We show that the nonlinear stage of modulational instability induced by parametric driving in the defocusing nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearized Floquet analysis.

Vertical gold nanogaps are created on microtubular cavities to explore the coupling between resonant light supported by the microcavities and surface plasmons localized at the nanogaps. Selective coupling of optical axial modes and localized surface plasmons critically depends on the exact location of the gold nanogap on the microcavities, which is conveniently achieved by rolling up specially designed thin dielectric films into three-dimensional microtube cavities. The coupling phenomenon is explained by a modified quasipotential model based on perturbation theory. Our work reveals the coupling of surface plasmon resonances localized at the nanoscale to optical resonances confined in microtubular cavities at the microscale, implying a promising strategy for the investigation of light-matter interactions.

We report on highly reflective spin-orbit geometric phase optical elements based on a helicity-preserving circular Bragg-reflection phenomenon. First, we present a dynamical geometric phase experiment using a flat chiral Bragg mirror. Then, we show that shaping such a geometric phase allows the efficient spin-orbit tailoring of light fields without the need to fulfill any condition on birefringent phase retardation, in contrast to the case of transmission spin-orbit optical elements. This is illustrated by optical vortex generation from chiral liquid crystal droplets in the Bragg regime that unveils spin-orbit consequences of the droplet’s curvature. Our results thus introduce a novel class of geometric phase elements—“Bragg-Berry” optical elements.

Generation of optical vortices is described in cholesteric liquid crystals with a singular point in the spatial distribution of a helix phase. The phenomenon uses the fact that a Bragg reflected light phase varies in proportion to the spatial phase of the helix, both at normal and oblique incidences. Our proposal enables high-efficiency, polychromatic generation of optical vortices without the need of a cumbersome fabrication process and fine-tuning.

We report the broadband characterization of the propagation of light through a multiple scattering medium by means of its multispectral transmission matrix. Using a single spatial light modulator, our approach enables the full control of both the spatial and spectral properties of an ultrashort pulse transmitted through the medium. We demonstrate spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape. Our approach opens new perspectives for fundamental studies of light-matter interaction in disordered media, and has potential applications in sensing, coherent control, and imaging.

The first experimental and theoretical evidence was provided for the non-negligible role of a diffusio-osmosis in the ion concentration polarization (ICP) layer, which had been reported to be in a high Peclet number regime. Under the assumption that the hydrated shells of cations were stripped out with the amplified electric field inside the ICP layer, its concentration profile possessed a steep concentration gradient at the stripped location. Since the concentration gradient drove a strong diffusio-osmosis, the combination of electro-osmotic and diffusio-osmotic slip velocity had a form of an anomalous nonmonotonic function with both a single- and multiple-cationic solution. A direct measurement of electrolytic concentrations around the layer quantitatively validated our new investigations. This non-negligible diffusio-osmotic contribution in a micro- and nanofluidic platform or porous medium would be essential for clarifying the fundamental insight of nanoscale electrokinetics as well as guiding the engineering of ICP-based electrochemical systems.

We measure experimentally the second-order coherence properties of supercontinuum generated in a photonic crystal fiber. Our approach is based on measuring separately the quasicoherent and quasistationary contributions to the cross-spectral density and mutual coherence functions using a combination of interferometric and nonlinear gating techniques. This allows us to introduce two-dimensional coherence spectrograms which provide a direct characterization and convenient visualization of the spectrotemporal coherence properties. The measured second-order coherence functions are in very good agreement with numerical simulations based on the generalized nonlinear Schrödinger equation. Our results pave the way towards the full experimental characterization of supercontinuum coherence properties. More generally, they provide a generic approach for the complete experimental measurement of the coherence of broadband sources.

We present a model system for strongly nonlinear transition waves generated in a periodic lattice of bistable members connected by magnetic links. The asymmetry of the on-site energy wells created by the bistable members produces a mechanical diode that supports only unidirectional transition wave propagation with constant wave velocity. We theoretically justify the cause of the unidirectionality of the transition wave and confirm these predictions by experiments and simulations. We further identify how the wave velocity and profile are uniquely linked to the double-well energy landscape, which serves as a blueprint for transition wave control.

