Hidden land and changing landscape: Narratives about Mount Khangchendzonga among the Lepcha and the Lhopo

This article explores contemporary ‘hidden land’ narrative constructs of Máyel Lyáng and Beyul Dremojong in Sikkim, India, as conceived by the Lepcha and the Lhopo, two ‘scheduled tribes’. Lepcha and Lhopo narratives about these hidden lands in Mount Khangchendzonga inform us about their contemporary and historical, indigenous and Buddhist contexts and the interactions between these contexts. Lhopo perspectives on the hidden Beyul Dremojong echo classical Tibetan Buddhist ‘revealed treasure’ guidebooks and exist within the complex and reciprocal relationship between the Lhopo and the land they inhabit; development initiatives are understood to have caused illness and death in the Lhopo community of Tashiding, often referred to as the geographical ‘center’ of Beyul Dremojong. Contemporary Lepcha comprehensions of Máyel Lyáng, described in oral narratives within an ethnic community whose cosmology is intimately connected with Mount Khangchendzonga, today show some influence of Lhopo interpretations of Beyul Dremojong and the treasure texts; they also reflect Lepcha fears about cultural dispersion. Present-day narratives about both hidden lands reference notable political events in modern Sikkimese history (encounters with the British; the Chinese occupation of Tibet)

Stability and asymptotic properties of a linearized hydrodynamic medium model for dispersive media in nanophotonics

We analyze the stability of a linearized hydrodynamical model describing the response of nanometric dispersive metallic materials illuminated by optical light waves that is the situation occurring in nanoplasmonics. This model corresponds to the coupling between the Maxwell system and a PDE describing the evolution of the polarization current of the electrons in the metal. We show the well posedness of the system, polynomial stability and optimal energy decay rate. We also investigate the numerical stability for a discontinuous Galerkin type approximation and several explicit time integration schemes.

Curvilinear DGTD method for nanophotonics applications

International audienceClassical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries are indifferently straight or curved. This approximation represents serious hindrance for high-order methods, since they limit the precision of the spatial discretization to second order. Thus, exploiting an enhanced representation of the physical geometry of a considered problem is in agreement with the natural procedure of high-order methods, such as the discontinuous Galerkin method. In the latter framework, we propose and validate an implementation of a high-order mapping for tetrahedra, and then focus on specific nanophotonics setups to assess the gains of the method in terms of memory and performances

Etude de convergence a-priori d'une méthode Galerkin Discontinue en maillage hybride et non-conforme pour résoudre les équations de Maxwell instationnaires

Nous nous intéressons ici à une méthode Garlerkin Discontinue en Domaine Temporel (GDDT) pour la résolution numérique du système des équations de Maxwell instationnaires. Cette méthode est formulée sur des maillages hybrides et non-conformes combinant une triangulation non-structurée pour la discrétisation des objets de formes irrégulières avec une quadrangulation structurée (composée d'éléments orthogonaux de grandes tailles) pour le reste du domaine de calcul. Au sein de chaque élément, le champ électromagnétique est approximé pour une interpolation nodale d'ordre arbitrairement élevé, on utilise un flux centré pour les intégrales de surfaces et un schéma saute-mouton d'ordre 2 pour l'intégration en temps des équations semi-discrétisées associées. Le principal but est d'améliorer la flexibilité et l'efficacité de la méthode GDDT. Nous formulons les schémas de discrétisation en 3D, nous exposons la preuve détaillée de l'analyse mathématique de convergence a-priori en 3D. Enfin, la performance et la convergence numérique sont démontrées pour différents cas tests en 2D

Stability and asymptotic properties of a linearized hydrodynamic medium model for dispersive media in nanophotonics

International audienceWe analyze the stability of a linearized hydrodynamical model describing the response of nanometric dispersive metallic materials illuminated by optical light waves that is the situation occurring in nanoplasmonics. This model corresponds to the coupling between the Maxwell system and a PDE describing the evolution of the polarization current of the electrons in the metal. We show the well posedness of the system, polynomial stability and optimal energy decay rate. We also investigate the numerical stability for a discontinuous Galerkin type approximation and several explicit time integration schemes.

Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media.

