New approach of diffraction of electromagnetic waves by a rough surface

We consider the diffraction of a plane wave by a rough surface. In the sake of simplicity the study is restricted to the case of perfectly conducting surfaces. Solving this problem is only possible by limiting the infinite rough surface to a window of width D. We show that we can obtain the diffraction pattern at infinity in the Fraunhofer zone from the modeling of diffraction by a grating with period D whose elementary pattern coincides with the rough surface in the window D. We give some numerical results for triangular profiles or rectified cosine. We show that for small heights we find that the most widely Kirchhoff approximation is very well checked. This modeling can be applied to Fraunhofer diffraction problem by a non-planar metal strip and the complementary problem of diffraction by a perfectly conducting screen, infinitely thin and with a slit of one or more periods

Diffraction gratings of isotropic negative phase-velocity materials

Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric--magnetic half--spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive or the negative negative phase-velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings - the Rayleigh-hypothesis method, a perturbative approach, and the C formalism - are extended here to encompass NPV gratings by a careful consideration of field representation inside the refracting half--space. Corrugations of both symmetric as well as asymmetric shapes are studied, as also the diversity of grating response to the linear polarization states of the incident plane wave. The replacement of PPV grating by its NPV analog affects only nonspecular diffraction efficiencies when the corrugations are shallow, and the effect on specular diffraction efficiencies intensifies as the corrugations deepen. Whether the type of the refracting material is NPV or PPV is shown to affect surface wave propagation as well as resonant excitation of surface waves.Comment: 28 pages, 10 figures in 27 file

Why is lateral root growth so variable? A framework to analyze growth variability among lateral roots and the possible roles of auxin and carbon

International audienceLateral root (LR) development is a major component of the efficiency of a plant to capture soil resources. A remarkable facet of lateral root behavior is stochasticity affecting the different stages of LR growth, leading to a large range of lateral root lengths along the primary root. It has been argued that such variability among LR could be an adaptive trait enabling a greater plasticity and efficiency of the root system in front of the spatial and temporal heterogeneity of soil resources (Forde, 2009). In order to characterize variability in LR growth and evaluate the role of hormonal and biochemical signals that might influence it, we analyzed the patterns of development of hundreds of lateral roots in a set of maize seedlings grown in rhizotrons. The SmartRoot toolbox was used to provide a comprehensive recording of individual root growth dynamics. Using a clustering method based on growth variables such as elongation rate and growth duration, we could identify 3 main different elongation patterns in maize LRs composed of accelerating, slowly decelerating and rapidly arrested LRs, as found in other species (Pagès, 1995). The molecular and cellular characterization of these root types revealed differences in meristem size, apical diameters as well as apical diameter variation. Moreover, fast growing roots showed increased sugar content along their tips. Finally, by affecting either the sugar or the auxin status (by pruning seminal roots or using auxin transport mutants) we differentially altered the proportion of the different root types, suggesting that both signals contribute to shape the root system in response to variations of environmental conditions.FORDE, B. (2009), J. Exp. Bot. 60 (14): 3989-4002PAGES, L. (1995), New Phytologist, 130: 503–50

Charge-Induced Fragmentation of Sodium Clusters

The fission of highly charged sodium clusters with fissilities X>1 is studied by {\em ab initio} molecular dynamics. Na_{24}^{4+} is found to undergo predominantly sequential Na_{3}^{+} emission on a time scale of 1 ps, while Na_{24}^{Q+} (5 \leq Q \leq 8) undergoes multifragmentation on a time scale \geq 0.1 ps, with Na^{+} increasingly the dominant fragment as Q increases. All singly-charged fragments Na_{n}^{+} up to size n=6 are observed. The observed fragment spectrum is, within statistical error, independent of the temperature T of the parent cluster for T \leq 1500 K. These findings are consistent with and explain recent trends observed experimentally.Comment: To appear in Physical Review Letter

Quenching dynamics in CdSe nanoparticles: surface-induced defects upon dilution

International audienceWe have analyzed the decays of the fluorescence of colloidal CdSe quantum dots (QDs) suspensions during dilution and titration by the ligands. A ligand shell made of a combination of trioctylphosphine (TOP), oleylamine (OA), and stearic acid (SA) stabilizes the as-synthesized QDs. The composition of the shell was analyzed and quantified using high resolution liquid state 1H nuclear magnetic resonance (NMR) spectroscopy. A quenching of the fluorescence of the QDs is observed upon removal of the ligands by diluting the stock solution of the QDs. The fluorescence is restored by the addition of TOP. We analyze the results by assuming a binomial distribution of quenchers among the QDs and predict a linear trend in the time-resolved fluorescence decays. We have used a nonparametric analysis to show that for our QDs, 3.0 0.1 quenching sites per QD on average are revealed by the removal of TOP. We moreover show that the quenching rates of the quenching sites add up. The decay per quenching site can be compared with the decay at saturation of the dilution effect. This provides a value of 2.88 0.02 for the number of quenchers per QD. We extract the quenching dynamics of one site. It appears to be a process with a distribution of rates that does not involve the ligands

