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We theoretically investigate the design of thin subwavelength gratings possessing high-reflectivity and high-$Q$ resonances when illuminated at normal incidence by a Gaussian beam. We compare the performances of single-period and dual-period rectangular gratings using Finite Element Method-based optimization and predict one to two orders of magnitude improvement in their transmission loss-linewidth product, which is the relevant figure of merit for e.g. resonant mirror-based microcavity applications.

We report on the theoretical and experimental investigations of optical microcavities consisting in the plane-plane arrangement of a broadband high-reflectivity mirror and a suspended one-dimensional grating mirror possessing a high-quality factor Fano resonance. By varying the length of these cavities from the millimeter to the few-micron range, we observe at short lengths the reduction of the spectral linewidth predicted to occur for such a Fano cavity as compared to a conventional broadband mirror cavity with the same length and internal losses. Such narrow linewidth and small modevolume microcavities with high-mechanical quality ultrathin mirrors will be attractive for a wide range of applications within optomechanics and sensing.

We report on the realization of ultrasensitive absolute pressure sensors based on silicon nitride membrane sandwiches. These sandwiches consist in a pair of highly-pretensioned, ultrathin (50 nm), large area (0.25 mm2) films, suspended parallel to each other and forming an ultrashort (500 nm), open cavity. The compression of a gas in this cavity leads to a strong squeeze film force, resulting in an increase in the membrane mechanical resonance frequencies which is directly proportional to the absolute gas pressure. These sandwiches show a record high responsitivity of >300 Hz/Pa in terms of squeeze film-induced frequency shift, which, combined with high quality factor mechanical resonances (Q>10^6), allows for bringing the sensitivity of absolute squeeze film pressure sensors down to the sub-millipascal level.

Patterns in biology can be considered as predetermined, or arising from a self-organizing instability. Variability in the pattern can thus be interpreted as a trace of an instability, growing out from noise. Variability can thus hint toward an underlying morphogenetic mechanism. Here we present the variability of the gastrovascular system of the Jellyfish Aurelia. In this variability emerge a typical biased reconnection between canals, and correlated reconnections. Both phenomena can be interpreted as traces of mechanistic effects, the swimming contractions on the tissue surrounding the gastrovascular canals, and the mean fluid pressure inside them, respectively. This reveals the gastrovascular network as a model system to study morphogenesis of circulation networks and the morphogenetic mechanisms at play.

A detailed investigation of the structural and vibrational properties of various prestressed silicon nitride membranes patterned with one-dimensional photonic crystal structures is presented. The tensile stress-related deformation of the structure in the vicinity of the patterned area is determined by Atomic Force Microscopy scans, while the resonance frequencies and quality factors of the out-of-plane membrane vibrations are measured using optical interferometry. We show that these noninvasive measurements, combined with results of finite element simulations, provide accurate knowledge on the tensile stress, the elasticity modulus and the density of these nanostructured thin films. The obtained results are interesting in two ways: first, they show that such highly reflective thin membranes already exploited in various photonics applications possess high-mechanical quality, which also makes them attractive for optomechanics and sensing applications. Second, they represent a nondestructive method to determine key material parameters which can be applicable to a broad range of fragile nanostructured thin films., Comment: 9 pages, 13 figures

We report on the design and experimental characterization of a suspended silicon nitride subwavelength grating possessing a polarization-independent guided-mode resonance at oblique incidence. At this resonant wavelength we observe that the transverse intensity profile of the transmitted beam is consistent with a first-order spatial differentiation of the incident beam profile in the direction of the grating periodicity, regardless of the incident light polarization. These observations are corroborated by full numerical simulations. The simple one-dimensional and symmetric design, combined with the thinness and excellent mechanical properties of these essentially loss-free dieletric films, is attractive for applications in optical processing, sensing and optomechanics.

