3.2.1 Core research topics

Our research activities are organized around core theoretical and methodological topics to address the above-listed modeling challenges.

High order DG methods. Designing numerical schemes that are high order accurate on general meshes, i.e., unstructured or hybrid structured/unstructured meshes, is a major objective of our core research activities in ATLANTIS. We focus on the family of Discontinuous Galerkin (DG) methods that has been extensively developed for wave propagation problems during the last 15 years. We investigate several variants, namely nodal DGTD for time-domain problems, and HDG (Hybridized DG) for frequency-domain problems, with the general goal of devising, analyzing and developing extensions of these methods in order to deal with the above-mentioned physical drivers: nonlinear features, in particular in relation with generation of higher order harmonics in electromagnetic wave interaction with nonlinear materials, and nonlinear models of electronic response in metallic and semiconductor materials; multiphysic couplings such as for instance when considering PDE models relevant to thermoplasmonics, optoelectronics and nanoelectronics. There are to date very few works promoting DG-type methods for these situations. Our methodological contributions of these methods eventually materialize in the DIOGENeS software suite.

Time integration for multiscale problems. Multiscale physical problems with complex geometries or heterogeneous media are extremely challenging for conventional numerical simulations. Adaptive mesh refinement is an attractive technique for treating such problems and will be developed in our research activities in ATLANTIS. Local mesh refinement imposes a severe stability condition on explicit time integration since the allowed maximal time step size is constrained by the smallest element in the mesh. We consider different ways to overcome this stability condition, especially by using implicit-explicit (IMEX) methods where a time implicit scheme is used only for the refined part of the mesh, and a time explicit scheme is used for the other part.

Reduced-order and surrogate modeling. Reduced-order modeling aims at reducing the computational requirements of costly high-fidelity solution methods while maintaining an acceptable level of accuracy. One of the most studied methods for establishing the reduced-order model is the Proper Orthogonal Decomposition (POD), also known as Karhunen-Loéve decomposition, principal component analysis, or singular value decomposition, which uses the solutions of high fidelity numerical simulations or experiments at certain time instants, typically called snapshots, to compute a set of POD basis vectors spanning a low-dimensional space. POD is very popular in the computational fluid dynamics field. However, the development of POD for electromagnetics has been more scarce. We study POD-based reduced-order modeling strategies in the context of a long term collaboration that has started in 2018 with researchers at the School of Mathematical Sciences of the University of Electronic Science and Technology of China and Southwest University of Finance & Economics, which are both located in Chengdu. In the context of this collabortaion, we have proposed and developed several reduced-order modeling techniques, from intrusive to fully data-driven and non-intrusive methods, for time-domain electromagnetics. Alternatively, several works in the recent years have promoted highly efficient surrogate modeling approaches based on Deep Neural Networks (DNNs) to achieve non-linear reduced-order modeling. This is also a novel direction of investigation that we have started to consider in 2023 in the team.

Scientific Machine Learning. Scientific Machine Learning (SciML) is a relatively new research field based on both machine learning (ML) and scientific computing tools. Its aim is the development of new methods to solve several kinds of problems, which can be forward solution of multidimensional partial differential equations, identification of parameters, or inverse problems. The methods that are investigated in this context must be robust, reliable and interpretable. These new SciML tools should also allow the natural inclusion of data in the numerical simulation in order to generate new results. We initiated in 2022 a new research direction on a particular family of DNNs referred as Physics-Informed Neural Networks (PINNs) 51 that we plan to investigate for PDE models that are relevant to nanophotonics with the goal of designing non-intrusive surrogate modeling approaches that require a minimal amount of training data.

Dealing with complex materials. Physically relevant simulations deal with increasing levels of complexity in the geometrical and/or physical characteristics of nanostructures, as well as their interaction with light. Standard simulation methods may fail to reproduce the underlying physical phenomena, therefore motivating the search for more sophisticated light-matter interaction numerical modeling strategies. A first direction consists in refining classical linear dispersion models and we put a special focus on deriving a complete hierarchy of models, that will encompass standard linear models to more complex and nonlinear ones (such as Kerr-type materials, nonlinear quantum hydrodynamic theory models, etc.). One possible approach relies on an accurate description of the Hamiltonian dynamics with intricate kinetic and exchange correlation energies, for different modeling purposes. A second direction is motivated by the study of 2D materials. A major concern is centered around the choice of the modeling approach between a full costly 3D modeling and the use of equivalent boundary conditions, that could in all generality be nonlinear. Assessing these two directions requires efficient dedicated numerical algorithms that are able to tackle several types of nonlinearities and scales.

Dealing with coupled models. Several of our target physical fields are multiphysics in essence and require going beyond the sole description of the electromagnetic response. In thermoplasmonics, the various phenomena (heat transfer through light concentration, bubbles formation and dynamics) call for different kinds of governing PDEs (Maxwell, conduction, fluid dynamics). Since, in addition, these phenomena can occur in significatively different space and time scales, drawing a quite complete picture of the underlying physics is a challenging task, both in terms of modeling and numerical treatment. In the nanoelectronics field, an accurate description of the electronic properties involves including quantum effects. A coupling between Maxwell’s and Schrödinger's equations (again at significantly different time and space scales) is a possible relevant scenario. In the optoelectronics field, the accurate prediction of semiconductors optical properties is a major concern. A possible strategy may require to solve both the electromagnetic and the drift-diffusion equations. In all these aforementioned examples, difficulties mainly arise both from the differences in physical nature as well as in the time/space scales at which each physical phenomenon occurs. Accurately modeling/solving their coupled interactions remains a formidable challenge.

