Stability mapping of bipartite tight-binding graphs with losses and gain: PTPT-symmetry and beyond.

We consider bipartite tight-binding graphs composed by N nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability p. Specifically, we measure the connectivity between the two sets with the parameter α, which is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. For general undirected-graph setups, the non-Hermitian Hamiltonian H(γ,α,N) of this model presents pseudo-Hermiticity, where γ is the loss/gain strength. However, we show that for a given graph setup H(γ,α,N) becomes PT-symmetric. In both scenarios (pseudo-Hermiticity and PT-symmetric), depending on the parameter combination, the spectra of H(γ,α,N) can be real even when it is non-Hermitian. Then we demonstrate, for both setups, that there is a well-defined sector of the γα-plane (which grows with N) where the spectrum of H(γ,α,N) is predominantly real.

Engineering of the Fano resonance spectral response with non-Hermitian metasurfaces by navigating between exceptional point and bound states in the continuum conditions.

We address the engineering of Fano resonances and metasurfaces, by placing it in the general context of open non-Hermitian systems composed of coupled antenna-type resonators. We show that eigenfrequency solutions obtained for a particular case of scattering matrix are general and valid for arbitrary antenna radiative rates, thanks to an appropriate transformation of parametric space by simple linear expansion and rotation. We provide evidence that Parity-Time symmetry phase transition path and bound states in continuum (BIC) path represent the natural axis of universal scattering matrix solutions in this parametric coupling-detuning plane and determine the main characteristics of Fano resonance. Specifically, we demonstrate the control of asymmetry and sharpness of Fano resonance through navigation between BIC and PT-symmetric phase transition exceptional point. In particular, we demonstrate a fully symmetric Fano resonance in a system of two coupled bright and dark mode resonators. This result goes beyond current wisdom on this topic and demonstrates the universality of scattering matrix eigenfrequency solutions highlighted in our study. The validity of our approach is corroborated through comparison with experimental and full 3D numerical simulations results published in the literature making it thus possible to grasp a large body of experimental work carried out in this field. The detrimental impact of absorption losses on the contrast of the Fano resonance, which must be two orders of magnitude lower than the radiative losses, is also evidenced.

Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices.

I extend to the case of complex matrices, rather than the case of real matrices as in a prior study, a method of iterating the operation of an "inflating random matrix" onto a state vector to describe complex growing systems. I show that the process also describes in this complex case a punctuated growth with quakes and stasis. I assess that under one such inflation step, the vector will shift to a really different one (quakes) only if the inflated matrix has sufficiently dominant new eigenvectors. The vector shall prefer stasis (a similar vector) otherwise, similar to the real-valued matrices discussed in a prior study. Specifically, in order to extend the model relevance, I assess that under various update schemes of the system's representative vector, the bimodal distribution of the changes of the dominant eigenvalue remains the core concept. Overall, I contend that the punctuations may appropriately address the issue of growth in systems combining a large weight of history and some sudden quake occurrences, such as economic systems or ecological systems, with the advantage that unpaired complex eigenvalues provide more degrees of freedom to suit real systems. Furthermore, random matrices could be the right meeting point for exerting thermodynamic analogies in a reasonably agnostic manner in such rich contexts, taking into account the profusion of items (individuals, species, goods, etc.) and their networked, tangled interactions 50+ years after their seminal use in R.M. May's famous "interaction induced instability" paradigm. Finally, I suggest that non-ergodic tools could be further applied for tracking the specifics of large-scale evolution paths and for checking the model's relevance to the domains mentioned above.

Positive role of the long luminescence lifetime of upconversion nanophosphors on resonant surfaces for ultra-compact filter-free bio-assays.

We introduce a compact array fluorescence sensor principle that takes advantage of the long luminescence lifetimes of upconversion nanoparticles (UCNPs) to deploy a filter-free, optics-less contact geometry, advantageous for modern biochemical assays of biomolecules, pollutants or cells. Based on technologically mature CMOS chips for ∼10 kHz technical/scientific imaging, we propose a contact geometry between assayed molecules or cells and a CMOS chip that makes use of only a faceplate or direct contact, employing time-window management to reject the 975 nm excitation light of highly efficient UCNPs. The chip surface is intended to implement, in future devices, a resonant waveguide grating (RWG) to enhance excitation efficiency, aiming at the improvement of upconversion luminescence emission intensity of UCNP deposited atop of such an RWG structure. Based on mock-up experiments that assess the actual chip rejection performance, we bracket the photometric figures of merit of such a promising chip principle and predict a limit of detection around 10-100 nanoparticles.

Optimal [Formula: see text] -symmetric switch features exceptional point.