The optical transmission of resonant guided-mode gratings patterned on suspended silicon nitride thin films and illuminated at normal incidence with a Gaussian beam are investigated both experimentally and theoretically. Effects due to the beam focusing and its finite size are accounted for by a phenomenological coupled mode model whose predictions are found to be in very good agreement with the experimentally measured spectra for various grating structures and beam sizes, and which allow for a detailed analysis of the respective magnitude of these effects. These results are highly relevant for the design and optimization of such suspended structured films which are widely used for photonics, sensing and optomechanics applications., Comment: 13 pages, 13 figures

The profile of suspended silicon nitride thin films patterned with one-dimensional subwavelength grating structures is investigated using Atomic Force Microscopy. We first show that the results of the profilometry can be used as input to Rigorous Coupled Wave Analysis simulations to predict the transmission spectrum of the gratings under illumination by monochromatic light at normal incidence and compare the results of the simulations with experiments. Secondly, we observe sharp vertical deflections of the films at the boundaries of the patterned area due to local modifications of the tensile stress during the patterning process. These deflections are experimentally observed for various grating structures and investigated on the basis of a simple analytical model as well as finite element method simulations.

We demonstrate first- and second-order spatial differentiation of an optical beam transverse profile using thin suspended subwavelength gratings. Highly reflective one-dimensional gratings are patterned on suspended 200 nm-thick silicon nitride membranes using Electron Beam Lithography and plasma etching. The optical transmission of these gratings, designed for illumination with either TM or TE polarized light, are experimentally measured under normal and oblique incidence and found to be in excellent agreement with the predictions of an analytical coupled-mode model as well as Rigorous Coupled Wave Analysis numerical simulations. High quality first- and second-order spatial differentiation of a Gaussian beam are observed in transmission at oblique and normal incidence, respectively. Such easy-to-fabricate, ultrathin and loss-free optical components may be attractive for beam shaping and optical information processing and computing.

Squeeze film pressure sensors, exploiting the dynamical modification of the mechanical properties of oscillating elements due to the compression of a fluid in a small gap region, allow for direct and absolute pressure measurements. This tutorial article discusses the working principles of membrane sandwich squeeze film pressure sensors, i.e. sensors consisting in a parallel arrangement of two large area, ultrathin suspended films forming a few-micron gap and immersed in a fluid, and focuses on their operation in the free molecular flow regime. The effects of gas pressure on the vibrations of the membrane resonators and their coupled dynamics are discussed in general terms before recent experimental implementations using high tensile stress silicon nitride membranes are presented., Comment: 8 pages, 10 figures

Noninvasive tuning of the mechanical resonance frequencies of suspended parallel nanomembranes in various monolithic arrays is achieved by piezoelectric control of their tensile stress. Parametric amplification of their thermal fluctuations is shown to be enhanced by the piezoelectric actuation and amplification factors of up to 20 dB in the sub-parametric oscillation threshold regime are observed.

We realize squeeze film pressure sensors using suspended, high mechanical quality silicon nitride membranes forming few-micron gap sandwiches. The effects of air pressure on the mechanical vibrations of the membranes are investigated in the range 10^-3-50 mbar and the intermembrane coupling induced by the gas is discussed in light of a squeeze film coupled-oscillator model. The high responsivity (several kHz/mbar) and the sub-pascal sensitivity of such simple pressure sensors are attractive for absolute and direct pressure measurements in rarefied air or high vacuum environments., Comment: 9 pages, 10 figures

Dynamic predictions of survival outcomes are of great interest to physicians and patients, since such predictions are useful elements of clinical decision-making. Joint modelling of longitudinal and survival data has been increasingly used to obtain dynamic predictions. A common assumption of joint modelling is that random-effects and error terms in the longitudinal sub-model are Gaussian. However, this assumption may be too restrictive, e.g. in the presence of outliers as commonly encountered in many real-life applications. A natural extension is to robustify the joint models by assuming more flexible distributions than Gaussian for the random-effects and/or error terms. Previous research reported improved performance of robust joint models compared to the Gaussian version in terms of parameter estimation, but dynamic prediction accuracy obtained from such approach has not been yet evaluated. In this study, we define a general robust joint model with t-distributed random-effects and error terms under a Bayesian paradigm. Dynamic predictions of graft failure were obtained for kidney transplant recipients from the French transplant cohort, DIVAT. Calibration and discrimination performances of Gaussian and robust joint models were compared for a validation sample. Dynamic predictions for two individuals are presented.

