Exciton-polariton topological insulator.

Topological insulators-materials that are insulating in the bulk but allow electrons to flow on their surface-are striking examples of materials in which topological invariants are manifested in robustness against perturbations such as defects and disorder1. Their most prominent feature is the emergence of edge states at the boundary between areas with different topological properties. The observable physical effect is unidirectional robust transport of these edge states. Topological insulators were originally observed in the integer quantum Hall effect2 (in which conductance is quantized in a strong magnetic field) and subsequently suggested3-5 and observed6 to exist without a magnetic field, by virtue of other effects such as strong spin-orbit interaction. These were systems of correlated electrons. During the past decade, the concepts of topological physics have been introduced into other fields, including microwaves7,8, photonic systems9,10, cold atoms11,12, acoustics13,14 and even mechanics15. Recently, topological insulators were suggested to be possible in exciton-polariton systems16-18 organized as honeycomb (graphene-like) lattices, under the influence of a magnetic field. Exciton-polaritons are part-light, part-matter quasiparticles that emerge from strong coupling of quantum-well excitons and cavity photons19. Accordingly, the predicted topological effects differ from all those demonstrated thus far. Here we demonstrate experimentally an exciton-polariton topological insulator. Our lattice of coupled semiconductor microcavities is excited non-resonantly by a laser, and an applied magnetic field leads to the unidirectional flow of a polariton wavepacket around the edge of the array. This chiral edge mode is populated by a polariton condensation mechanism. We use scanning imaging techniques in real space and Fourier space to measure photoluminescence and thus visualize the mode as it propagates. We demonstrate that the topological edge mode goes around defects, and that its propagation direction can be reversed by inverting the applied magnetic field. Our exciton-polariton topological insulator paves the way for topological phenomena that involve light-matter interaction, amplification and the interaction of exciton-polaritons as a nonlinear many-body system.

Improving techniques for diagnostics of laser pulses by compact representations.

We propose and demonstrate, numerically and experimentally, use of sparsity as prior information for extending the capabilities and performance of techniques and devices for laser pulse diagnostics. We apply the concept of sparsity in three different applications. First, we improve a photodiode-oscilloscope system's resolution for measuring the intensity structure of laser pulses. Second, we demonstrate the intensity profile reconstruction of ultrashort laser pulses from intensity autocorrelation measurements. Finally, we use a sparse representation of pulses (amplitudes and phases) to retrieve measured pulses from incomplete spectrograms of cross-correlation frequency-resolved optical gating traces.

Topologically protected bound states in photonic parity-time-symmetric crystals.

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

Accelerating diffraction-free beams in photonic lattices.

We study nondiffracting accelerating paraxial optical beams in periodic potentials, in both the linear and the nonlinear domains. In particular, we show that only a unique class of z-dependent lattices can support a true accelerating diffractionless beam. Accelerating lattice solitons, autofocusing beams and accelerating bullets in optical lattices are systematically examined.

Sparsity-based single-shot subwavelength coherent diffractive imaging.

Coherent Diffractive Imaging (CDI) is an algorithmic imaging technique where intricate features are reconstructed from measurements of the freely diffracting intensity pattern. An important goal of such lensless imaging methods is to study the structure of molecules that cannot be crystallized. Ideally, one would want to perform CDI at the highest achievable spatial resolution and in a single-shot measurement such that it could be applied to imaging of ultrafast events. However, the resolution of current CDI techniques is limited by the diffraction limit, hence they cannot resolve features smaller than one half the wavelength of the illuminating light. Here, we present sparsity-based single-shot subwavelength resolution CDI: algorithmic reconstruction of subwavelength features from far-field intensity patterns, at a resolution several times better than the diffraction limit. This work paves the way for subwavelength CDI at ultrafast rates, and it can considerably improve the CDI resolution with X-ray free-electron lasers and high harmonics.

Third Trimester Structural and Diffusion Brain Imaging after Single Intrauterine Fetal Death in Monochorionic Twins: MRI-Based Cohort Study.

BACKGROUND AND PURPOSE: Single intrauterine fetal death increases the risk of antenatal brain lesions in the surviving twin. We evaluated the prevalence of structural brain lesions, biometry, and diffusivity on routine third trimester MR imaging performed following single intrauterine fetal death. MATERIALS AND METHODS: In a retrospective MR imaging-based cohort study, we compared 29 monochorionic twins complicated with single intrauterine fetal death (14 following laser ablation treatment for twin-to-twin transfusion syndrome, 8 following selective fetal reduction, and 7 spontaneous) with 2 control cohorts (49 singleton fetuses and 28 uncomplicated twin fetuses). All fetuses in the single intrauterine fetal death group underwent fetal brain MR imaging as a routine third trimester evaluation. Structural brain lesions were analyzed. Cerebral biometry and diffusivity were measured and compared. RESULTS: Brain lesions consistent with the evolution of prior ischemic injury were found in 1 of 29 fetuses, not detected by ultrasound. No acute brain infarction, hemorrhage, or cortical abnormalities were found. Supratentorial biometric measurements in the single intrauterine fetal death group were significantly smaller than those in the singleton group, but not significantly different from those in the uncomplicated twin group. There were no significant differences in ADC values of the cerebral hemispheres, basal ganglia, and pons between the single intrauterine fetal death group and either control group. CONCLUSIONS: Although smaller brain biometry was found, normal diffusivity in surviving twins suggests normal parenchymal microstructure. The rate of cerebral structural injury was relatively low in our cohort, arguing against the routine use of fetal brain MR imaging in twin pregnancies complicated with single intrauterine fetal death. Larger prospective studies are necessary to guide appropriate surveillance protocol and parental counseling in twin pregnancies complicated by single intrauterine fetal death.

Modulation instability and pattern formation in spatially incoherent light beams.