We consider the optimization problem of least energy-cost path in open systems that are described by non-Hermitian Hamiltonians. We apply it to find the optimal gain-loss profile for a non-uniform PT-symmetric coupler performing a binary transfer function. We bring evidence that the gain-loss profile fulfilling this requirement corresponds to a non-conventional situation where light intensity is conserved at every point along the PT-symmetric system. Besides, we find that the optimal profile corresponds to a practically important case of optical switching operation achieved with minimal amount of aggregate amplification level. We show that switching architectures using such type of gain-loss profiles are much more advantageous than conventional uniform PT-symmetric couplers in terms of gain and energy. Furthermore, this type of optimal profile turns out to be robust against fabrication imperfections. This opens new prospects for functional applications of PT-symmetric devices in photonics.

Simple wealth distribution model causing inequality-induced crisis without external shocks.

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent "r>g" (return rate > growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the "water-divide" of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.

Low-index nanopatterned barrier for hybrid oxide-free III-V silicon conductive bonding.

Oxide-free bonding of a III-V active stack emitting at 1300-1600 nm to a silicon-on-insulator wafer offers the capability to electrically inject lasers from the silicon side. However, a typical 500-nm-thick silicon layer notably attracts the fundamental guided mode of the silicon + III-V stack, a detrimental feature compared to established III-V Separate-Confinement Heterostructure (SCH) stacks. We experimentally probe with photoluminescence as an internal light source the guiding behavior for oxide-free bonding to a nanopatterned silicon wafer that acts as a low-index barrier. We use a sub-wavelength square array of small holes as an effective "low-index silicon" medium. It is weakly modulated along one dimension (superperiodic array) to outcouple the resulting guided modes to free space, where we use an angle-resolved spectroscopy study. Analysis of experimental branches confirms the capability to operate with a fundamental mode well localized in the III-V heterostructures.

Real time hybridization studies by resonant waveguide gratings using nanopattern imaging for Single Nucleotide Polymorphism detection.

2D imaging of biochips is particularly interesting for multiplex biosensing. Resonant properties allow label-free detection using the change of refractive index at the chip surface. We demonstrate a new principle of Scanning Of Resonance on Chip by Imaging (SORCI) based on spatial profiles of nanopatterns of resonant waveguide gratings (RWGs) and its embodiment in a fluidic chip for real-time biological studies. This scheme allows multiplexing of the resonance itself by providing nanopattern sensing areas in a bioarray format. Through several chip designs we discuss resonance spatial profiles, dispersion and electric field distribution for optimal light-matter interaction with biological species of different sizes. Fluidic integration is carried out with a black anodized aluminum chamber, advantageous in term of mechanical stability, multiple uses of the chip, temperature control and low optical background. Real-time hybridization experiments are illustrated by SNP (Single Nucleotide Polymorphism) detection in gyrase A of E. coli K12, observed in evolution studies of resistance to the antibiotic ciprofloxacin. We choose a 100 base pairs (bp) DNA target (~30 kDa) including the codon of interest and demonstrate the high specificity of our technique for probes and targets with close affinity constants. This work validates the safe applicability of our unique combination of RWGs and simple instrumentation for real-time biosensing with sensitivity in buffer solution of ~10 pg/mm². Paralleling the success of RWGs sensing for cells sensing, our work opens new avenues for a large number of biological studies.

Submicrometer 3D structures fabrication enabled by one-photon absorption direct laser writing.

We demonstrate a new 3D fabrication method to achieve the same results as those obtained by the two-photon excitation technique, by using a simple one-photon elaboration method in a very low absorption regime. Desirable 2D and 3D submicrometric structures, such as spiral, chiral, and woodpile architectures, with feature size as small as 190 nm have been fabricated, by using just a few milliwatts of a continuous-wave laser at 532 nm and a commercial SU8 photoresist. Different aspects of the direct laser writing based on ultralow one-photon absorption (LOPA) technique are investigated and compared with the TPA technique, showing several advantages, such as simplicity and low cost.

Switching using PT symmetry in plasmonic systems: positive role of the losses.

We analyze the operation of 2 × 2 switches composed of two coupled waveguides operating on the basis of parity-time (PT) symmetry: the two waveguides differ through their gain or loss factors and not through the real part of their propagation constant. Plasmonics constitutes a preferred application for such systems, since combination of plasmonics with gain is increasingly mastered. The exact PT-symmetric case (gain and loss of identical absolute value) is considered as well as various unbalanced cases, thanks to their respective switching diagrams. Although perfect signal-conserving cross and bar states are not always possible in the latter cases, they can nevertheless form the basis of very good switches if precise design rules are followed. We draw from the analysis what the optimal configurations are in terms of, e.g., guide gain or gain-length product to operate the switch. Many analytical or semi-analytical results are pointed out. A practical example based on the coupling of a long-range surface-plasmon-polariton and a polymeric waveguide having gain is provided.