We investigate the electromechanical actuation of a pair of suspended silicon nitride membranes forming a monolithic optomechanical array. By controlling the membrane resonators' tensile stress via a piezoelectrically controlled compressive force applied to the membrane chip we demonstrate noninvasive tuning of their mechanical mode spectrum, as well as strong intermode electromechanical coupling. Piezoelectric actuation is also shown to enhance the nonlinear response of the membranes, which is evidenced either by parametric amplification of the fundamental mode thermal fluctuations or by resonant driving of these modes into high amplitude states. Such an electro-optomechanical membrane array represents an attractive tunable and versatile platform for sensing, photonics and optomechanics applications., Comment: 6 pages, 5 figures

We present a general framework for cavity quantum electrodynamics with strongly frequency-dependent mirrors. The method is applicable to a variety of reflectors exhibiting sharp internal resonances as can be realized, for example, with photonic-crystal mirrors or with two-dimensional atomic arrays around subradiant points. Our approach is based on a modification of the standard input--output formalism to explicitly include the dynamics of the mirror's internal resonance. We show how to directly extract the interaction tuning parameters from the comparison with classical transfer matrix theory and how to treat the non-Markovian dynamics of the cavity field mode introduced by the mirror's internal resonance. As an application within optomechanics, we illustrate how a non-Markovian Fano cavity possessing a flexible photonic crystal mirror can provide both sideband resolution as well as strong heating suppression in optomechanical cooling. This approach, amenable to a wide range of systems, opens up possibilities for using hybrid frequency-dependent reflectors in cavity quantum electrodynamics for engineering novel forms of light-matter interactions.

We report on the realization of silicon nitride membranes with enhanced and electrically tunable reflectivity. A subwavelength one-dimensional grating is directly patterned on a suspended 200 nm-thick, high stress commercial film using electron beam lithography. A Fano resonance is observed in the transmission spectrum of TM polarized light impinging on the membrane at normal incidence, leading to an increase in its reflectivity from 10% to 78% at 937 nm. The observed spectrum is compared to the results of rigorous coupled wave analysis simulations based on measurements of the grating transverse profile through localized cuts of the suspended film with a Focused Ion Beam. By mounting the membrane chip on a ring piezoelectric transducer and applying a compressive force to the substrate we subsequently observe a shift of the transmission spectrum by 0.23 nm., Comment: 8 pages, 5 figures

Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals. Based on these findings, we illustrate numerically how the application of such optical potentials can be used to tailor the normal mode spectra and patterns of multi-dimensional Coulomb crystals. The results represent, among others, important steps towards controlling the crystalline structure of Coulomb crystals, investigating heat transfer processes at the quantum limit and quantum simulations of many-body systems., Comment: 6+12 pages. arXiv admin note: substantial text overlap with arXiv:1703.05089

Radiation pressure forces in cavity optomechanics allow for efficient cooling of vibrational modes of macroscopic mechanical resonators, the manipulation of their quantum states, as well as generation of optomechanical entanglement. The standard mechanism relies on the cavity photons directly modifying the state of the mechanical resonator. Hybrid cavity optomechanics provides an alternative approach by coupling mechanical objects to quantum emitters, either directly or indirectly via the common interaction with a cavity field mode. While many approaches exist, they typically share a simple effective description in terms of a single force acting on the mechanical resonator. More generally, one can study the interplay between various forces acting on the mechanical resonator in such hybrid mechanical devices. This interplay can lead to interference effects that may, for instance, improve cooling of the mechanical motion or lead to generation of entanglement between various parts of the hybrid device. Here, we provide such an example of a hybrid optomechanical system where an ensemble of quantum emitters is embedded into the mechanical resonator formed by a vibrating membrane. The interference between the radiation pressure force and the mechanically modulated Tavis--Cummings interaction leads to enhanced cooling dynamics in regimes in which neither force is efficient by itself. Our results pave the way towards engineering novel optomechanical interactions in hybrid optomechanical systems., Comment: 19 pages, 5 figures

