Marcel FILOCHE

Résumé: The editors introduce the feature issue on “Beyond Order: Random, Aperiodic, and Hyperuniform Photonic Materials,” which includes nine articles.

Résumé: Localization of electronic wave functions in modern two-dimensional (2D) materials such as graphene can impact drastically their transport and magnetic properties. The recent localization landscape (LL) theory has brought many tools and theoretical results to understand such localization phenomena in the continuous setting, but with very few extensions so far to the discrete realm or to tight-binding Hamiltonians. In this paper, we show how this approach can be extended to almost all known 2D lattices and propose a systematic way of designing LL even for higher dimensions. We demonstrate in detail how this LL theory works and predicts accurately not only the locations, but also the energies of localized eigenfunctions in the low- and high-energy regimes for the honeycomb and hexagonal lattices, making it a highly promising tool for investigating the role of disorder in these materials.

Résumé: Band gap tunability of lead mixed halide perovskites makes them promising candidates for various applications in optoelectronics. Here we use the localization landscape theory to reveal that the static disorder due to iodide:bromide compositional alloying contributes at most 3 meV to the Urbach energy. Our modeling reveals that the reason for this small contribution is due to the small effective masses in perovskites, resulting in a natural length scale of around 20 nm for the “effective confining potential” for electrons and holes, with short-range potential fluctuations smoothed out. The increase in Urbach energy across the compositional range agrees well with our optical absorption measurements. We model systems of sizes up to 80 nm in three dimensions, allowing us to accurately reproduce the experimentally observed absorption spectra of perovskites with halide segregation. Our results suggest that we should look beyond static contribution and focus on the dynamic temperature dependent contribution to the Urbach energy.

Résumé: The diffraction and absorption of waves by a system with both absorbing properties and irregular geometry is an open physical problem. A more reachable and closely related question is the understanding of wave oscillations in confined systems containing an absorbing material with an irregular shape. This has to be solved to understand why anechoic chambers (electromagnetic or acoustic) do work better with irregular absorbing walls. The answer to this question could also be used in other fields such as light or microwave absorption, or also to improve the performances of break-waters in order to damp sea-waves. It is found here that, in resonators containing an irregular shaped absorbent material, there appears a new type of mode localization. This phenomemon, that we call “astride” localization, describes the fact that these modes exist in both the lossless and the lossy regions. It is these modes that are particularly efficient in dissipating the energy of waves excited in the non-absorbing region.

Résumé: Based on numerical studies, we show that localisation is a common phenomenon in resonators exhibiting some kind of geometrical complexity. In two- dimensional (2d) shallow cavities of irregular shape, localisation effects are due to spatial decoherence in a major fraction of the volume. In 2d shallow cavities of regular geometry with embedded absorbing material of irregular shape, one observes the appearance of eigenmodes localised in both, the absorbing and the non-absorbing media. Those modes are thought to be responsible for increased dissipation. These results may be a hint to understand why natural or practical systems absorbing wave energy are found, or built, with complex geometry.

Résumé: Semi-permeable interfaces of irregular geometry accessed by diffusion exhibit complex transfer properties. In particular, their transfer impedance is the non-trivial result of the interplay between their geometry and their physical properties. In this paper, we present a new method that we call toposcopy. Its aim is to solve the “inverse impedance spectroscopy problem”, namely to retrieve the geometrical features of an irregular interface from a “black box” measurement of its transfer impedance only. From previous studies, one knows that all the possible information about the geometry of an interface that can be extracted from a measurement of its impedance consists in its harmonic geometrical spectrum, a set of spectral characteristics of the Dirichlet- to-Neumann operator of the same interface. Here, we first describe how the toposcopy technique permits to retrieve the main components of the harmonic geometrical spectrum and to deduce from them characteristic geometrical features of the interface. The toposcopy is then tested numerically for several irregular interfaces of either simple or complex shape. It is finally shown that this method gives access to the characteristics lengths of these interfaces and, when these lengths are sufficiently different, allows to separate and quantify their respective contributions to the interface impedance.

Résumé: The present study is concerned with the properties of 2D shallow cavities having an irregular boundary. The eigenmodes are calculated numerically on various examples, and it is shown first that, whatever the shape and characteristic sizes of the boundary, irregularity always induces an increase of localized eigenmodes and a global decrease of the existence surface of the eigenmodes. Besides, irregular cavities are shown to exhibit specific damping properties. As expected, the increased damping, compared to a regular cavity, is related first to the larger perimeter to surface ratio. But more interestingly, there is a specific enhancement of the dissipation for those modes that are localized near the boundary, modes which are favored by the geometric irregularity.