Surface plasmon polaritons on thin-slab metal gratings

Ian R. Hooper and J. Roy Sambles, Physical Review B, Vol. 67, article 235404 (2003). "Copyright © 2003 by the American Physical Society."In a recently published paper [U. Schröter and D. Heitmann, Phys. Rev. B 60, 4992 (1999)] an unexpected result occurred when light was incident upon a periodically corrugated thin metal film when the corrugations on the two interfaces were identical and in phase with each other. It was observed that it was not possible to excite the surface plasmon polariton on the metal surface facing away from the incoming light, and they ascribed this to the lack of a thickness variation within the metal. In this paper a somewhat different interpretation of their results is presented, which shows that the surface plasmon polariton (SSP) is in fact very weakly excited on the transmission side of such structures. It is explained why this coupling is so weak in terms of the cancellation of the evanescent diffracted orders from the two diffractive surfaces and how, by changing the phase between the grating on either surface, this coupling becomes much stronger. An explanation for the observation that SPP excitation on such structures may lead to either transmission maxima or minima is also presented

Rough droplet model for spherical metal clusters

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\Delta$. We derive a simple analytic approximate expression determining $\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\Delta\simeq 0.6$ \AA~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.Comment: 20 pages, 4 figures, important modifications of the presentation, to appear in Phys. Rev.

Emma M. Payne, Casting the Parthenon Sculptures from the Eighteenth Century to the Digital Age

Depuis une vingtaine d’années, on assiste à un mouvement de récupération des collections de moulages, après des décennies où elles ont été malmenées. Tout au long du xixe siècle, les moulages ont eu une grande importance dans la réception de l’Antiquité. On les utilisait pour l’étude, l’enseignement et la collection. Pour l’étude, car ils permettaient aux chercheurs de comparer des œuvres, donc de bâtir une histoire de l’art, de faire de la Kopienforschung et de se rapprocher des œuvres orig..

Photonic bandgaps for grating-coupled waveguide modes with a silver tunnel barrier

Copyright © 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This is the published version of an article published in New Journal of Physics Vol. 9, article 251. DOI: 10.1088/1367-2630/9/8/251The optical properties of a periodically modulated photoresist waveguide structure has been explored using the Kretschmann–Raether configuration with a thin silver tunnel barrier. A detailed experimental study of how wavelength-scale periodic texture modifies the dispersion of the guided modes in the visible range for a wide range of azimuthal angles is presented. Fitting the observed in-plane momenta of the modes to predictions from a multilayer, multishape differential grating theory model allows the identities of each of the modes to be confirmed. In addition, the intensities obtained experimentally are compared favourably with those predicted from a theoretical model. Such a waveguide structure can produce not only the photonic bandgaps at the Brillouin zone boundary, but also bandgaps within the Brillouin zone caused by the Bragg scattered guided modes anti-crossing with the unscattered modes. All of these photonic bandgaps have potential applications controlling spontaneous emission in devices

Surface plasmon polaritons on narrow-ridged short-pitch metal gratings

Ian R. Hooper and J. Roy Sambles, Physical Review B, Vol. 66, article 205408 (2002). "Copyright © 2002 by the American Physical Society."The reflectivity of short pitch metal gratings consisting of a series of narrow Gaussian ridges in the classical mount has been modeled as a function of frequency and in-plane wave vector (the plane of incidence containing the grating vector) for various ridge heights. Surface plasmon polaritons (SPP’s) are found to be excited even in the zero-order region of the spectrum. These may result in strong absorption of radiation polarized with its electric field in the plane of incidence (transverse magnetic). For zero in-plane wave vector the SPP modes consist of a symmetric charge distribution on either side of the grating ridges, a family of these modes existing with different numbers of field maxima per grating period. Because of the charge symmetry these modes may only be coupled to at angles away from normal incidence where strong resonant absorption may then occur. The dispersion of these SPP modes as a function of the in-plane wave vector is found to be complex arising from the formation of very large band gaps due to the harmonic content of the grating profile, the creation of a pseudo high-energy mode, and through strong interactions between different SPP bands