PhD Position F/M [DOCT2024-ATLANTIS] Advanced numerical modeling for time-varying metasurface modulation

The Inria centre at Université Côte d'Azur includes 37 research teams and 8 support services. The centre's staff (about 500 people) is made up of scientists of different nationalities, engineers, technicians and administrative staff. The teams are mainly located on the university campuses of Sophia Antipolis and Nice as well as Montpellier, in close collaboration with research and higher education laboratories and establishments (Université Côte d'Azur, CNRS, INRAE, INSERM ...), but also with the regiona economic players.
With a presence in the fields of computational neuroscience and biology, data science and modeling, software engineering and certification, as well as collaborative robotics, the Inria Centre at Université Côte d'Azur  is a major player in terms of scientific excellence through its results and collaborations at both European and international levels.

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.

The last  ten years have  seen an impressive  amount of work  aimed at developing thin  metamaterials to control the wavefront of  light and design planar photonic  devices. The concept of the  metasurface is at the heart of almost all discoveries in this  field.  Metasurfaces are arrays   of   optically   thin    elements,   called   meta-atoms or nanoresonators,  that enable  optical  behaviors distinctly  different from    those     observed    in conventional three-dimensional metamaterials. However,  most of the planar  photonic devices proposed to date  are based on  passive metasurfaces whose functions  are fixed during fabrication. In other words, the geometrical characteristics of nanoresonators  are  set  a  priori to  achieve  the  desired  optical functionality.    However,   modern applications   require   dynamic manipulation  of  light  waves  through the  application  of  external stimuli.   In general,  this  is achieved  by  fixing the  geometrical characteristics  of the  nano-resonators and  forming the  metasurface building blocks from active  materials such as phase-change materials, liquid  crystals  or  electro-optically responsive  materials.   In  a passive metasurface,  the refractive  index of the  nano-resonators is modulated in space  while remaining fixed in time. On  the other hand, the ultrafast modulation  of light, on the order of  a fraction of the optical  frequency,  offers  exceptional prospects  for  applications, particularly  with  the  emerging  innovative  concept  of  space-time modulated  metasurfaces.

Numerical modeling is an essential path to study space-time metasurface modulation. Generally speaking, one needs to model rigorously inside Maxwell’s equations heterogeneous materials with time-varying response. The well-known Finite-Difference-Time Domain (FDTD) method [TH05] has been considered for this task, but the existing works are rather rare and limited to simple applications [Liu04]. The FDTD method solves the time-domains Maxwell equation on a structured (Cartesian) grid. FDTD is a conceptually simple and computationally efficient numerical method but its accuracy is limited when dealing with complex geometries and in the presence of multiscale features such as the ones raised when modeling the interaction of an electromagnetic wave with space-time modulated materials. Alternative approaches making use of an unstructured (finite element type) grid.   The Discontinuous Galerkin Time-Domain (DGTD) method [Viq15] is such an approach, which is nowadays very popular in the computational electromagnetic community. DGTD can be viewed as a blending of classical (continuous) finite element and finite volume methods, merging the best of these two families of methods (i.e. high order accuracy, flexibility with regards to the type of mesh used for discretization of complex objects, etc.). The DGTD fullwave solver introduced in [Viq15]  is one component of the DIOGENeS software suite.

In the present Ph.D. project, a first objective will be to formalize and develop the appropriate modeling for solving Maxwell’s equations with space-time material variations. In particular, we will rely on and extend the high order DGTD method initially introduced in [Viq15]. The second objective will be to apply the developed rigorous fullwave DGTD solver to the study and design of space-time modulated metasurfaces. For that purpose, we will benefit from our experience in the field of passive metasurface design [MELS19, MELS21] for optimizing spatiotemporal metasurfaces at optical and NIR regimes, and achieve exceptional and exotic functionalities at the optical frequency speed. This Ph.D. will take place in the Atlantis project-team at the Inria research center at Université Côte d’Azur in Sophia Antipolis. Moreover, this Ph.D. project will be conducted in close collaboration with our physical partners for the indispensable physical interpretation and potential applications.

[GE11] N. Yu, P. Genevet, M.A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso and Z. Gaburro, « Light propagation with phase discontinuities: generalized laws of reflection and refraction », Science, Vol. 334, pp. 333–337 (2011)

[HAS14] D. Lin, P. Fan, E. Hasman and M.L. Brongersma, « Dielectric gradient metasurface optical elements », Science, Vol. 345, pp. 298-302 (2014)

[EL22] E. Mikheeva, C. Kyrou, F. Bentata, S. Khadir, S. Cueff and P. Genevet. « Space and time modulations of light with metasurfaces: recent progress and future prospects », ACS Photonics, Vol. 9, No. 5, pp. 1458–1482 (2022)

[ST22] S. Taravati and G. V. Eleftheriades, « Microwave space-time modulated metasurfaces », ACS Photonics, Vol. 9, No. 2, pp. 305-318 (2022)

[GX19] X. Guo, Y. Ding, Y. Duan and X. Ni , « Nonreciprocal metasurface with space–time phase modulation », Light: Science & Applications, Vol. 8, No. 123 (2019)

[MELS19] M.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)

[MELS21] M.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)

[Viq15] J. Viquerat. Simulation of electromagnetic waves propagation in nano-optics with a high-order discontinuous Galerkin time-domain method. Ph.D. thesis, University of Nice-Sophia Antipolis (2015)

[Liu04] X. Liu. The use of the FDTD method for electromagnetic analysis in the presence of time-varying media. PhD thesis, University of Ottawa (2024)

[TH05] A. Taflove and S.C. Hagness. Computational electrodynamics: the finite-difference time- domain method - 3rd ed. Artech House Publishers (2005)

Typical profile: MSc in scientific computing, modeling and simulation.

Skills :

• Basic knowledge of numerical resolution of PDEs for computational physics
• Introduction to finite difference / finite volume / finite element methods
• Basic knowledge of electromagnetism
• Software development using Fortran 95 and Python

• 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

Duration: 36 months
Location: Sophia Antipolis, France
Gross Salary per month: 2100€ brut per month (year 1 & 2) and 2190€ brut per month (year 3)