Broadband vectorial ultrathin optics with experimental efficiency up to 99% in the visible region via universal approximators.

Integrating conventional optics into compact nanostructured surfaces is the goal of flat optics. Despite the enormous progress in this technology, there are still critical challenges for real-world applications due to the limited operational efficiency in the visible region, on average lower than 60%, which originates from absorption losses in wavelength-thick (≈ 500 nm) structures. Another issue is the realization of on-demand optical components for controlling vectorial light at visible frequencies simultaneously in both reflection and transmission and with a predetermined wavefront shape. In this work, we developed an inverse design approach that allows the realization of highly efficient (up to 99%) ultrathin (down to 50 nm thick) optics for vectorial light control with broadband input-output responses in the visible and near-IR regions with a desired wavefront shape. The approach leverages suitably engineered semiconductor nanostructures, which behave as a neural network that can approximate a user-defined input-output function. Near-unity performance results from the ultrathin nature of these surfaces, which reduces absorption losses to near-negligible values. Experimentally, we discuss polarizing beam splitters, comparing their performance with the best results obtained from both direct and inverse design techniques, and new flat-optics components represented by dichroic mirrors and the basic unit of a flat-optics display that creates full colours by using only two subpixels, overcoming the limitations of conventional LCD/OLED technologies that require three subpixels for each composite colour. Our devices can be manufactured with a complementary metal-oxide-semiconductor (CMOS)-compatible process, making them scalable for mass production at low cost.

Generalized Maxwell projections for multi-mode network Photonics.

The design of optical resonant systems for controlling light at the nanoscale is an exciting field of research in nanophotonics. While describing the dynamics of few resonances is a relatively well understood problem, controlling the behavior of systems with many overlapping states is considerably more difficult. In this work, we use the theory of generalized operators to formulate an exact form of spatio-temporal coupled mode theory, which retains the simplicity of traditional coupled mode theory developed for optical waveguides. We developed a fast computational method that extracts all the characteristics of optical resonators, including the full density of states, the modes quality factors, and the mode resonances and linewidths, by employing a single first principle simulation. This approach can facilitate the analytical and numerical study of complex dynamics arising from the interactions of many overlapping resonances, defined in ensembles of resonators of any geometrical shape and in materials with arbitrary responses.

Perfect secrecy cryptography via mixing of chaotic waves in irreversible time-varying silicon chips.

Protecting confidential data is a major worldwide challenge. Classical cryptography is fast and scalable, but is broken by quantum algorithms. Quantum cryptography is unclonable, but requires quantum installations that are more expensive, slower, and less scalable than classical optical networks. Here we show a perfect secrecy cryptography in classical optical channels. The system exploits correlated chaotic wavepackets, which are mixed in inexpensive and CMOS compatible silicon chips. The chips can generate 0.1 Tbit of different keys for every mm of length of the input channel, and require the transmission of an amount of data that can be as small as 1/1000 of the message's length. We discuss the security of this protocol for an attacker with unlimited technological power, and who can access the system copying any of its part, including the chips. The second law of thermodynamics and the exponential sensitivity of chaos unconditionally protect this scheme against any possible attack.

Broadband Epsilon-near-Zero Reflectors Enhance the Quantum Efficiency of Thin Solar Cells at Visible and Infrared Wavelengths.

The engineering of broadband absorbers to harvest white light in thin-film semiconductors is a major challenge in developing renewable materials for energy harvesting. Many solution-processed materials with high manufacturability and low cost, such as semiconductor quantum dots, require the use of film structures with thicknesses on the order of 1 µm to absorb incoming photons completely. The electron transport lengths in these media, however, are 1 order of magnitude smaller than this length, hampering further progress with this platform. Herein, we show that, by engineering suitably disordered nanoplasmonic structures, we have created a new class of dispersionless epsilon-near-zero composite materials that efficiently harness white light. Our nanostructures localize light in the dielectric region outside the epsilon-near-zero material with characteristic lengths of 10-100 nm, resulting in an efficient system for harvesting broadband light when a thin absorptive film is deposited on top of the structure. By using a combination of theory and experiments, we demonstrate that ultrathin layers down to 50 nm of colloidal quantum dots deposited atop the epsilon-near-zero material show an increase in broadband absorption ranging from 200% to 500% compared to a planar structure of the same colloidal quantum-dot-absorber average thickness. When the epsilon-near-zero nanostructures were used in an energy-harvesting module, we observed a spectrally averaged 170% broadband increase in the external quantum efficiency of the device, measured at wavelengths between 400 and 1200 nm. Atomic force microscopy and photoluminescence excitation measurements demonstrate that the properties of these epsilon-near-zero structures apply to general metals and could be used to enhance the near-field absorption of semiconductor structures more widely. We have developed an inexpensive electrochemical deposition process that enables scaled-up production of this nanomaterial for large-scale energy-harvesting applications.

Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems.

We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.

Period doubling induced by thermal noise amplification in genetic circuits.

Rhythms of life are dictated by oscillations, which take place in a wide rage of biological scales. In bacteria, for example, oscillations have been proven to control many fundamental processes, ranging from gene expression to cell divisions. In genetic circuits, oscillations originate from elemental block such as autorepressors and toggle switches, which produce robust and noise-free cycles with well defined frequency. In some circumstances, the oscillation period of biological functions may double, thus generating bistable behaviors whose ultimate origin is at the basis of intense investigations. Motivated by brain studies, we here study an "elemental" genetic circuit, where a simple nonlinear process interacts with a noisy environment. In the proposed system, nonlinearity naturally arises from the mechanism of cooperative stability, which regulates the concentration of a protein produced during a transcription process. In this elemental model, bistability results from the coherent amplification of environmental fluctuations due to a stochastic resonance of nonlinear origin. This suggests that the period doubling observed in many biological functions might result from the intrinsic interplay between nonlinearity and thermal noise.

