2019-02128 - Post-Doctoral Research Visit F/M Computation of electromagnetic quasi-normal modes in nanostructures using contour integration techniques

Contract type : Fixed-term contract

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

Level of experience : From 3 to 5 years

About the research centre or Inria department

The Inria Sophia Antipolis - Méditerranée center counts 34 research teams as well as 8 support departments. The center's staff (about 500 people including 320 Inria employees) is made up of scientists of different nationalities (250 foreigners of 50 nationalities), engineers, technicians and administrative staff. 1/3 of the staff are civil servants, the others are contractual agents. The majority of the center’s research teams are located in Sophia Antipolis and Nice in the Alpes-Maritimes. Four teams are based in Montpellier and two teams are hosted in Bologna in Italy and Athens. The Center is a founding member of Université Côte d'Azur and partner of the I-site MUSE supported by the University of Montpellier.


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.


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.



Main activities

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.

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage


Gross Salary: 2653 € per month