Photonic crystal light-emitting sources.

Photonic crystals (PhCs) are periodically structured optical media offering the opportunity for spontaneous emission (SpE) to be strongly controlled in spatial terms (directions) or in absolute terms (rates). We discuss the application of this concept for practical light-emitting sources, summarizing the principles and actual merits of various approaches based on two- and three-dimensional PhCs. We take into consideration the numerous constraints on real-world light-emitting structures and materials. The various mechanisms through which modified photonic bands and band gaps can be used are first revisited in view of their use in light sources. We then present an in-depth discussion of planar emitters and enhanced extraction of light thanks to grating diffraction. Applications to conventional III-V semiconductors and to III-nitrides are reviewed. Comparison with random surface roughening reveals some common physical limitations. Some advanced approaches with complex structures or etched active structures are also discussed. Finally, the most promising mechanism to enhance the SpE rate, the Purcell effect, is considered. Its implementation, including through plasmonic effects, is shown to be effective only for very specific sources. We conclude by outlining the mix of physics and material parameters needed to grasp the relevant issues.

"Peak tracking chip" for label-free optical detection of bio-molecular interaction and bulk sensing.

A novel imaging method for bulk refractive index sensing or label-free bio-molecular interaction sensing is presented. This method is based on specially designed "Peak tracking chip" (PTC) involving "tracks" of adjacent resonant waveguide gratings (RWG) "micropads" with slowly evolving resonance position. Using a simple camera the spatial information robustly retrieves the diffraction efficiency, which in turn transduces either the refractive index of the liquids on the tracks or the effective thickness of an immobilized biological layer. Our intrinsically multiplex chip combines tunability and versatility advantages of dielectric guided wave biochips without the need of costly hyperspectral instrumentation. The current success of surface plasmon imaging techniques suggests that our chip proposal could leverage an untapped potential to routinely extend such techniques in a convenient and sturdy optical configuration toward, for instance for large analytes detection. PTC design and fabrication are discussed with challenging process to control micropads properties by varying their period (step of 2 nm) or their duty cycle through the groove width (steps of 4 nm). Through monochromatic imaging of our PTC, we present experimental demonstration of bulk index sensing on the range [1.33-1.47] and of surface biomolecule detection of molecular weight 30 kDa in aqueous solution using different surface densities. A sensitivity of the order of 10(-5) RIU for bulk detection and a sensitivity of the order of ∼10 pg mm(-2) for label-free surface detection are expected, therefore opening a large range of application of our chip based imaging technique. Exploiting and chip design, we expect as well our chip to open new direction for multispectral studies through imaging.

Implementation of PT symmetric devices using plasmonics: principle and applications.

The so-called PT symmetric devices, which feature ε((-x)) = ε((x))* associated with parity-time symmetry, incorporate both gain and loss and can present a singular eigenvalue behaviour around a critical transition point. The scheme, typically based on co-directional coupled waveguides, is here transposed to the case of variable gain on one arm with fixed losses on the other arm. In this configuration, the scheme exploits the full potential of plasmonics by making a beneficial use of their losses to attain a critical regime that makes switching possible with much lowered gain excursions. Practical implementations are discussed based on existing attempts to elaborate coupled waveguide in plasmonics, and based also on the recently proposed hybrid plasmonics waveguide structure with a small low-index gap, the PIROW (Plasmonic Inverse-Rib Optical Waveguide).

Photonic crystal patterning of luminescent sol-gel films for light extraction.

Structured luminescent thin films are investigated in the context of improved light extraction of phosphors for solid-state-lighting applications. Thin films composed of a sol-gel titania matrix doped with europium chelates are studied as a model system. These films, patterned with a square photonic lattice by soft nanoimprint lithography, are characterized by angle-resolved fluorescence. Modeling of this simple technique is shown to fit well the experimental data, revealing in great detail the guided modes of the film and their extraction parameters. An eightfold extraction enhancement factor of the film emission is measured. To further improve the extraction efficiency, we investigate the role of an additional low-index mesoporous silica underlayer through its influence on the guided modes of different polarizations and their interactions with the photonic crystal. Results obtained on model systems open the way towards the optimization of light-emitting devices, using a strategy of dielectric microstructure engineering using the sol-gel process.

General recipe for flatbands in photonic crystal waveguides.

