Bragg solitons in topological Floquet insulators.

We consider a topological Floquet insulator consisting of two honeycomb arrays of identical waveguides having opposite helicities. The interface between the arrays supports two distinct topological edge states, which can be resonantly coupled by additional weak longitudinal refractive index modulation with a period larger than the helix period. In the presence of Kerr nonlinearity, such coupled edge states enable topological Bragg solitons. Theory and examples of such solitons are presented.

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.

Radiation-loss management in modulated waveguides.

In this work, we discuss the management of radiation loss in photonic waveguides. As an experimental basis, we introduce a new technique of fabricating waveguides with tunable loss, which is particularly useful when implementing non-Hermitian (PT-symmetric) systems. To this end, we employ laser-written waveguides with a transverse sinusoidal modulation, which causes well-controllable radiation losses of almost arbitrary amount. Numerical simulations support our experimental findings. Our study shows that the radiation loss not only depends on the local waveguide curvature but also is influenced by interference effects. As a consequence, the loss is a nonmonotonous function of the bending parameters, such as period length.

Impact of loss on the wave dynamics in photonic waveguide lattices.

We analyze the impact of loss in lattices of coupled optical waveguides and find that, in such a case, the hopping between adjacent waveguides is necessarily complex. This results not only in a transition of the light spreading from ballistic to diffusive, but also in a new kind of diffraction that is caused by loss dispersion. We prove our theoretical results with experimental observations.

Photonic coherent state transfer with Hamiltonian dynamics.

We report the observation of near-perfect light wave transfer by emulating quantum state transfer on a lattice with Hamiltonian dynamics, i.e., time-dependent intersite couplings. The structure transferring a single waveguide excitation over 11 sites with a fidelity of 0.93 works for classical light as well as single photons. As our implementation of perfect quantum state transfer uses a photonic setting, we introduce polarization as a new degree of freedom to the transport protocol. We demonstrate rotation operations of up to 40° on polarization during state transfer.

Superballistic growth of the variance of optical wave packets.

We experimentally demonstrate that hybrid ordered-disordered photonic lattices can generate faster than the ballistic growth of the second moment of a spreading wave packet for parametrically large time intervals.

Mobility transition from ballistic to diffusive transport in non-Hermitian lattices.

Within all physical disciplines, it is accepted that wave transport is predetermined by the existence of disorder. In this vein, it is known that ballistic transport is possible only when a structure is ordered, and that disorder is crucial for diffusion or (Anderson-)localization to occur. As this commonly accepted picture is based on the very foundations of quantum mechanics where Hermiticity of the Hamiltonian is naturally assumed, the question arises whether these concepts of transport hold true within the more general context of non-Hermitian systems. Here we demonstrate theoretically and experimentally that in ordered time-independent -symmetric systems, which are symmetric under space-time reflection, wave transport can undergo a sudden change from ballistic to diffusive after a specific point in time. This transition as well as the diffusive transport in general is impossible in Hermitian systems in the absence of disorder. In contrast, we find that this transition depends only on the degree of dissipation.

Self-trapping threshold in disordered nonlinear photonic lattices.

We investigate numerically and experimentally the influence of coupling disorder on the self-trapping dynamics in nonlinear one-dimensional optical waveguide arrays. The existence of a lower and upper bound of the effective average propagation constant allows for a generalized definition of the threshold power for the onset of soliton localization. When compared to perfectly ordered systems, this threshold is found to decrease in the presence of coupling disorder.

Dynamic localization in Glauber-Fock lattices.

Glauber-Fock lattices refer to a special class of semi-infinite tight-binding lattices with inhomogeneous hopping rates which are found in certain simple solid state, quantum optics and quantum field theoretical models. Here it is shown that dynamic localization, i.e. suppression of quantum diffusion and periodic quantum self-imaging by an external sinusoidal force (Dunlap and Kenkre 1986 Phys. Rev. B 34 3625), can be exactly realized in Glauber-Fock lattices, in spite of inhomogeneity of hopping rates and lattice truncation.

Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices.

We demonstrate quantum walks of a photon pair in a spatially extended Einstein-Podolsky-Rosen state coupled into an on-chip multiport photonic lattice. By varying the degree of entanglement we observe Anderson localization for pairs in a separable state and Anderson colocalization for pairs in an Einstein-Podolsky-Rosen entangled state. In the former case, each photon localizes independently, while in the latter neither photon localizes, but the pair colocalizes--revealing unexpected survival of the spatial correlations through strong disorder.

Optical analogues for massless dirac particles and conical diffraction in one dimension.

We demonstrate that light propagating in an appropriately designed lattice can exhibit dynamics akin to that expected from massless relativistic particles as governed by the one-dimensional Dirac equation. This is accomplished by employing a waveguide array with alternating positive and negative effective coupling coefficients, having a band structure with two intersecting minibands. Through this approach optical analogues of massless particle-antiparticle pairs are experimentally realized. One-dimensional conical diffraction is also observed for the first time in this work.

Vacuum instability and pair production in an optical setting.

In the Dirac-sea picture, the physics of pair production and instability of the quantum electrodynamics vacuum in presence of an oscillating electric field resembles the phenomenon of interband transition of light waves in photonic superlattices induced by a geometric curvature. We realize a binary wave guide superlattice with a curved optical axis mimicking dynamical pair production induced by two counterpropagating ultrastrong laser pulses. Our optical analogue enables visualization of formation of electron-positron pair in physical space as splitting of a wave packet, originally representing an electron in the Dirac sea.

Biphoton generation in quadratic waveguide arrays: a classical optical simulation.

Quantum entanglement became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals provides an efficient source for entangled photon pairs, so-called biphotons. However, SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional arrays can be simulated through classical optical beam propagation in a two-dimensional photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-like inequality.

Nonlinear localized modes in Glauber-Fock photonic lattices.

We study a nonlinear Glauber-Fock lattice and the conditions for the excitation of localized structures. We investigate the particular linear properties of these lattices, including linear localized modes. We investigate numerically nonlinear modes centered in each site of the lattice. We found a strong disagreement of the general tendency between the stationary and the dynamical excitation thresholds. We define a new parameter that takes into account the stationary and dynamical properties of localized excitations.

Anderson cross-localization.

We report Anderson localization in two-dimensional optical waveguide arrays with disorder in waveguide separation introduced along one axis of the array, in an uncorrelated fashion for each waveguide row. We show that the anisotropic nature of such disorder induces a strong localization along both array axes. The degree of localization in the cross-axis remains weaker than that in the direction in which disorder is introduced. This effect is illustrated both theoretically and experimentally.

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.

Anderson localization in a periodic photonic lattice with a disordered boundary.

We investigate experimentally the light evolution inside a two-dimensional finite periodic array of weakly coupled optical waveguides with a disordered boundary. For a completely localized initial condition away from the surface, we find that the disordered boundary induces an asymptotic localization in the bulk, centered around the initial position of the input beam.

Negative coupling between defects in waveguide arrays.

We report on the experimental demonstration of negative coupling constants between defect guides in a waveguide lattice. We find that coupling can only be negative if the defects are negative and an odd number of lattice sites is between the defect guides.

Observation of the gradual transition from one-dimensional to two-dimensional Anderson localization.

We study the gradual transition from one-dimensional (1D) to two-dimensional (2D) Anderson localization upon transformation of the dimensionality of disordered waveguide arrays. An effective transition from a 1D to a 2D system is achieved by increasing the number of rows forming the arrays. We observe that, for a given disorder level, Anderson localization becomes weaker with increasing numbers of rows-hence the effective dimension.