We investigate the optical properties of microcavities with suspended subwavelength structured mirrors, such as high-contrast gratings or two-dimensional photonic crystals slabs, and focus in particular on the regime in which the microcavity free-spectral range is larger than the width of a Fano resonance of the highly reflecting structured mirror. In this unusual regime, the transmission spectrum of the microcavity essentially consists in a single mode, whose linewidth can be significantly narrower than both the Fano resonance linewidth and the linewidth of an equally short cavity without structured mirror. This generic interference effect---occuring in any Fabry-Perot resonator with a strongly wavelength-dependent mirror---can be exploited for realizing small modevolume and high quality factor microcavities and, if high mechanical quality suspended structured thin films are used, for optomechanics and optical sensing applications., Comment: 4 pages, 5 figures

The effects of pressure on micromechanical air-filled cavities made by a pair of suspended, parallel silicon nitride membranes are investigated in the free molecular and quasi-molecular regimes. Variations of the fundamental drummode mechanical resonant frequencies and damping with air pressure are determined by means of optical interferometry. A kinetic damping linear friction force and a positive resonant frequency shift due to the compression of the fluid between the membranes are observed to be proportional with pressure in the range 0.01-10 mbars. For resonators with near-degenerate modes hybridization of the modes due to this squeeze film effect is also observed and well accounted for by a simple spring-coupled oscillator model., Comment: 4 pages, 3 figures

We experimentally investigate the transient dynamics of an optical cavity field interacting with large ion Coulomb crystals in a situation of electromagnetically induced transparency (EIT). EIT is achieved by injecting a probe field at the single photon level and a more intense control field with opposite circular polarization into the same mode of an optical cavity to couple Zeeman substates of a metastable level in 40Ca+ ions. The EIT interaction dynamics are investigated both in the frequency-domain - by measuring the probe field steady state reflectivity spectrum - and in the time-domain - by measuring the progressive buildup of transparency. The experimental results are observed to be in excellent agreement with theoretical predictions taking into account the inhomogeneity of the control field in the interaction volume, and confirm the high degree of control on light-matter interaction that can be achieved with ion Coulomb crystals in optical cavities., Comment: 15 pages, 10 figures

We demonstrate light-induced localization of Coulomb-interacting particles in multi-dimensional structures. Subwavelength localization of ions within small multi-dimensional Coulomb crystals by an intracavity optical standing wave field is evidenced by measuring the difference in scattering inside symmetrically red- and blue-detuned optical lattices and is observed even for ions undergoing substantial radial micromotion. These results are promising steps towards the structural control of ion Coulomb crystals by optical fields as well as for complex many-body simulations with ion crystals or for the investigation of heat transfer at the nanoscale, and have potential applications for ion-based cavity quantum electrodynamics, cavity optomechanics and ultracold ion chemistry.

We investigate structural resonances in multi-element optical resonators and provide a roadmap for the description of the interaction of single extended cavity modes with quantum emitters or mechanical resonators. Using a first principle approach based on the transfer matrix formalism we analyze, both numerically and analytically, the static and dynamical properties of three- and four-mirror cavities. We investigate in particular conditions under which the confinement of the field in specific subcavities allows for enhanced light-matter interactions in the context of cavity quantum electrodynamics and cavity optomechanics.

