Photonic crystals can be designed to control and confine light. Since the introduction of the concept by Yablonovitch and John two decades ago, there has been a quest for the optimal structure, i.e., the periodic arrangement of dielectric and air that maximizes the photonic band gap. Based on numerical optimization studies, we have discovered some surprisingly simple geometric properties of optimal planar band gap structures. We conjecture that optimal structures for gaps between bands $n$ and $n+1$ correspond to $n$ elliptic rods with centers defined by the generators of an optimal centroidal Voronoi tessellation (transverse magnetic polarization) and to the walls of this tessellation (transverse electric polarization).

We show that long wave–short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.

As frequently observed in common life, a jet of a viscous liquid impacting on a horizontal surface does not remain straight but instead buckles and folds periodically. We report experiments with planar (ribbonlike) jets of silicone oil impacting the free surface of the same liquid and describe the way in which jet folds incorporate air. It is shown that air ingestion proceeds through different modes, each of them acting as a source of monodisperse bubbles and featuring a threshold in jet height. These sources result from the breakup of remarkable cuspidal structures, produced by the recession of air domains within liquid folds.

We report an ultrafast synchrotron x-ray phase-contrast imaging study of the primary breakup mechanism of a coaxial air-assisted water jet. There exist great similarities between the primary (jet) and the secondary (drop) breakup, and in the primary breakup on different length scales. A transition from a ligament- to a membrane-mediated breakup is identified around an effective Weber number ${\mathrm{We}}^{\prime }\sim 13$. This observation reveals the critical role an effective Weber number plays in determining the atomization process and strongly supports the cascade breakup model.

We study, theoretically and experimentally, the nonlinear dynamics of a wave packet launched inside a trap potential. Increasing the power of the wave packet transforms its dynamics from linear tunneling through a potential barrier, to soliton tunneling, and eventually, above a well-defined threshold, to the ejection of a soliton from the potential trap.

We experimentally demonstrate the possibility of retrieving the spatial coherence of an infrared source by using an up-conversion interferometer. Sum-frequency generation in Ti-diffused periodically poled lithium-niobate waveguides in both arms of the interferometer is used to convert the infrared into the visible domain. The fringe contrast of the interference pattern in the visible domain permits us to resolve the spatial separation of two uncorrelated pointlike infrared sources, which simulate a binary star. The validity of these measurements is confirmed through a simultaneous comparison with a reference interferometer working in the infrared domain.

We contrast the two situations in which either a light beam is incident on a moving medium or a moving optical image is incident on a stationary medium. The principle of relativity suggests that the effects on the light of propagating through the medium should be similar. We find, however, that there are subtle differences which we can understand in terms of the relative alignment of the Poynting and wave vectors. Our analysis and experiments investigate both translational motion and rotation.

We study high-order harmonic generation in excited media using a four-wave-mixing-like configuration. We analyze the spatial profile of high harmonics emitted by a grating of rotationally excited molecules as a function of the pump-probe delay. We demonstrate a dramatic improvement in the contrast of the diffracted signal relative to the total high harmonic signal. This allows us to observe subtle effects in the rotational wave packet excitation such as the pump-intensity dependence of the wave packet dynamics. High harmonic transient grating spectroscopy can be extended to all forms of molecular excitation and to weak resonant excitation.

We investigate chimera states in a ring of identical phase oscillators coupled in a time-delayed and spatially nonlocal fashion. We find novel clustered chimera states that have spatially distributed phase coherence separated by incoherence with adjacent coherent regions in antiphase. The existence of such time-delay induced phase clustering is further supported through solutions of a generalized functional self-consistency equation of the mean field. Our results highlight an additional mechanism for cluster formation that may find wider practical applications.

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

Fractal scatterings in weak solitary-wave interactions are analyzed for generalized nonlinear Schrödiger equations (GNLS). Using asymptotic methods, these weak interactions are reduced to a universal second-order map. This map gives the same fractal-scattering patterns as those in the GNLS equations both qualitatively and quantitatively. Scaling laws of these fractals are also derived.