We present a general recipe for tailoring flat dispersion curves in photonic crystal waveguides. Our approach is based on the critical coupling criterion that equates the coupling strength of guided modes with their frequency spacing and results in a significant number of the modes lying collectively in the slow-light regime. We first describe the critical coupling scheme in photonic crystal waveguides using a simple coupled mode theory model. We also determine that canonical photonic crystal waveguides natively correspond to strongly coupled modes. Based on these analyses, our design recipe is as follows: Tune the profile of the first Fourier component of the waveguide periodic dielectric boundary to lower the coupling strength of the guided modes down to its critical value. We check that this generalized tuning may be accomplished by adjusting any desired optogeometric parameter such as hole size, position, index etc. We explore the validity of this general approach down to the narrow two-missing rows waveguides. The interest of this method is to circumvent most of the common trial-and-error procedures for flatband engineering.

Detection of biological macromolecules on a biochip dedicated to UV specific absorption.

This work describes an ultraviolet biosensing technique based on specific molecular absorption detected with a previously developed spectrally selective aluminum gallium nitride (AlGaN) based detector. Light absorption signal of DNA and proteins, respectively at 260 nm and 280 nm, is used to image biochips. To allow detection of protein or DNA monolayers at the surface of a biochip, we develop contrast-enhancing multilayer substrates. We analyze them through models and experiments and validate the possibility of measuring absorptions of the order of 10(-3). These multilayer structures display a high reflectivity, and maximize the interaction of the electric field with the biological element at the chip surface. Optimization of the experimental absorption, which includes effects such as roughness of the biochip, spectral and angular resolution of the optics, illumination, etc., is carried out with an inorganic ultraviolet absorber (titanium dioxide) deposit. We obtained an induced absorption contrast enhanced by a factor of 4.0, conferring enough sensitivity to detect monolayers of DNA or proteins. Experimental results on an Escherichia coli histidine-tagged methionyl-tRNA synthetase protein before and after complexation with an anti-polyHis specific antibody validate our biosensing technique. This label-free optical method may be helpful in controlling biochip coatings, and subsequent biological coupling at the surface of a biochip.

Quantitative analysis of enhanced light irradiance in waveguide-based fluorescent microarrays.

Probing microarray assays in the presence of a hybridization mix retrieves precious information on hybridization kinetics. However, in common detection schemes, useful surface signals compete with the high supernatant background from labelled targets in the mix. A known solution consists in exciting specifically the microarray surface with evanescent fields. Configurations using planar optical waveguides to produce such fields are shown here to present also a dramatic excitation irradiance enhancement at the guide/surrounding matter interface. We compare theoretically and experimentally a guided excitation with a classical external excitation. A full electromagnetic analysis predicts an irradiance increase higher than 10(4) for adequately tailored waveguides. We deposited high-index TiO(2) sol-gel waveguides on glass substrates according to best simulations. Quantitative enhancement analysis exploiting actual biological fluorescent spots perfectly confirms the irradiance amplification effect of a thin waveguide. The impact of amplification on the design of biochip readers is discussed since it leaves ample margin for simple and low-cost light couplers, advantageous in affordable readers and sensor systems.

GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55 microm.

We haves realized and measured a GaAs nanocavity in a slab photonic crystal based on the design by Kuramochi et al. [Appl. Phys. Lett. 88, 041112 (2006)]. We measure a quality factor Q=700,000, which proves that ultrahigh Q nanocavities are also feasible in GaAs. We show that owing to larger two-photon absorption in GaAs nonlinearities appear at the microwatt level and will be more functional in gallium arsenide than in silicon nanocavities.

Innovative integrated system for real-time measurement of hybridization and melting on standard format microarrays.

Despite the great popularity and potential of microarrays, their use for research and clinical applications is still hampered by lengthy and costly design and optimization processes, mainly because the technology relies on the end point measurement of hybridization. Thus, the ability to monitor many hybridization events on a standard microarray slide in real time would greatly expand the use and benefit of this technology, as it would give access to better prediction of probe performance and improved optimization of hybridization parameters. Although real-time hybridization and thermal denaturation measurements have been reported, a complete walk-away system compatible with the standard format of microarrays is still unavailable. To address this issue, we have designed a biochip tool that combines a hybridization station with active mixing capability and temperature control together with a fluorescence reader in a single compact benchtop instrument. This integrated live hybridization machine (LHM) allows measuring in real time the hybridization of target DNA to thousands of probes simultaneously and provides excellent levels of detection and superior sequence discrimination. Here we show on an environmental single nucleotide polymorphism (SNP) model system that the LHM enables a variety of experiments unachievable with conventional biochip tools.

Integration of grating couplers with a compact photonic crystal demultiplexer on an InP membrane.

We demonstrate the integration of a 30% efficient grating coupler with a compact photonic crystal wavelength demultiplexer (DeMUX). The DeMUX has seven output channels that are spaced 10 nm apart and is aimed at coarse WDM applications. The integrated devices are realized on a high-index-contrast InP membrane using a simple benzocyclobutene wafer bonding technique. Cross talks of -10 to -12 dB for four channels 20 nm apart are obtained without optimization.