatial self-trapping of light can occur in soft matter encompassing a wide class of new materials such as colloids, foams, gels, fractal aggregates, etc. We develop a general nonlocal theory that allows one to relate the properties of the trapped state of Maxwell equations to the measurable static structure factor of the specific material. We give numerical evidence for stable trapping in fractal aggregates and suggest also the possibility of soliton spectroscopy of soft matter.

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system—a saline jet descending through a salinity gradient—which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a conduit of viscously entrained fluid, whose upward recirculation braids the jet, and nearly confines transverse mixing to the narrow conduit. We show that the underlying jet structure and certain scaling relations follow from similarity solutions to the fluid equations and the physics of Kelvin-Helmholtz instabilities.