This revised report has been publihed see: http://imajna.oxfordjournals.org/content/33/2/432This study is concerned with the solution of the time domain Maxwell's equations in a dispersive propagation media by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of equations is solved using a centered flux discontinuous Galerkin formulation for the discretization in space and a second order leap-frog scheme for the integration in time. The numerical treatment of the dispersive model relies on an Auxiliary Differential Equation (ADE) approach similarly to what is adopted in the Finite Difference Time Domain (FDTD) method. Stability estimates are derived through energy estimations and the convergence is proved for both the semi-discrete and the fully discrete case.On s'intéresse à la résolution numérique des équations de Maxwell en domaine temporel en milieu dispersif par une méthode Galerkin discontinue. Le caractère dispersif est ici pris en compte par le modèle de Debye. La méthode de résolution étudiée couple une formulation Galerkin discontinue à flux centré pour la discrétisation en espace et un schéma saute mouton du second ordre pour l'intégration en temps. Le traitement numérique du modèle dispersif repose sur une approche par équation différentielle auxiliaire à l'image de ce qui est réalisé dans la méthode de différences finies en domaine temporel. On étudie la stabilité du schéma résultant via des estimations d'énergie et prouvons la convergence des schémas semi-discrets et totalement discrets

Travelling Waves for the Nonlinear Schrödinger Equation with General Nonlinearity in Dimension Two

International audienceWe investigate numerically the two dimensional travelling waves of the Nonlinear Schrödinger Equation for a general nonlinearity and with nonzero condition at infinity. In particular, we are interested in the energy-momentum diagrams. We propose a numerical strategy based on the variational structure of the equation. The key point is to characterize the saddle points of the action as minimizers of another functional, that allows us to use a gradient flow. We combine this approach with a continuation method in speed in order to obtain the full range of velocities. Through various examples, we show that even though the nonlinearity has the same behaviour as the well-known Gross-Pitaevskii nonlinearity, the qualitative properties of the travelling waves may be extremely different. For instance, we observe cusps, a modified (KP-I) asymptotic in the transonic limit, various multiplicity results and ''one dimensional spreading'' phenomena

A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects

The interaction of light with metallic nanostructures is of increasing interest for various fields of research. When metallic structures have sub-wavelength sizes and the illuminating frequencies are in the regime of metal's plasma frequency, electron interaction with the exciting fields have to be taken into account. Due to these interactions, plasmonic surface waves can be excited and cause extreme local field enhancements (e.g. surface plasmon polariton electromagnetic waves). Exploiting such field enhancements in applications of interest requires a detailed knowledge about the occurring fields which can generally not be obtained analytically. For the latter mentioned reason, numerical tools as well as a deeper understanding of the underlying physics, are absolutely necessary. For the numerical modeling of light/structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2~nm to 25~nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this work, we present a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local dispersion model relevant to plasmonics. While the method is presented in the general 3d case, numerical results are given for 2d simulation settings only

Discontinuous Galerkin Time Domain Methods for Nonlocal Dispersion Models and Electron Beam Modeling in the Context of Nanoplasmonics

International audienceThis contribution consists of two main parts: non-local dispersion models and the numerical modeling of single electron beams. Both subjects are discussed in the context of computational nanophotonics for metallic nano-structures. Non-local dispersion models take into account the non-local nature of mutual electron interaction in the electron gas for metallic nano-structures. Contrary to local models (Drude, Drude-Lorentz,...), non-local models allow additional solutions such as electron density waves that can travel inside the metal bulk [1, 2]. However, these effects only appear for structures at the size of 2 nm to 25 nm. Electron beams traveling in the vicinity or inside metallic nano structures excite plasmons. Microscopy techniques like Electron Energy Loss Spectroscopy (EELS) and Cathodoluminescence (CL) are examples of applications. These technologies exploit the electron-plasmon interaction in order to measure plasmonic mode patterns [3]. Both physical aspects are numerically modeled in 3D discontinuous Galerkin time domain (DGTD) framework in order to provide a deeper understanding of the underlying physics

Discontinuous Galerkin Time-Domain method for nanophotonics

International audienceThe numerical study of electromagnetic wave propagation in nanophotonic devices requires among others the integration of various types of dispersion models , such as the Drude one, in numerical methodologies. Appropriate approaches have been extensively developed in the context of the Finite Differences Time-Domain (FDTD) method, such as in [1] for example. For the discontinuous Galerkin time-domain (DGTD), stability and convergence studies have been recently realized for some dispersion models, such as the Debye model [2]. The present study focuses on a DGTD formulation for the solution of Maxwell's equations coupled to (i) a Drude model and (ii) a generalized dispersive model. Stability and convergence have been proved in case (i), and are under study in case (ii). Numerical experiments have been made on classical situations, such as (i) plane wave diffraction by a gold sphere and (ii) plane wave reflection by a silver slab