Internship Position F/m Advanced Computational Design of Nanostructured Photonic Devices

_Le descriptif de l’offre ci-dessous est en Anglais_

**Type de contrat**: CDD

**Niveau de diplôme exigé**: Bac + 5 ou équivalent

**Autre diplôme apprécié**: Master in applied mathematics or scientific computing

**Fonction**: Stagiaire de la recherche

**A propos du centre ou de la direction fonctionnelle**:
The Inria center at Université Côte d'Azur includes 42 research teams and 9 support services. The center’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 regional 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.

**Contexte et atouts du poste**:
Beside the above-mentioned high-fidelity DG-based electromagnetic solvers, the team is also actively studying reduced-order modeling (ROM) strategies in the context of time-domain electromagnetics by studying the applicability of the proper orthogonal decomposition (POD) method. In this ROM approach, a reduced subspace with a significantly smaller dimension is constructed by a set of POD basis vectors extracted offline from snapshots that are extracted from simulations with a high order DGTD (Discontinuous Galerkin Time-Domain) electromagnetic solver **[1-2]**. In particular, a non-intrusive POD-based ROM has been developed for the solution of parameterized time-domain electromagnetic scattering problems where considered parameters are the electric permittivity and the temporal variable **[7]**. Although the non-intrusive POD-based ROM method introduced in **[7]** provides encouraging results, it is not as efficient and robust as one would expect and it does not allow to account for a parametrized geometry. In particular, the hyperbolic nature of the underlying PDE system, i.e., the system of time-domain Maxwell equations, is known to represent a challenging issue for linear reduction methods such as POD. In practice, a large number of modes is required therefore hampering the obtention of an efficient ROM strategy. Therefore, searching for alternative ROM strategies for nanophotonics remains an active and important line of reserach of teh Atlantis project-team.

**[1]** 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, Dec 2015.

**[3]** E. Agullo, L. Giraud, A. Gobé, M. Kuhn, S. Lanteri and L. Moya. _High order HDG method and domain decomposition solvers for frequency‐domain electromagnetics_. Int. J. Numer. Model. Electr. Netw. Dev. Fields, Vol. 33, No. 2 (2019)

**[4]** 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)

**[5]** 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)

**[6]** 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)

**[7]** K. Li, T.Z. Huang, L. Li and S. Lanteri. _Non-intrusive reduced-order modeling of parameterized electromagnetic scattering problems using cubic spline interpolation_. J. Sci. Comp., Vol. 87, Art. no. 52 (2021)

**Mission confiée**:
The objective of this internship is twofold:

- One one hand, the existing numerical methodology combining the high-fidelity fullwave DGTD solver **[1]-[2]** and the statistical learning-based global optmization method **[4]-[5]** will be used to study different nanostructuring strategies for improving light absorption in a simplified yet representative model of photonic devices relevant to digital imaging technology;
- On the other hand, a detailed assessment of state-of-the-art ROM techniques will be conducted to identify possible paths to extend the approach developed in **[7]**in view of dealing efficiently with the inverse design of large-scale photonic devices such as a realistic CMOS imager.

This internship work is expected to be a first step toward a PhD project that will be concerned with the development of an advanced computational design methodology for studying and improving the performance of CMOS imagers. Thi