PhD Position F/M Reduced-order modeling and global optimization for the robust design of Gap Plasmon Resonators

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.

Context and scientific environment of the project.
This PhD project is part of a collaborative multidisciplinary project between the Atlantis project-team from Inria Research  Center at  Université Côte d'Azur and Institut  Pascal at Université Clermont  Auvergne, in the context of the ANR SWAG-P project that has started in  January 2024 and that is funding the PhD.

The Atlantis project-team gathers researchers in numerical mathematics and computational physics, with an interdisciplinary focus.  The team has developed a specific expertise in  the efficient numerical modeling of propagation of  electromagnetic wave  in complex  media with  a strong emphasis on  nanoscale light-matter  interactions. Through  the years, the  Atlantis team  has developed  a strong  expertise in  the design, analysis  and development  of  dedicated  efficient numerical  methods (based on  high order accurate Discontinuous  Galerkin finite elements methods). More recently, the team  has also acquired a know-how of  numerical  optimization  using  various techniques,  and  a  solid experience on high performance computing practices (parallel numerical algorithms and  parallelization strategies for  large-scale problems). This materializes concretely through  the DIOGENeS software suite [Diog] that has already proven its  crucial efficiency in nanophotonics.  DIOGENeS will be  the corner stone  to numerically address the  various complex scenarios in this PhD project.

The Elena team at the Pascal Institute works closely with the Atlantis project-team on different subjects in plasmonics. Both teams have known each other and collaborated for years, particularly on advanced physical descriptions of the optical response of metals. Members of the Elena team specialize in modeling, physics-based numerical simulation, and optimization of nanophotonic structures ranging from plasmonic resonators to multilayer structures.

Description of the PhD project.
Designing efficient nanoscale biosensors is currently an active field of research in  nanophotonics.  Several criteria such  as cheapness of fabrication,  miniaturization   and  high  sensitivity   are  strongly desirable. However,  meeting all  these criteria at  the same  time is challenging.    In  this   problematic,   optical  based   biosensors, consisting   in plasmonic nano-resonators,   sound   very promising. Plasmonic waves can manifest  when the electrons of a metal are  collectively excited  by  light, and  the  exploitation of  their peculiar  optical   properties  (such  as  light   confinement,  light focusing) are the subject of intense research.  A single nanocube of a few tens of nanometers on a  dielectric film deposited on a thin metal layer  is  a perfect  illustration  of  a typical  plasmonic  resonant structure.   The latter  exhibits, in  particular, a  special kind  of plasmonic    wave   called    a   gap    plasmon   (existing    in   a metal-dielectric-metal gap).   As such, this  simple device acts  as a powerful individual gap plasmon resonator. It has in particular proved to  have  a  high  and  easy measurable  optical  sensitivity  to  any environment change. This makes this device a very good candidate to be exploited as  an elementary  brick in patches  to design  an efficient biosensor.

To achieve  this objective, it is thus  of high importance to be able to characterize and optimize the optical response of single and multiple such resonators.   Moreover, due to  their high sensitivity, it  is in particular  essential to  study the  influence of  any environment  or geometrical change.  In addition,  the (possibly costly and difficult) use of direct  experiments to address this  problem, numerical methods are  of  high  importance  and   provide  essential support  in  this characterization  step.  Providing  accurate  and efficient  numerical simulations in this context is highly challenging and requires robust discretization  strategies  and  algorithms. The PhD project is part of this overall picture and will focus on the following aspects.

On the one hand, one objective of the PhD project is to carry out a comprehensive numerical study of the  sensitivity of the  optical  response  of  a given  Gap  Plasmon Resonator  (GPR) to  e.g.  variation  of optical  indices and geometrical parameters  (metal layer width, spacer  size, cubes sizes, rounding of  the corners of  the cubes, etc.). To achieve  this goal, Uncertainty  Quantification  (UQ)  from   the  perspective  of  robust optimization techniques will be used [El:21b],  by building on and extend the pre-existing Bayesian optimization tools implemented in the DIOGENeS software tool.

On the other hand, prohibitive computational time of direct simulations of arrangement of a large number of cubes is unavoidable. It motivates the development of a smart strategy for fast characterization of the realistic GPR-based biosensors; this will be another challenging objective of the PhD project. The recent achievements (obtained in another context, see e.g. [Pi:24]) using non-linear reduced order model techniques based on artificial neural networks (ANN) will be the starting point in order to build an innovative reduced order modeling methodology able to quickly map the parameters of interests of a GPR-based biosensor (optical indices, typical sizes and geometries, illumination frequency, etc.) to its optical response (cross section, phase profile, field intensity, steepness and position of the Fano profile).

Project progress
Several  steps  are  envisaged,  which   may  depend  on  the  precise background of the candidate. She/He will first have to become familiar with the  global  physical  context  of  the  project:  classical  optics, nanoplasmonics and gap plasmons resonators. He/She will  also have  to acquire the  necessary basic  knowledge of numerical methodologies and discretization strategies used to address optical  simulation  in  the   framework  of  the  DIOGENeS  software tool. This mandatory  step will then allow the candidate  to get into and  correctly use  this software  tool. To  put this  into practice, several direct simulations of settings related to the project will be carried out. The  candidate will also get into  sensitivity analysis techniques from the perspective  of robust optimizations through a complete bibliographical work  (see e.g. [El:21a], [El:21b]) and study some specific GPR configurations. On the other side, she/he will investigate the recent works on reduced order modelling based on ANN (see e.g. [Pi:24], [Fr:22], [Du:23]) and extend this approach in the present PhD context. As a result, he/she will propose and assess a new methodology allowing for the development of an efficient characterizing tool for GPR-resonators. On a practical side, all the developments of the PhD will be followed by the members of the consortium of the ANR SWAG-P project. Moreover, the PhD candidate will be actively participate in the activities (meetings, interactions...) of this project.

[El:21a] Elsawy,  M. M.,  Gourdin, A., Binois,  M., Duvigneau, R.,  Felbacq,  D.,  Khadir,  S.,   P.   Genevet,  Lanteri,  S., Multiobjective statistical learning optimization of RGB metalens, ACS Photonics, 8(8), 2498-2508 (2021)
[El:21b] M.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)
[Diog]    DIOGENeS:   a    DG-based    software   suite    for nano-optics. https://diogenes.inria.fr/
[Pi:24] F. Pichi, B. Moya and J.S. Hesthaven, A graph convolutional autoencoder approach to model order reduction for parametrized PDEs, Journal of Computational Physics, 501 (2024) 1 2762
[Fr:22] S. Frescal and A. Manzoni, POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition, Computer Methods in Applied Mechanics and Engineering, Vol. 388, pp. 114181 (2022)
[Du:23] J. Duan and J.S. Hesthaven, Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems, Journal of Computational Physics, Vol. 497, pp. 112621 (2023)

Technical skills and level required :

Sound knowledge of numerical analysis for PDEs
Sound knowledge of Machine Learning / Deep Learning with Artificial Neural Networks
Basic knowledge of physics of electromagnetic wave propagation

Software development skills : Python and Fortran 2003, parallel programming with MPI and OpenMP

Languages :good level of spoken and written english

Relational skills :team worker (verbal communication, active listening, motivation and commitment

• 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)