Résumé: The theory of Laplacian transport towards and across irregular surfaces is reformulated in terms of the Dirichlet-to-Neumann operator and its spectral characteristics. This permits us to obtain an exact equivalent circuit for the impedance of a working interface of arbitrary shape. The important result is that only very few eigenmodes of this operator do govern the entire response of a macroscopic system. This property drastically simplifies the understanding of irregular or prefractal interfaces. The results can be applied in electrochemistry, physiology and chemical engineering, fields where exchange processes across surfaces with complex geometry are ubiquitous.

Résumé: This paper presents seven results on irregular systems that are both new and can be described simply. The first three results are related to dynamical and static properties of gradient percolation. Firstly, it is shown that the transient regimes which lead to self-organized gradient percolation due to corrosion do not scale like gradient percolation itself. Secondly, it is shown that there is no diffusion front in 1-D but there exists a zone of fluctuations with a size of the order of the system size. Thirdly, the geometry of realistic intermetallic contacts in 3-D is shown to be closely related to that of diffusion fronts, but different. The two next results are related to reactive irregular surfaces. Firstly, molecular dynamics results indicates that, in 2-D, the size of the active zone of purely absorptive surfaces in the Knudsen diffusion regime is larger than that found in the molecular diffusion regime. Secondly, it is then shown that, in this last regime, the particles that really interacts with the surface, remains near the surface within a distance equal to the unscreened perimeter length. The following topic is related to the vibrations of deterministic surface fractals: with very good approximation, the extended disordered modes can be described as a superposition of regular (non-localized) trivial modes of the initiator of the fractal morphology. Finally, it is shown that the diffusion reorganized This paper presents seven results on irregular systems that are both new and can be described simply. The first three results are related to dynamical and static properties of gradient percolation. Firstly, it is shown that the transient regimes which lead to self-organized gradient percolation due to corrosion do not scale like gradient percolation itself. Secondly, it is shown that there is no diffusion front in 1-D but there exists a zone of fluctuations with a size of the order of the system size. Thirdly, the geometry of realistic intermetallic contacts in 3-D is shown to be closely related to that of diffusion fronts, but different. The two next results are related to reactive irregular surfaces. Firstly, molecular dynamics results indicates that, in 2-D, the size of the active zone of purely absorptive surfaces in the Knudsen diffusion regime is larger than that found in the molecular diffusion regime. Secondly, it is then shown that, in this last regime, the particles that really interacts with the surface, remains near the surface within a distance equal to the unscreened perimeter length. The following topic is related to the vibrations of deterministic surface fractals: with very good approximation, the extended disordered modes can be described as a superposition of regular (non-localized) trivial modes of the initiator of the fractal morphology. Finally, it is shown that the diffusion reorganized

Résumé: Peripheral airways combine branched tubes for ventilation with the gas exchanging alveoli in the pulmonary acini, defined as the complex of airways supplied by one first order respiratory or transitional bronchiole. In this part, the replenishment of oxygen at the alveolar surface occurs by a combination of convective air flow with diffusion of oxygen in the air. The transition between convection and diffusion depends on the morphometric properties of the airways. The design of the peripheral airways in the acinus of the human lung is described quantitatively on the basis of measurements obtained on casts of the acinar airways. Comparable data for rat and rabbit are also discussed. On the basis of this morphometric information, a typical path model for human acinar airways is derived. These studies also form the basis for advanced modeling studies of gas exchange and ventilation. In particular the problems occurring because of diffusional screening and the design conditions for minimizing this effect are discussed.

Résumé: An exact ‘‘branch by branch’’ calculation of the diffusional flux is proposed for partially absorbed random walks on arbitrary tree structures. In the particular case of symmetric trees, an explicit analytical expression is found which is valid whatever the size of the tree. Its application to the respiratory phenomena in pulmonary acini gives an analytical description of the crossover regime governing the human lung efficiency.

Résumé: The progressive deactivation of catalytic surfaces, either by parallel or serial fouling, is a key problem in heterogeneous catalysis. A mathematical model of the deactivation of a catalytic reactor is presented. It is shown that this dynamical model can be turned into the study of the steady-state non-linear response of the same system but for a virtual species. This mapping of the problem permits to obtain analytical results such as the duration of the reactor or its total production. As an example, one shows how a fractal surface would respond in such a deactivation process. Finally, a way to control the time dependency of the reactor production is suggested.

