2022-05151 - Post-Doctoral Research Visit F/M Advanced computational design of cascaded metadeflectors for an ultra-flat antenna system

Contract type : Fixed-term contract

Renewable contract : Oui

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 Université Côte d’Azur center counts 36 research teams as well as 7 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.


The present postdoctoral project is part of a collaborative project between the Atlantis project-team from the Inria Research Center at Université Côte d'Azur,  (2) Thales R&T in Palaiseau, France, which is the main multidisciplinary research center of Thales group, and one of the main world players in professional electronics (3) and Nanoe in Ballainvilliers, France, whcih is  a SME (Small and Medium Entreprise) specialized  in development and fabrication of innovative ceramic materials for the industries.

Atlantis is  a joint project-team  between Inria and  the Jean-Alexandre Dieudonné Mathematics Laboratory at  Université Côte d'Azur. 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) modelling nanoscale light-matter interaction problems. In this context, the team is  developing  the   DIOGENeS  [https://diogenes.inria.fr/]  software suite,  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.


Enabling the Internet accessibility in mobility, in particular on board of public land and air transport (trains, buses, airliners), as well as the access to secure communication servers (for combat aircraft or military vehicles, etc.)requires the development of agile, ultra-flat and low-cost Ka-band antennas. Nonetheless, meeting the targeted performance while ensuring a low-profile and cost-effective antenna is a major challenge. To address it, the antenna architecture proposed in this project consists of a planar radiating panel associated with two compact deflectors, whose rotation ensures the beam-steering capacity. Moreover, the compactness and the moderate cost of the deflectors can be obtained thanks to the subwavelength structuration of a dielectric matter by usingadditive manufacturing. Indeed, the sub-wavelength patterning technique has recently shown the possibility to realize antenna components much thinner than their homogeneous bulk counterparts, with equivalent or even better radiofrequency performance.

In this context, the general objective of the present postdoctoral project is to develop an advanced numerical methodology for the virtual design of subwavelength structured deflectors and their cascading to achieve an ultra-flat Ka-band antenna system composed of two such metadeflectors. For this purpose, we will rely on recent achievements in our Inria team for the design of optical metasurfaces. More precisely, in [3] we have proposed and demonstrated an inverse design methodology that combines a high order finite element solver for time-domain nanophotonics [1] with a statistical learning-based global optimization method [2], which has been further extended for the multiobjective optimization of an achromatic metalens [3] and robust optimization of metadeflectors [4]. Here, our specific objectives will be (1) to adapt this inverse design methodology to the microwave regime and, (2) to substantially increase its computational efficiency for coping with the large-scale nature of the underlying application. For what concern the second objective, we will investigate two complementary directions: on the one hand, the evaluation cost of the objective function at each optimization iteration could be drastically reduced by designing a reduced order model for the parametrized time-domain Maxwell equations taking into account both material and geometry parameters (our recent contributions in [6]-[7] will serve as a basis for this research); on the other hand, the availability of both high and low fidelity electromagnetic solvers motivates the possibility of leveraging multifidelity optimization [8].

[1] S. Lanteri, C. Scheid and J. Viquerat. Analysis of a generalized dispersive model coupled to a DGTD method with application to nanophotonics. SIAM Journal on Scientific Computing, Vol. 39, No. 3, pp. A831–A859, 2017.

[2] Jones. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, Vol. 13, No. 4, pp. 455-492, 1998.

[3] M.R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M.S. Mohamed and P. Genevet, « Global optimization of metasurface designs using statistical learning methods », Scientific Reports, Vol. 9, No. 17918, 2019.

[4] M.R. Elsawy, A. Gourdin, M. Binois, R. Duvigneau, D. Felbacq, S. Khadir, P. Genevet and S. Lanteri, « Multiobjective statistical learning optimization of RGB metalens », ACS Photonics, Vol. 8, No. 8, pp. 2498–2508, 2021.

[5] M.R. Elsawy, M. Binois, R. Duvigneau, S. Lanteri and P. Genevet, « Optimization of metasurfaces under geometrical uncertainty using statistical learning », Optics Express, Vol. 29, pp. 29887-29898, 2021.

[6] Li, T.-Z. Huang, L. Li and S. Lanteri, « POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell's equations », Journal of Computational Physics, Vol. 396, pp. 106-128, 2019.

[7] Li, T.-Z. Huang, L. Li and S. Lanteri, « Non-intrusive reduced-order modeling of parameterized electromagnetic scattering problems using cubic spline interpolation », Journal of Scientific Computing, Vol. 87, Art. no. 52, 2021.

[8] L. Gratiet and J. Garnier. Recursive co-kriging model for design of computer experiments with multiple levels of fidelity. International Journal Uncertainty Quantification, Vol. 4, No. 5, pp. 365–386, 2014.


Main activities

Main activities: (1) Theoretical investigation of the mathematical and numerical techniques for reduced order modeling and multifidelity optimization, (2) formulation and study of the novel methodologies for addressing the above-mentioned specific objectives, (3) software development and validation activities, (4) application of novel methodologies to the desiggn of cascaded metadeflectors for an ultra-flat antenna system and, (5)   scientific publications, participation to conferences and technical meetings with the project partners.

Complementary activities: partiicpation to the development and valorization of the DIOGENeS software plaform with the other members of the Atlantis project-team.

The postdoctoral project will be carried out within a tight collaboration with Thales R&T (for the antenna system design) and with Nanoe (for the fabrication of the demonstrators). During the mission, occasional stays (1-2 weeks each time) will be organized at Thales R&T. The postdoctoral fellow will be able to benefit from Thales's expertise in the application fields of electronic and antenna components. He/she will work with a research engineer from Thales R&T on the design and optimization of the cascaded metadeflectors for an ultra-flat antenna system.



Academic background: Ph.D. in applied mathematics or scientific computing or electrical engineering.

Required knowledge and skills

  • Theory and methodology: computational electromagnetics, finite element methods for PDEs, reduced order modeling, numerical optimization
  • Programming: Fortran 2008, Python, MPI, OpenMP

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