We show that suitable photonic metamaterial structures can support lossless surface waves of the form envisaged by Dyakonov. The idea we put forward is based on the birefringent properties of photonic crystals in the long-wavelength limit, and uses the metamaterial anisotropy of the structures to meet the resonance conditions at which Dyakonov surface waves exist. Implementation of this concept can lead to the first experimental observation of Dyakonov waves, and might open the door to the realization of widely tunable sensing devices based on the unique properties of such waves.

Feedback control with different and independent delay times is introduced and shown to be an efficient method for stabilizing fixed points (equilibria) of dynamical systems. In comparison to other delay based chaos control methods multiple delay feedback control is superior for controlling steady states and works also for relatively large delay times (sometimes unavoidable in experiments due to system dead times). To demonstrate this approach for stabilizing unstable fixed points we present numerical simulations of Chua's circuit and a successful experimental application for stabilizing a chaotic frequency doubled Nd-doped yttrium aluminum garnet laser.

Self-consistent finite-mode approximations for both Euler and Navier-Stokes equations for vorticity on a sphere are constructed and extended to the case of a rotating sphere, aiming at application to ocean and atmosphere modeling. In the absence of dissipation they preserve the specific Hamiltonian structure of hydrodynamics and have, at each level of approximation, an appropriate number of integrals of motion, which is not the case for standard schemes.

We report on random lasing in a disordered system in which the multiple scattering feedback mechanism can be switched from a three-dimensional random walk to a quasi-two-dimensional type of transport. The emission from this system is anisotropic, extraordinary polarized, and is controlled via an external electric field. The phenomenon is observed in dye-doped polymer dispersed liquid crystals and makes use of the strong scattering anisotropies in these materials.

We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer and are fully confirmed by numerical simulations. The existence of each kind of localized structure is put in relation to a corresponding delocalized pattern observed. A quantitative evaluation of the range of pump parameter allowing bistability between localized structures is given. The phenomenon reported results to be robust in parameter space.

Curious spectral properties of an ensemble of random unitary matrices appearing naturally in the quantization of a simple interval-exchange map are investigated. It is demonstrated that, under certain conditions on map parameters, local spectral statistics of this ensemble tends to the semi-Poisson distribution with arbitrary integer or half-integer level repulsion at small distances depending on time-reversal symmetry of the map.

A correlation-type reciprocity theorem is used to show that the elastodynamic Green's function of any inhomogeneous medium (random or deterministic) can be retrieved from the cross correlation of two recordings of a wave field at different receiver locations at the free surface. Unlike in other derivations, which apply to diffuse wave fields in random media or irregular finite bodies, no assumptions are made about the diffusivity of the wave field. In a second version, it is assumed that the wave field is diffuse due to many uncorrelated sources inside the medium.

Entrainment by a pacemaker, representing an element with a higher frequency, is numerically investigated for several classes of random networks which consist of identical phase oscillators. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks can thus exhibit frequency locking to the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.

A liquid jet plunging into a container of liquid often entrains a thin film of air with it, producing bubbles. This bubble production is detrimental to many industrial processes, such as filling a container with a molten glass or polymer, or in coating processes. Conversely, in making a foam, one uses this effect; hence it is important to control the rate of bubble production. Here, we measure the amount of air entrained by a viscous jet over a wide range of parameters and explain the phenomenon theoretically. Simple scaling arguments are shown to predict entrainment rates over 4 orders of magnitude in the dimensionless jet speed.

We demonstrate experimentally that phase-conjugate techniques can be used to achieve super-resolution focusing of electromagnetic waves in a multipath indoor environment at 2.45 GHz. The focusing phenomena was used to direct independent signals to two locations separated by approximately one-half wavelength, thereby creating two simultaneous channels at the same frequency. An increase in channel capacity is shown to be achievable by an experimental transmission of a 1 Mbps signal over two channels created using a four element phase-conjugate array.

We have observed low-threshold optical hyperparametric oscillations in a high-$Q$ fluorite whispering gallery mode resonator. The oscillations result from the resonantly enhanced four-wave mixing occurring due to Kerr nonlinearity of the material. We demonstrate that, because of the narrow bandwidth of the resonator modes as well as the high efficiency of the resonant frequency conversion, the oscillations produce stable narrow-band beat-note of the pump, signal, and idler waves. A theoretical model for this process is described.