Résumé: The possibility to renormalize random walks is used to study numerically the oxygen diffusion and permeation in the acinus, the diffusion cell terminating the mammalian airway tree. This is done in a 3D tree structure which can be studied from its topology only. The method is applied to the human acinus real morphology as studied by Haefeli-Bleuer and Weibel in order to compute the respiratory efficiency of the human lung. It provides the first quantitative evidence of the role of diffusion screening in real 3D mammalian respiration. The net result of this study is that, at rest, the efficiency of the human acinus is only of order 33%. Application of these results to CO2 clearance provides for the first time a theoretical support to the empirical relation between the O2 and CO2 partial pressures in blood.

Résumé: The problem of the Laplacian transfer across an irregular resistive interface (a membrane or an electrode) is investigated with use of the Brownian self-transport operator. This operator describes the transfer probability between two points of a surface, through Brownian motion in the medium neighbour- ing the surface. This operator governs the flux across a semi-permeable membrane as diffusing particles repetitively hit the surface until they are finally absorbed. In this paper, we first give a theoretical study of the properties of this operator for a planar membrane. It is found that the net effect of a decrease of the surface permeability is to induce a broadening of the region where a particle, first hitting the surface on one point, is finally absorbed. This result constitutes the first analytical justification of the Land Surveyor Approximation, a formerly developed method used to compute the overall impedance of a semi-permeable membrane. In a second step, we study numerically the properties of the Brownian self-transport operator for selected irregular shapes.

Résumé: Uniform flow distribution in a symmetric volume can be realized through a symmetric branched tree. It is shown here, however, by 3D numerical simulation of the Navier-Stokes equations, that the flow partitioning can be highly sensitive to deviations from exact symmetry if inertial effects are present. The flow asymmetry is quantified and found to depend on the Reynolds number. Moreover, for a given Reynolds number, we show that the flow distribution depends on the aspect ratio of the branching elements as well as their angular arrangement. Our results indicate that physiological variability should be severely restricted in order to ensure adequate fluid distribution through a tree.

Résumé: The concept of an active zone in Laplacian transport is used to obtain an ana- lytical approximation for the reactive effectiveness of a pore with an arbitrary rough geometry. We show that this approximation is in very good agreement with direct numerical simulations performed over a wide range of diffusion-reaction conditions (i.e., with or without screening effects). In particular, we find that in most practical situations, the effect of roughness is to increase the intrinsic reaction rate by a geometrical factor, namely the ratio between the real and the apparent surface area. We show that this simple geometrical piece of information is suf- ficient to characterize the reactive effectiveness of a pore, in spite of the complex morphological features it might possess.

Résumé: Numerical simulations of the water dissolution of a random ternary solid are presented. The three elements represent silica, soluble oxides (alkalis and boron) and quasi-insoluble oxides (Al2O3, ZrO2, Fe2O3, . . .). The soluble species are dissolved immediately when they are in contact with the solution. Their proportion is kept below the percolation threshold. For the other species, one introduces a model of dissolution-recondensation. It is shown that the dissolution rate constants should be dependent on the bonding environment in order to include surface tension. The condensation fluxes are proportional to the concentration of each species in solution. In the dynamic regime (no recondensation), one observes the congruent dissolution of silica and soluble species, after a short initial phase of selective extraction of the soluble species. The common rate of dissolution decreases with the proportion of insoluble species and increases sharply with that of soluble species. This is mainly due to the formation of a porous hydrated layer whose active surface area increases markedly with the proportion of soluble species. In the static regime (finite solution volume), the equilibrium solubility of silica decreases with the proportion of insoluble species and is practically independent of the proportion of soluble species. The porous hydrated layer is rearranged and almost free of soluble species. The ripening of the surface layer makes it protective and inhibits further extraction of the soluble species. These results are in general agreement with the experimental observations on the dissolution of durable glasses.

Résumé: We describe a simple way to understand the non-linear response of an irregular resistive electrode in d=2. It is based on the concept of an active zone in the Laplacian transfer to and across irregular interfaces. It applies to arbitrary electrode geometry and permits to compute the flux across an irregular electrode from its geometry without solving the Laplace problem. The simplifying arguments that are used are tested numerically on prefractal models of the geometrical irregularity. One finds that, for electrodes following a local Butler–Volmer response, the Tafel slope depends on the geometry. It is shown that the measure of the cell impedance leads to the determination of the actual active potential. It also gives the mean size of a part of the electrode with a surface impedance equal to the electrolyte bulk resistivity