Nonlinearly-enhanced energy transport in many dimensional quantum chaos.

By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter.

Single-molecule imaging with x-ray free-electron lasers: dream or reality?

X-ray free-electron lasers (XFEL) are revolutionary photon sources, whose ultrashort, brilliant pulses are expected to allow single-molecule diffraction experiments providing structural information on the atomic length scale of nonperiodic objects. This ultimate goal, however, is currently hampered by several challenging questions basically concerning sample damage, Coulomb explosion, and the role of nonlinearity. By employing an original ab initio approach, we address these issues showing that XFEL-based single-molecule imaging will be only possible with a few-hundred long attosecond pulses, due to significant radiation damage and the formation of preferred multisoliton clusters which reshape the overall electronic density of the molecular system at the femtosecond scale.

Statistical analysis of complex systems with nonclassical invariant measures.

I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a general formalism based on the Ablowitz-Kaup-Newell-Segur scheme, I demonstrate how to build an invariant measure and, within a one-dimensional phase space, how to develop a suitable thermodynamics. A detailed example is provided with a universal model of wave propagation, with reference to a transparent potential sustaining gray solitons. The system shows a rich thermodynamic scenario, with a free-energy landscape supporting phase transitions and controllable emergent properties. I finally discuss the origin of such behavior, trying to identify common denominators in the area of complex dynamics.

Ultrashort pulse propagation and the Anderson localization.

We investigate the dynamics of a 10 fs light pulse propagating in a random medium by the direct solution of the three-dimensional Maxwell equations. Our approach employs molecular dynamics to generate a distribution of spherical scatterers and a parallel finite-difference time-domain code for the vectorial wave propagation. We calculate the disorder-averaged energy velocity and the decay time of the transmitted pulse versus the localization length for an increasing refractive index.

Condensation in disordered lasers: theory, 3D+1 simulations, and experiments.

The complex processes underlying the generation of a coherent emission from the multiple scattering of photons and wave localization in the presence of structural disorder are still mostly unexplored. Here we show that a single nonlinear Schrödinger equation, playing the role of the Schwalow-Townes law for standard lasers, quantitatively reproduces experimental results and three-dimensional time-domain parallel simulations of a colloidal laser system.

Free-energy transition in a gas of noninteracting nonlinear wave particles.

We investigate the dynamics of a gas of noninteracting particlelike soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by employing methods of the statistical mechanics of chaos. In particular, we show that a suitable free energy undergoes a metamorphosis as the input excitation is increased, thereby developing a first-order phase transition whose measurable manifestation is the formation of shock waves. This demonstrates that even the simplest phase-space dynamics, involving independent (uncoupled) degrees of freedom, can sustain critical phenomena.

Nonlinear optics in the X-ray regime: nonlinear waves and self-action effects.

We study the nonlinear refraction of X-rays in highly ionized condensed matter by using a classical model of a cold electron plasma in a lattice of still ions coupled with Maxwell equations. We discuss the existence and stability of nonlinear waves. As a real-world example, we consider beam self-defocusing in crystalline materials (B, C, Li, Na). We predict that nonlinear processes become comparable to the linear ones for focused beams with powers of the order of mc(3)/ro (approximately 10 GW), the classical electron power. As a consequence, nonlinear phenomena are expected in currently exploited X-ray Free-Electron Lasers and in their future developments.

Mode competitions and dynamical frequency pulling in Mie nanolasers: 3D ab-initio Maxwell-Bloch computations.

We investigate the process of light matter interaction in a spherical Mie nanolaser. We derive a rigorous theory based on a three dimensional vector set of Maxwell-Bloch equations and solve the resulting equations through a parallel Finite-Difference Time-Domain Maxwell- Bloch (FDTD-MB) code. Our results predicts a rich physical scenario, ranging from nontrivial vectorial energy matter interplay in the pre-lasing regime to mode competitions and dynamical frequency pulling phenomena. Application of these effects could favor the realization of largely-tunable, nonlinearly controlled nanolaser devices.

Spatial solitons in nematic liquid crystals: from bulk to discrete.

We review theoretical and experimental results on spatial solitons in nematic liquid crystalline cells, including two-dimensional solitons in bulk and discrete solitons in one-dimensional waveguide arrays. In bulk we describe the propagation of continuous solitons in the presence of adjustable walk-off, their interaction with light-induced defects and refraction-reflection at a voltage-tunable interface. In optical lattices we address the transition from discrete diffraction to localization, as well as all-optical beam steering.

Bile acid transformation by the intestinal flora and cholesterol saturation in bile. Effects of Streptococcus faecium administration.

In 8 normal subjects the daily administration for 30 days of at least 750 X 10(6) Streptococcus faecium, a bacteria producing substances acting against Clostridia and other intestinal microorganisms reduced the cholesterol saturation and the molar percentage of deoxycholic acid (DCA) in bile. The percentage of cholic acid (CA) and chenodeoxycholic acid (DCA) increased significantly in feces, whereas lithocholic acid (LCA) decreased from 49.2 to 40.5%. In vitro fecal samples of subjects taking S. faecium transformed more slowly CA to DCA and CDCA to LCA. Moreover, 7-ketolithocholic seems an intermediate step in the biotransformation of CDCA to LCA. During SF administration, the anaerobic bacteria count of feces decreases, whereas aerobic bacteria increase; the changes of fecal flora may reduce the degradation of primary bile acids influencing the bile acid composition in both the bile and the intestine.