2019-02128 - Post-Doctorant F/H Computation of electromagnetic quasi-normal modes in nanostructures using contour integration techniques

Type de contrat : CDD

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

Niveau d'expérience souhaité : De 3 à 5 ans

A propos du centre ou de la direction fonctionnelle

Le centre Inria Sophia Antipolis - Méditerranée compte 34 équipes de recherche, ainsi que 8 services d’appui à la recherche. Le personnel du centre (500 personnes environ dont 320 salariés Inria) est composé de scientifiques de différentes nationalités (250 personnes étrangères sur 50 nationalités), d’ingénieurs, de techniciens et d’administratifs. 1/3 du personnel est fonctionnaire, les autres sont contractuels. La majorité des équipes de recherche du centre sont localisées à Sophia Antipolis et Nice dans les Alpes-Maritimes. Quatre équipes sont implantées à Montpellier et deux équipes sont hébergés l'une à Bologne et l'autre à Athènes. Inria est membre fondateur d’Université Côte d'Azur et partenaire de l’I-site MUSE porté par l’Université de Montpellier.

Contexte et atouts du poste

This postdoctoral project will be conducted in the Nachos project-team at the Inria Sophia Antipolis-Méditerranée research center, in close collaboration with researchers from the Hiepacs project-team at the Inria Bordeaux - Sud-Ouest research center.

Nachos is  a  joint   project-team  between  Inria   and  the Jean-Alexandre Dieudonné  Mathematics Laboratory at  University Nice Sophia  Antipolis.   The  team   gathers  applied  mathematicians  and computational scientists who  are collaboratively undertaking research activities aiming at the design, analysis, development and application of innovative  numerical methods  for systems of  partial differential equations (PDEs) modeling nanoscale light-matter interaction problems. In this  context, the team  is developing the DIOGENeS  software suite [https://diogenes.inria.fr/],  which implements  several Discontinuous Galerkin  (DG) type  methods  tailored  to the  systems  of time-  and frequency-domain  Maxwell equations  possibly coupled  to differential equations  modeling  the behaviour  of  propagation  media at  optical frequencies. DIOGENeS is a unique numerical framework leveraging the capabilities of DG techniques for the simulation of multiscale problems relevant to nanophotonics and nanoplasmonics.

Hiepacs is a joint project-team with Bordeaux INP, Bordeaux University and CNRS (LaBRI UMR 5800).  The overarching objectiveof  the activities of the team is to perform efficiently frontier simulations arising from challenging research and industrial multiscale applications. The solution of these challenging problems require a multidisciplinary approach involving applied mathematics, computational and computer sciences. In applied mathematics, it essentially involves advanced numerical schemes. In computational science, it involves massively parallel computing and the design of highly scalable algorithms and codes to be executed on emerging extreme scale platforms. Through this approach, Hiepacs intends to contribute to all steps that go from the design of new high-performance more scalable, robust and more accurate numerical schemes to the optimized implementations of the associated algorithms and codes on veryhigh performance supercomputers. A central topic of the team is high performance solvers for linear algebra problems including sparse direct solver for heterogeneous platforms, hybrid direct/iterative solvers based on algebraic domain decomposition, linear Krylov solvers and eignesolvers.

Mission confiée

The recent  advances of nanoscale fabrication  techniques have enabled the  design  and manufacture  of  deep  subwavelength structures  that interact with light in exceptional ways.  Such nanostructures are used as building blocks  of a new generation of  nanophotonic devices, such as, for  instance, photovoltaic cells  for solar energy  harvesting or microLEDs for efficient light extraction. Numerical  simulations  are  very  helpful to  better  understand  the properties of these nanostructures,  and improve their efficiency.  In practice,  nanoscale  light-matter  interactions  can  be  studied  by considering the  system of Maxwell  equations with suitable  models of physical dispersion  in materials  (e.g., metals  and semiconductors). The  design  of  accurate  and efficient  numerical  methods  and  the development  of  scalable solvers  for  these  PDE models,  which  are capable  of dealing  with  large-scale three-dimensional  nanophotonic devices, is of paramount importance.