We have investigated the intensity dependence of high-order harmonic generation in argon when the two shortest quantum paths contribute to the harmonic emission. For the first time to our knowledge, experimental conditions were found to clearly observe interference between these two quantum paths that are in excellent agreement with theoretical predictions. This result is a first step towards the direct experimental characterization of the full single-atom dipole moment and demonstrates an unprecedented accuracy of quantum path control on an attosecond time scale.

We demonstrate that directed transport of topological solitons in damped, biharmonically driven Frenkel-Kontorova chains can be strongly enhanced by introducing suitable phase disorder into the asymmetric periodic driving. From a collective coordinate formalism, we theoretically deduce an effective deterministic equation of motion governing the dynamics of the soliton center-of-mass for which we predict the dependence of maximal soliton drift on disorder strength according to recently proposed general scaling laws concerning directed transport induced by symmetry breaking of temporal forces. We find that these results are in excellent agreement with those of computer simulations of the original Frenkel-Kontorova chains.

We provide a theory of dynamo ($\alpha$ effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the $\alpha$ effect is reduced by the shear even in the absence of magnetic field. The $\alpha$ effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun.

A novel thermal convection cell consisting of half a soap bubble heated at the equator is introduced to study thermal convection and the movement of isolated vortices. The soap bubble, subject to stratification, develops thermal convection at its equator. A particular feature of this cell is the emergence of isolated vortices. These vortices resemble hurricanes or cyclones and similarities between our observed structures and these natural objects are found. This is brought forth through a study of the mean square displacement of these objects showing signs of superdiffusion.

We study the spatial and temporal structure of nonlinear states formed by parametrically excited waves on a fluid surface (Faraday instability), in a highly dissipative regime. Short-time dynamics reveal that 3-wave interactions between different spatial modes are only observed when the modes’ peak values occur simultaneously. The temporal structure of each mode is functionally described by the Hill’s equation and is unaffected by which nonlinear interaction is dominant.

We study the heat current $J$ in a classical one-dimensional disordered chain with on-site pinning and with ends connected to stochastic thermal reservoirs at different temperatures. In the absence of anharmonicity all modes are localized and there is a gap in the spectrum. Consequently $J$ decays exponentially with system size $N$. Using simulations we find that even a small amount of anharmonicity leads to a $J\sim 1/N$ dependence, implying diffusive transport of energy.

Lagrangian studies of the local temperature mixing and heat transport in turbulent Rayleigh-Bénard convection are presented, based on three-dimensional direct numerical simulations. Contrary to vertical pair distances, the temporal growth of lateral pair distances agrees with the Richardson law, but yields a smaller Richardson constant due to correlated pair motion in plumes. Our results thus imply that Richardson dispersion is also found in anisotropic turbulence. We find that extremely large vertical accelerations appear less frequently than lateral ones and are not connected with rising or falling thermal plumes. The height-dependent joint Lagrangian statistics of vertical acceleration and local heat transfer allow us to identify a zone which is dominated by thermal plume mixing.

An anomalously long transient is needed to achieve a steady pressurization of a fluid when forced to flow through micronarrowed channels under constant mechanical driving. This phenomenon, known as the “bottleneck effect” is here revisited from a different perspective, by using confined displacements of interfacial fluids. Compared to standard microfluidics, such effect admits in this case a neat quantitative characterization, which reveals intrinsic material characteristics of flowing monolayers and permits to envisage strategies for their controlled micromanipulation.

It has been known for over six decades that the dissolution of minute amounts of high molecular weight polymers in wall-bounded turbulent flows results in a dramatic reduction in turbulent skin friction by up to 70%. First principles simulations of turbulent flow of model polymer solutions can predict the drag reduction (DR) phenomenon. However, the essential dynamical interactions between the coherent structures present in turbulent flows and polymer conformation field that lead to DR are poorly understood. We examine this connection via dynamical simulations that track the evolution of hairpin vortices, i.e., counter-rotating pairs of quasistreamwise vortices whose nonlinear autogeneration and growth, decay and breakup are centrally important to turbulence stress production. The results show that the autogeneration of new vortices is suppressed by the polymer stresses, thereby decreasing the turbulent drag.