Polycapillary x-ray focusing devices are built from hundreds of thousands of bent microcapillaries that are stacked into hexagonal arrays. We show that intrinsic point defects of the optics (e.g., missing or larger capillaries) lead to the formation of multiple x-ray images of an object positioned in the focal plane. These images can be recorded in parallel, and can provide spatial resolution that is limited by the defect size and not by the focal spot size. In a proof-of-principle experiment, we demonstrate submicron resolution, which has not yet been achieved with polycapillary focusing optics. Tailored optics with a controlled distribution of “defects” could be used for multimodal nanoscale x-ray imaging with laboratory setups.

We propose a scheme that enables the deterministic generation of single phonons at gigahertz frequencies triggered by single photons in the near infrared. This process is mediated by a quantum dot embedded on chip in an optomechanical circuit, which allows for the simultaneous control of the relevant photonic and phononic frequencies. We devise new optomechanical circuit elements that constitute the necessary building blocks for the proposed scheme and are readily implementable within the current state-of-the-art of nanofabrication. This will open new avenues for implementing quantum functionalities based on phonons as an on-chip quantum bus.

New propagation regimes for light arise from the ability to tune the dielectric permittivity to extremely low values. Here, we demonstrate a universal approach based on the low linear permittivity values attained in the $\epsilon$-near-zero (ENZ) regime for enhancing the nonlinear refractive index, which enables remarkable light-induced changes of the material properties. Experiments performed on Al-doped ZnO (AZO) thin films show a sixfold increase of the Kerr nonlinear refractive index ($n_2$) at the ENZ wavelength, located in the 1300 nm region. This in turn leads to ultrafast light-induced refractive index changes of the order of unity, thus representing a new paradigm for nonlinear optics.

We present a method of locally inverting the sign of the coupling term in tight-binding systems, by means of inserting a judiciously designed ancillary site and eigenmode matching of the resulting vertex triplet. Our technique can be universally applied to all lattice configurations, as long as the individual sites can be detuned. We experimentally verify this method in laser-written photonic lattices and confirm both the magnitude and the sign of the coupling by interferometric measurements. Based on these findings, we demonstrate how such universal sign-flipped coupling links can be embedded into extended lattice structures to impose a ${\mathbb{Z}}_2$-gauge transformation. This opens a new avenue for investigations on topological effects arising from magnetic fields with aperiodic flux patterns or in disordered systems.

The cross-correlation of a diffuse wave field converges toward the difference between the anticausal and causal Green’s functions between two points. This property has paved the way to passive imaging using ambient noise sources. In this Letter, we investigate Green’s function retrieval in electromagnetism. Using a model based on the fluctuation dissipation theorem, we demonstrate theoretically that the cross-correlation function strongly depends on the absorption properties of the receivers. This is confirmed in measurements within a reverberation chamber. In contrast to measurements with noninvasive probes, we show that only the anticausal Green’s function can be retrieved with a matched antenna. Finally, we interpret this result as an equivalent time-reversal experiment with an electromagnetic sink.

Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.

We explore a prototypical two-dimensional massive model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge vortices in a way that preserves the total vorticity. These conclusions are found not to be restricted to the case of cubic two-dimensional nonlinearities but are found to be extended to the case of quintic nonlinearity, as well as to that of three spatial dimensions. Our results also reveal nontrivial differences with respect to the better understood nonrelativistic analogue of the model, namely the nonlinear Schrödinger equation.

We investigate the properties of two-dimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system’s periodicity. This creates a natural set of degeneracies that can undergo thresholdless $\mathcal{P}\mathcal{T}$ transitions. We derive a $\mathbf{k}·\mathbf{p}$ perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless $\mathcal{P}\mathcal{T}$ transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a $\mathcal{P}\mathcal{T}$-superprism effect, and unidirectional behavior.

We demonstrate the occurrence of anomalous diffusion of dissipative solitons in a “simple” and deterministic prototype model: the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions. The main features of their dynamics, induced by symmetric-asymmetric explosions, can be modeled by a subdiffusive continuous-time random walk, while in the case dominated by only asymmetric explosions, it becomes characterized by normal diffusion.