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 advanced numerical methods for solving 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 also includes a component dedicated to the optimization of geometrical characteristics of nanostructures driven by some performance objective in the contex of inverse design strategies of nanophotonic setups. DIOGENeS is a unique numerical framework leveraging the capabilities of DG techniques for the simulation of multiscale problems relevant to nanophotonics and nanoplasmonics.
One important line of research of the team during the last years has been dedicated to improve the capabilities of these numerical tools to produce novel inverse design methodologies for optical metasurfcaes. In the last decade metasurfaces, i.e. 2D arrays of optical nanoantennas with subwavelength size and separation [1] have revolutionized the field of linear optics with the promise to replace bulky and difficult-to-align optical components with ultrathin and flat devices like metagratings, metalenses and metaholograms, which can also implement new functionalities in terms of aberrations correction and arbitrary wavefront shaping. In the recent years, by combining a high-fidelity DG-based fullwave solver in the time-domain [2] with a statistical learning-based global optimization method [3], we have introduced innovative inverse design methodologies for mono-objective optimization of metadeflectors [4], multi-objective optimization of RGB metalenses [5] and robust optimization of metadeflectors [6].
[1] W. Chen, A.Y. Zhu and F. Capasso. Flat optics with dispersion-engineered metasurfaces. Nature Review Material, vol. 5, 604 (2020)
[2] 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)
[3] D. Jones. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, Vol. 13, No. 4, pp. 455-492 (1998)
[4] M. 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. Elsawy, A. Gourdin, M. Binois, R. Duvigneau, D. Felbacq, S. Khadir, P. Genevet an S. Lanteri, Multiobjective statistical learning optimization of RGB metalens, ACS Photonics, Vol. 8, No. 8, pp. 2498–2508 (2021)
[6] M. Elsawy, M. Binois, R. Duvigneau, S. Lanteri, and P. Genevet, Optimization of metasurfaces under geometrical uncertainty using statistical learning, Optics Express 29(19), 29887–29898 (2021)