In  this  context, the  development  of  modal-type solvers  based  on so-called Quasi-Normal Modes (QNMs)  for the study  of resonant features  of  nanophotonic  and  plasmonic  devices  is  receiving  an increasing interest [1].   Indeed, once computed, QNMs can  be  combined to  recover  a  nanostructure  response in  a  large frequency  range.   However,  computing   QNMs  is  a  computationally expensive  task, which  amounts  to solving  a (sometimes  non-linear) generalized  eigenvalue   problem  for   the  underlying   PDE  model. Promising approaches to solve this  problem, which we will consider in this postdoctoral project, are based on Contour Integration (CI) techniques [2]-[3].  Contrary to traditional approaches that rely  on well-established numerical linear algebra techniques for the computation of eigenvalues and eigenvectors of the matrix  operator resulting from a  mesh-based discretization of the  underlying PDE  model,  in  the CI  formalism,  one uses  complex contour  integration to  calculate  the  eigenvectors associated  with eigenvalues that  are located inside  some user-defined region  in the complex  plane. One  attractive feature  of this  approach is  that it naturally induces  a parallel  process by  dividing the  complex plane into a collection of disjoint regions where eigenpairs can be computed concurrently.

Principales activités

In this postdoctoral project we will combine the expertise and knowhow of two  Inria project-teams.  The  Nachos project-team of  the Inria Sophia Antipolis-Méditerranée research center designs and develops fullwave solvers  for nanoscale  light-matter interactions,  which are based on high order discontinuous Galerkin methods. The methodological contributions    of    the    team    are    materialized    in    the DIOGENeS  [https://diogenes.inria.fr]  software  suite,   which is dedicated   to  computational   nanophotonics.   Several   high  order discontinuous Galerkin methods are implemented in this software suite for      solving      the      PDE     models      in      time-domain [4] and        frequency-domain [5] settings. The Hiepacs project-team of Inria  Bordeaux -  Sud-Ouest designs  and develops  scalable numerical linear  algebra  solvers  for  general  large  sparse  linear  matrix systems.    The  methodological   contributions   of   the  team   are materialized                         in                          the MaPHyS [https://gitlab.inria.fr/solverstack/maphys] algebraic domain       decomposition       solver         and       in       the Fabulous  [https://gitlab.inria.fr/solverstack/fabulous] versatile and flexible library  that implements block Krylov iterative methods for the solution of  linear systems of equations with multiple right-hand sides.

The  postdoctoral  fellow will  be  in  charge  of investigating,  implementing  and  assessing different  techniques  to compute  QNMs   of  three-dimensional  nanostructures.   He   will  in particular          study         the          FEAST         algorithm [3]  and       Beyn's      approach [2]  He will  rely on  the frequency-domain  DG solver  [5],   the    MaPHyS   algebraic   domain decomposition  solver and  numerical linear  algebra methods  from the Fabulous  library for  the design  of high  performance tools  for the computation of QNMs.  After  validating his initial implementations of these tools on synthetic examples, he will develop a new component of the  DIOGENeS  software   suitewhich  will  be   dedicated  to  the computation and exploitation  of QNMs for the  analysis of large-scale nanophotonic devices.

[1]  P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.P. Hugonin, Light interaction with photonic and plasmonic resonances, Las. Phot. Rev. 12 (2018), 1700113.
[2]  W.J. Beyn, An integral method for solving nonlinear eigenvalue problems, Lin. Alg. Appl. 236 (2012), 3839–3863.
[3]  B. Gavin, A. Miedlar, and E. Polizzi, FEAST eigensolver for nonlinear eigenvalue problems, J. Comput. Sci. 27 (2018), 107–117.
[4]  S. Lanteri, C. Scheid, and J. Viquerat, Analysis of a generalized dispersive model coupled to a DGTD method with application to nanophotonics, SIAM J. Sci. Comp. 39 (2017), no. 3, 831–859.
[5]  L. Li, S. Lanteri, and R. Perrussel, A hybridizable discontinuous Galerkin method com- bined to a Schwarz algorithm for the solution of 3d time-harmonic Maxwell’s equations, J. Comput. Phys. 256 (2014), 563–581.



Candidates must hold a PhD degree in applied mathematics or scientific computing.

Required knowledge and skills are:  a sound knowledge of  numerical analysis and development of finite element type methods for solving PDEs and numerical linear algebra techniques; a concrete experience in numerical modeling for computational electromagnetics; strong software development skills, preferably in Fortran 95/2008; a first experience with programming models for high performance computing systems.

A previous research exprience in computational nanophotonics will clearly be an asset for this position.


  • Restauration subventionnée
  • Transports publics remboursés partiellement
  • Congés: 7 semaines de congés annuels + 10 jours de RTT (base temps plein) + possibilité d'autorisations d'absence exceptionnelle (ex : enfants malades, déménagement)
  • Possibilité de télétravail (après 6 mois d'ancienneté) et aménagement du temps de travail
  • Équipements professionnels à disposition (visioconférence, prêts de matériels informatiques, etc.)
  • Prestations sociales, culturelles et sportives (Association de gestion des œuvres sociales d'Inria)
  • Accès à la formation professionnelle
  • Sécurité sociale


Salaire: 2653 € brut mensuel