Electromagnetic properties of periodic two-dimensional subwavelength structures consisting of closely packed inclusions of materials with negative dielectric permittivity $ϵ$ in a dielectric host with positive ${ϵ}_h$ can be engineered using the concept of multiple electrostatic resonances. Fully electromagnetic solutions of Maxwell's equations reveal multiple wave propagation bands, with the wavelengths much longer than the nanostructure period. Some of these bands are described using the quasistatic theory of the effective dielectric permittivity ${ϵ}_{\mathrm{q}\mathrm{s}}$. Those bands exhibit multiple cutoffs and resonances which are found to be related to each other through a duality condition. An additional propagation band characterized by a negative magnetic permeability is found. Imaging with subwavelength resolution in that band is demonstrated.

We introduce a model for the kinetics of grating formation during holographic recording in optically excitable two-state systems. An unexpected characteristic time dependence of the diffraction efficiency is found. We show that it originates from a nonlinear transformation of the light interference pattern into a refractive-index profile. Our findings strongly resemble and explain by nature the experimental data of two-state systems in general, here represented by two examples: sodium nitroprusside and terbium gallium garnet.

A first-principles numerical model for crumpling of a stiff tethered membrane is introduced. This model displays wrinkles, ridge formation, ridge collapse, and initiation of stiffness divergence. The amplitude and wavelength of the wrinkles and the scaling exponent of the stiffness divergence are consistent with both theory and experiment. Close to the stiffness divergence further buckling is hindered by the nonzero thickness of the membrane, and its elastic behavior becomes similar to that of dry granular media. No change in the distribution of contact forces can be observed at the crossover, implying that the network of ridges is then simultaneously a granular force-chain network.

The ultrafast dephasing of waveguide-plasmon polaritons in metallic photonic crystal slabs is investigated in the femtosecond regime by second-order nonlinear autocorrelation. We find a drastic modification of the dephasing rates due to interaction between localized particle plasmons and optical waveguide modes and subsequent modification of the photonic density of states. In the strong coupling regime our measurements give clear evidence for the appearance of ultrafast polaritonic beat phenomena. All experimental results agree well with theoretical simulations based on a coupled damped harmonic oscillator model.

It was recently conjectured that $1/f$ noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavior of the excitation energy fluctuations power spectrum. The theory gives excellent agreement with numerical calculations and reproduces to a good approximation the $1/f$ ($1/f^2$) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.

The consistency of a nonlinear system's response to a repeated complex waveform drive signal is an important consideration in classical and quantum systems as diverse as lasers, neuronal networks, and manufacturing plants. We show from a consideration of different characteristic waveforms that there is typically an optimal drive amplitude for the most consistent response; internal noise sources dominate for small amplitude driving while deterministic system nonlinearity reduces consistency for large amplitudes. We test this general concept and its measurement experimentally and numerically on the specific example of a laser system.

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The lengths of the transients strongly depend on the network connectivity and vary by several orders of magnitude, with maximum transient lengths at intermediate connectivities. The dynamics of the transients exhibit a novel form of robust synchronization. An approximation to the largest Lyapunov exponent characterizing the chaotic nature of the transient dynamics is calculated analytically.

It is commonly understood that the retrieval of a complex-valued object from its diffraction pattern using a support constraint is a difficult problem, the more so if the support is symmetric. In this Letter we show that, for just such a symmetric support, use of an iterative algorithm in which the basic iteration is specified by a difference map converges routinely. All that is required is sufficient oversampling in the diffraction pattern coupled with judicious choices of the parameters defining the difference map.

We introduce a new all-optical mechanism that can compress the bandwidth of light pulses to absolute zero, and bring them to a complete stop. The mechanism can be realized in a system consisting of a waveguide side coupled to tunable resonators, which generates a photonic band structure that represents a classical analogue of the electromagnetically induced transparency. The same system can also achieve a time-reversal operation. We demonstrate the operation of such a system by finite-difference time-domain simulations of an implementation in photonic crystals.