We report on the optical and mechanical characterization of arrays of parallel micromechanical membranes. Pairs of high-tensile stress, 100 nm-thick silicon nitride membranes are assembled parallel with each other with separations ranging from 8.5 to 200 $\mu$m. Their optical properties are accurately determined using a combination of broadband and monochromatic illuminations and the lowest vibrational mode frequencies and mechanical quality factors are determined interferometrically. The results and techniques demonstrated are promising for investigations of collective phenomena in optomechanical arrays., Comment: 5 pages, 5 figures

Optomechanical arrays made of structured flexible dielectrics are a promising system for exploring quantum and many-body optomechanical phenomena. We generalize investigations of the optomechanical properties of periodic arrays of one-dimensional scatterers in optical resonators to the case of vibrating membranes whose thickness is not necessarily small with respect to the optical wavelength of interest. The array optical transmission spectrum and its optomechanical coupling with a linear Fabry-Perot cavity field are investigated both analytically and numerically., Comment: 7 pages, 6 figures

We investigate the transport of phonons between $N$ harmonic oscillators in contact with independent thermal baths and coupled to a common oscillator, and derive an expression for the steady state heat flow between the oscillators in the weak coupling limit. We apply these results to an optomechanical array consisting of a pair of mechanical resonators coupled to a single quantised electromagnetic field mode by radiation pressure as well as to thermal baths with different temperatures. In the weak coupling limit this system is shown to be equivalent to two mutually-coupled harmonic oscillators in contact with an effective common thermal bath in addition to their independent baths. The steady state occupation numbers and heat flows are derived and discussed in various regimes of interest., Comment: 18 pages, 3 figures

We investigate the dynamics of a mechanical resonator in which is embedded an ensemble of two-level systems interacting with an optical cavity field. We show that this hybrid approach to optomechanics allows for enhanced effective interactions between the mechanics and the cavity field, leading for instance to ground state cooling of the mechanics, even in regimes, like the unresolved sideband regime, in which standard radiation pressure cooling would be inefficient., Comment: 9 pages, 4 figures

We investigate periodic optomechanical arrays as reconfigurable platforms for engineering the coupling between multiple mechanical and electromagnetic modes and for exploring many-body phonon dynamics. Exploiting structural resonances in the coupling between light fields and collective motional modes of the array, we show that tunable effective long-range interactions between mechanical modes can be achieved. This paves the way towards the implementation of controlled phononic walks and heat transfer on densely-connected graphs as well as the coherent transfer of excitations between distant elements of optomechanical arrays., Comment: 11 pages, 7 figures

We demonstrate that it is possible, with sub-micron precision, to locate the absolute center of a Fabry-P\'erot resonator oriented along the rf-field-free axis of a linear Paul trap through the application of two simultaneously resonating optical fields. In particular, we apply a probe field, which is near-resonant with an electronic transition of trapped ions, simultaneously with an off-resonant strong field acting as a periodic AC Stark-shifting potential. Through the resulting spatially modulated fluorescence signal we can find the cavity center of an 11.7 mm-long symmetric Fabry- P\'erot cavity with a precision of $\pm$135 nm, which is smaller than the periodicity of the individual standing wave fields. This can e.g. be used to position the minimum of the axial trap potential with respect to the center of the cavity at any location along the cavity mode., Comment: 6 pages, 4 figures; Text edited for clarity, results unchanged

We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend the results of [A. Xuereb, C. Genes, and A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]. We show that operating at the points where the array is transmissive results in linear optomechanical coupling strengths between the cavity field and collective motional modes of the array that may be several orders of magnitude larger than is possible with an equivalent reflective ensemble. We describe and interpret these effects in detail and investigate the nature of the scaling laws of the coupling strengths for the different transmissive points in various regimes., Comment: 14 pages, 14 figures, comments welcome. This is an expanded version of arXiv:1202.6210 with added interpretation and analysis

We present a scheme to strongly enhance the readout sensitivity of the squared displacement of a mobile scatterer placed in a Fabry-P\'erot cavity. We investigate the largely unexplored regime of cavity electrodynamics in which a highly reflective element positioned between the end mirrors of a symmetric Fabry-P\'erot resonator strongly modifies the cavity response function, such that two longitudinal modes with different spatial parity are brought close to frequency degeneracy and interfere in the cavity output field. In the case of a movable middle reflector we show that the interference in this generic "optical coalescence" phenomenon gives rise to an enhanced frequency shift of the peaks of the cavity transmission that can be exploited in optomechanics., Comment: 5 pages, 3 figures