We report on the experimental observation of modulation instability of partially spatially incoherent light beams in noninstantaneous nonlinear media and show that in such systems patterns can form spontaneously from noise. Incoherent modulation instability occurs above a specific threshold that depends on the coherence properties (correlation distance) of the wave packet and leads to a periodic train of one-dimensional filaments. At a higher value of nonlinearity, the incoherent one-dimensional filaments display a two-dimensional instability and break up into self-ordered arrays of light spots. This discovery of incoherent pattern formation reflects on many other nonlinear systems beyond optics. It implies that patterns can form spontaneously (from noise) in diverse nonlinear many-body systems involving weakly correlated particles, such as atomic gases at (or near) Bose-Einstein condensation temperatures and electrons in semiconductors at the vicinity of the quantum Hall regime.

Optical transitions and Rabi oscillations in waveguide arrays.

It is theoretically demonstrated that Rabi interband oscillations are possible in waveguide arrays. Such transitions can take place in optical lattices when the unit-cell is periodically modulated along the propagation direction. Under phase-matching conditions, direct power transfer between two Floquet-Bloch modes can occur. In the nonlinear domain, periodic oscillations between two different lattice solitons are also possible.

Soliton dynamics and self-induced transparency in nonlinear nanosuspensions.

We study spatial soliton dynamics in nano-particle suspensions. Starting from the Nernst-Planck and Smoluchowski equations, we demonstrate that in these systems the underlying nonlinearities as well as the nonlinear Rayleigh losses depend exponentially on optical intensity. Two different nonlinear regimes are identified depending on the refractive index contrast of the nanoparticles involved and the interesting prospect of self-induced transparency is demonstrated. Soliton stability is systematically analyzed for both 1D and 2D configurations and their propagation dynamics in the presence of Rayleigh losses is examined. The possibility of synthesizing artificial nonlinearities using mixtures of nanosuspensions is also considered.

Incoherent white-light solitons in nonlinear periodic lattices.

We predict the existence of lattice solitons made of incoherent white light: lattice solitons made of light originating from an ordinary incandescent light bulb. We find that the intensity structure and spatial power spectra associated with different temporal frequency constituents of incoherent white-light lattice solitons (IWLLSs) arrange themselves in a characteristic fashion, with the intensity structure more localized at higher frequencies, and the spatial power spectrum more localized at lower frequencies; the spatial correlation distance is larger at lower frequency constituents of IWLLSs. This characteristic shape of incoherent white-light lattice solitons reflects the fact that diffraction is stronger for lower temporal frequency constituents, while higher frequencies experience stronger effective nonlinearity and deeper lattice structure.

Composite multihump vector solitons carrying topological charge

We propose composite solitons carrying topological charge: multicomponent two dimensional [ (2+1)D] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The "spin" carried by these multimode composite solitons suggests 3D soliton interactions in which the particlelike behavior includes spin, in addition to effective mass, linear, and angular momenta.

Cantor set fractals from solitons

We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.

Modulation instability of incoherent beams in noninstantaneous nonlinear media

We show that modulation instability can exist with partially spatially incoherent light beams in a noninstantaneous nonlinear environment. For such incoherent modulation instability to occur, the value of the nonlinearity has to exceed a threshold imposed by the degree of spatial coherence.

Eliminating the transverse instabilities of kerr solitons

We show analytically, numerically, and experimentally that a transversely stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk medium. The transverse instability of the soliton is completely eliminated if it is made sufficiently incoherent along the transverse dimension. We derive a criterion for the threshold of transverse instability that links the nonlinearity to the largest transverse correlation distance for which the 1D soliton is stable.

Bright spatial solitons on a partially incoherent background

We present the first observation of incoherent antidark spatial solitons in noninstantaneous nonlinear media. This new class of soliton states involves bright solitons on a partially incoherent background of infinite extent. In the case where the nonlinearity is of the Kerr type, their existence is demonstrated analytically by means of an exact solution. Computer simulations and experiments indicate that these incoherent antidark solitons can propagate in a stable fashion provided that the spatial coherence of their background is reduced below the incoherent modulation instability threshold.

Interactions between two-dimensional composite vector solitons carrying topological charges.

We present a comprehensive study of interactions (collisions) between two-dimensional composite vector solitons carrying topological charges in isotropic saturable nonlinear media. We numerically study interactions between such composite solitons for different regimes of collision angle and report numerous effects which are caused solely by the "spin" (topological charge) carried by the second excited mode. The most intriguing phenomenon we find is the delayed-action interaction between interacting composite solitons carrying opposite spins. In this case, two colliding solitons undergo a fusion process and form a metastable bound state that decays after long propagation distances into two or three new solitons. Another noticeable effect is spin-orbit coupling in which angular momentum is being transferred from "spin" to orbital angular momentum. This phenomenon occurs at angles below the critical angle, including the case when the initial soliton trajectories are in parallel to one another and lie in the same plane. Finally, we report on shape transformation of vortex component into a rotating dipole-mode solitons that occurs at large collision angles, i.e., at angles for which scalar solitons of all types simply go through one another unaffected.

Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media.

We analytically demonstrate the existence of white light solitons in logarithmically saturable noninstantaneous nonlinear media. This incoherent soliton has elliptic Gaussian intensity profile, and elliptic Gaussian spatial correlation statistics. The existence curve of the soliton connects the strength of the nonlinearity, the spatial correlation distance as a function of frequency, and the characteristic width of the soliton. For this soliton to exist, the spatial correlation distance must be smaller for larger temporal frequency constituents of the beam.

Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media.

We show that three approaches previously developed to describe partially incoherent wave propagation in inertial nonlinear media are in fact equivalent. This equivalence is formally established through the evolution of the mutual coherence function and by means of Karhunen-Loeve expansions.