Résumé: We showed recently that the high-salt transition of poly[d(G-C)] z poly[d(G-C)] between B-DNA and Z-DNA (at [NaCl] 5 2.25 M or [MgCl2] 5 0.7 M) can be ascribed to the lesser electrostatic free energy of the B form, due to better immersion of the phosphates in the solution. This property was incorporated in cylindrical DNA models that were analyzed by Poisson-Boltzmann theory. The results are insensitive to details of the models, and in fair agreement with experiment. In contrast, the Z form of the poly[d(G-m5C)] duplex is stabilized by very small concentrations of magnesium. We now show that this striking difference is accommodated quantitatively by the same electrostatic theory, without any adjustable parameter. The different responses to magnesium of the methylated and nonmethylated polymers do not come from stereospecific cation-DNA interactions: they stem from an experimentally derived, modest difference in the nonelectrostatic component of the free energy difference (or NFED) between the Z and B forms. The NFED is derived from circular DNA measurements. The differences between alkaline earth and transition metal ions are explained by weak coordination of the latter. The theory also explains the induction of the transition by micromolar concentrations of cobalt hexammine, again without specific binding or adjustable parameters. Hence, in the case of the B-Z transition as in others (e.g., the folding of tRNA and of ribozymes), the effect of multivalent cations on nucleic acid structure is mediated primarily by nonspecific ion-polyelectrolyte interactions. We propose this as a general rule for which convincing counter-examples are lacking.

Résumé: The flux across resistive irregular interfaces driven by a force deriving from a Laplacian potential is computed on a rigorous basis. The theory permits one to relate the size of the active zone Aact. to the derivative of the spectroscopic impedance Zspect.(r) with respect to the surface resistivity r through: d(Zspect.)/dr = A_act^−1 . It is shown that the macroscopic transfer properties through a system of arbitrary shape are determined by the characteristics of a first-passage interface-interface random walk operator. More precisely, it is the distribution of the harmonic measure (or normalized primary current) on the eigenmodes of this linear operator that controls the transfer. In addition, it is also shown that, whatever the dimension, the impedance of a weakly polarizable electrode for any irregular geometry scales under a homothety transformation as L^d−1, L being the size of the system and d its topological dimension. In this new formalism, the question addressed in the title is transformed in a open mathematical question: “Knowing the distribution of the harmonic measure on the eigenmodes of the self-transport operator, can one retrieve the shape of the interface?”

Résumé: This paper presents a self-consistent 1-D multiquantum-well laser simulation in which, for the ®rst time, the SchroÈ dinger equation is solved over the whole quantum-well zone, taking into account well-to-well coupling. The computed light-intensity curve is com- pared with experimental results for an InGaAs/InGaAsP multiquantum-well laser and also with simpli®ed models. The quantum calculation has an important in ̄uence on the carrier density pro®le in the active region. This results in a signi®cant difference in the estimation of the threshold current with respect to other simpli®ed models.

Résumé: We present a detailed numerical test of the coarse-graining method proposed by Sapoval to compute the flux through an irregular interface in the case where the local response is inhomogeneously distributed. It is shown, through comparison with detailed finite elements simulations, that this method permits to deduce the flux across an irregular interface from its topography only, as for example in the case of non-uniform polarizability in electrochemistry. The interest of the method lies in its computational simplicity. It then constitutes an essential step towards the understanding of the flux across irregular interfaces in non-linear regimes.

Résumé: We demonstrate theoretically and experimentally that one-dimensional plasmons confined in doped wires are either extended or longitudinally confined when the lateral width of the wires is periodically modulated. Theoretical dispersion curves, calculated within a classical framework, reproduce well the experimental dis- persion deduced from Raman scattering on deep etched modulated wires. Zone-edge gap openings, increasing with the modulation amplitude, are exhibited. We show that deep etching allows good control of complex geometries and provides quasiabrupt boundary conditions.

Résumé: We report here on the design and the first realization of a grating-assisted horizontal directional coupler filter exhibiting a highly reduced polarization sensitivity. The filter, which is based on InP-InGaAsP materials, is particularly suitable for integration in a 1.3/spl plusmn/1.3 μm duplexer. A polarization dependence below 1 dB has been measured for the separation of two 10 nm wide channels, respectively centered at 1.28 μm and 1.32 μm, for a rejection ratio of 10 dB.

Résumé: We report what is to our knowledge the first optimization of a spot size transformer by use of a periodically segmented waveguide for photonic integrated circuits based on InP. It is shown that a nonlinear variation of the segmentation ratio along the propagation direction allows one to make an adiabatic transition of a short length. A simple method based on the study of a beveled edge transition is presented for the optimization of such a device. Internal losses in the transition region as low as 1.2 dB are obtained between a coupling waveguide and a simple heterostructure waveguide, with a very high transition spot size expansion factor.

Résumé: The emitter base threshold voltage is found to be a very effcient method of characterising p-type dopant diffusionin highly doped heterojunction bipolar transistors. Simulated curves have been successfully used to determine the amount of diffusion at different doping levels, showing the ability of MOCVD to achieve a high base doping level without any dopant diffusion.