We report one-dimensional pinning of a single ion by an optical lattice. The lattice potential is produced by a standing-wave cavity along the rf-field-free axis of a linear Paul trap. The ion's localization is detected by measuring its fluorescence when excited by standing-wave fields with the same period, but different spatial phases. The experiments agree with an analytical model of the localization process, which we test against numerical simulations. For the best localization achieved, the ion's average coupling to the cavity field is enhanced from 50% to 81(3)% of its maximum possible value, and we infer that the ion is bound in a lattice well with over 97% probability., Comment: 5 pages, 4 figures; Text edited for clarity, results unchanged

The goal of this work is to follow the displacement and possible deformation of a free particle in a fluid flow in 2D axi-symmetry, 2D or 3D using the classical finite elements method without the usual drawbacks finite elements bring for fluid-structure interaction, i.e. huge numerical problems and strong mesh distortions. Working with finite elements is a choice motivated by the fact that finite elements are well known by a large majority of researchers and are easy to manipulate. The method we describe in this paper, called the camera method, is well adapted to the study of a single particle in a network and most particularly when the study focuses on the particle behaviour. The camera method is based on two principles: 1/ the fluid structure interaction problem is restricted to a neighbourhood of the particle, thus reducing drastically the number of degrees of freedom of the problem; 2/ the neighbourhood mesh moves and rotates with the particle, thus avoiding most of the mesh distortions that occur in a standard ALE method. In this article, we present the camera method and the conditions under which it can be used. Then we apply it to several examples from the literature in 2D axi-symmetry, 2D and 3D., Comment: 24 pages, 19 figures

We investigate the collective optomechanics of an ensemble of scatterers inside a Fabry-Perot resonator and identify an optimized configuration where the ensemble is transmissive, in contrast with the usual reflective optomechanics approach. In this configuration, the optomechanical coupling of a specific collective mechanical mode can be several orders of magnitude larger than the single-element case, and long-range interactions can be generated between the different elements since light permeates throughout the array. This new regime should realistically allow for achieving strong single-photon optomechanical coupling with massive resonators, realizing hybrid quantum interfaces, and exploiting collective long-range interactions in arrays of atoms or mechanical oscillators., Comment: 11 pages, 12 figures

Quantum storage and retrieval of light in ion Coulomb crystals using cavity electromagnetically induced transparency is investigated theoretically. It is found that, when both the control and probe fields are coupled to the same cavity mode, their transverse mode profile affects the quantum memory efficiency in a non-trivial way. Under such conditions the control field parameters and crystal dimensions that maximize the memory efficiency are calculated., Comment: 15 pages, 7 figures

The transmission of a probe field experiencing electromagnetically induced transparency and optical switching in an atomic medium enclosed in an optical cavity is investigated. Using a semiclassical input-output theory for the interaction between an ensemble of four-level atoms and three optical cavity fields coupled to the same spatial cavity mode, we derive the steady-state transmission spectra of the probe field and discuss the dynamics of the intracavity field buildup. The analytical and numerical results are in good agreement with recent experiments with ion Coulomb crystals [M. Albert et al., Nature Photon. 5, 633 (2011)]., Comment: 11 pages, 9 figures

We propose to realize a passive optical quantum swapping device which allows for the exchange of the quantum fluctuations of two bright optical fields interacting with a coherent atomic medium in an optical cavity. The device is based on a quantum interference process between the fields within the cavity bandwidth arising from coherent population trapping in the atomic medium., Comment: 5 pages, 4 figures

A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between large ion Coulomb crystals in a linear quadrupole radiofrequency ion trap and a single field mode of a moderately high-finesse cavity are described in detail. Theoretical models based on a semiclassical approach are applied in assessment of the experimental results of [P. F. Herskind et al., Nature Phys. 5, 494 (2009)] and of complementary new measurements. Generally, a very good agreement between theory and experiments is obtained., Comment: 15 pages, 15 figures