High performance computing (HPC). HPC is transversal to almost all the other research topics considered in the team, and is concerned with both numerical algorithm design and software development. We work toward taking advantage of fine grain massively parallel processing offered by GPUs in modern exascale architectures, by revisiting the algorithmic structure of the computationally intensive numerical kernels of the high order DG-based solvers that we develop in the framework of the DIOGENeS software suite.

3.2.2 Complementary topics

Beside the above-discussed core research topics, we have also identified additional topics that are important or compulsory in view of maximizing the impact in nanophotonics or nanophononics of our core activities and methodological contributions.

Numerical optimization. Inverse design has emerged rather recently in nanophotonics, and is currently the subject of intense research as witnessed by several reviews 48. Artificial Intelligence (AI) techniques are also increasingly investigated within this context 54. In ATLANTIS, we will extend the modeling capabilities of the DIOGENeS software suite by using statistical learning techniques for the inverse design of nanophotonic devices. When it is linked to the simulation of a realistic 3D problem making use of one of the high order DG and HDG solvers we develop, the evaluation of a figure of merit is a costly process. Since a sufficiently large input data set of candidate designs, as required by using Deep Learning (DL), is generally not available, global optimization strategies relying on Gaussian Process (GP) models are considered in the first place. This activity will be conducted in close collaboration with researchers of the ACUMES project-team. In particular, we investigate GP-based inverse design strategies that were initially developed for optimization studies in relation with fluid flow problems 40-41 and fluid-structure interaction problems 52.

Uncertainty analysis and quantification. The automatic inverse design of nanophotonic devices enables scientists and engineers to explore a wide design space and to maximize a device performance. However, due to the large uncertainty in the nanofabrication process, one may not be able to obtain a deterministic value of the objective, and the objective may vary dramatically with respect to a small variation in uncertain parameters. Therefore, one has to take into account the uncertainty in simulations and adopt a robust design model 45. We study this topic in close collaboration with researchers of the ACUMES project-team one on hand, and researchers at TU Braunschweig in Germany.

Numerical linear algebra. Sparse linear systems routinely appear when discretizing frequency-domain wave-matter interaction PDE problems. In the past, we have considered direct methods, as well as domain decomposition preconditioning coupled with iterative algorithms to solve such linear systems 15. In the future, we would like to further enhance the efficiency of our solvers by considering state-of-the-art linear algebra techniques such as block Krylov subspace methods 33, or low-rank compression techniques 50. We will also focus on multi-incidence problems in periodic structures, that are relevant to metagrating or metasurface design. Indeed, such problems lead to the resolution of several sparse linear systems that slightly differ from one another and could benefit from dedicated solution algorithms. We will collaborate with researchers of the CONCACE (Inria center at Université de Bordeaux) industrial project-team to develop efficient and scalable solution strategies for such questions.

7.1.1 DIOGENeS

• Name:
  DIscOntinuous GalErkin Nanoscale Solvers
• Keywords:
  High-Performance Computing, Computational electromagnetics, Discontinuous Galerkin, Computational nanophotonics
• Functional Description:
  The DIOGENeS software suite provides several tools and solvers for the numerical resolution of light-matter interactions at nanometer scales. A choice can be made between time-domain (DGTD solver) and frequency-domain (HDGFD solver) depending on the problem. The available sources, material laws and observables are very well suited to nano-optics and nano-plasmonics (interaction with metals). A parallel implementation allows to consider large problems on dedicated cluster-like architectures.
• URL:
  https://­diogenes.­inria.­fr/
• Contact:
  Stéphane Lanteri

8.1.1 Time-domain numerical modeling of gain media

Participants: Stéphane Descombes, Stéphane Lanteri, Cédric Legrand, Gian Luca Lippi [INPHYNI laboratory, Sophia Antipolis].

In laser physics, gain or amplification is a process where the medium transfers part of its energy to an incident electromagnetic radiation, resulting in an increase in optical power. This is the basic principle of all lasers. Quantitatively, gain is a measure of the ability of a laser medium to increase optical power. Modeling optical gain requires to study the interaction of the atomic structure of the medium with the incident electromagnetic wave. Indeed, electrons and their interactions with electromagnetic fields are important in our understanding of chemistry and physics. In the classical view, the energy of an electron orbiting an atomic nucleus is larger for orbits further from the nucleus of an atom. However, quantum mechanical effects force electrons to take on discrete positions in orbitals. Thus, electrons are found in specific energy levels of an atom. In a semiclassical setting, such transitions between atomic energy levels are generally described by the so-called rate equations. These rate equations model the behavior of a gain material, and they need to be solved self-consistently with the system of Maxwell equations. So far, the resulting coupled system of Maxwell-rate equations has mostly been considered in a time-domain setting using the FDTD method for which several extensions have been proposed. In the context of the PhD of Cédric Legrand, we study an alternative numerical modeling approach based on a high order DGTD method. This year, we have proposed a first variant that extends the DGTD method introduced in 42. This novel DGTD method has been formulated and analyzed in the three-dimensional case. A fully discrete stability analysis has been conducted and a computer implementation has been finalized. Numerical validations are underway before proceeding to a concrete application in the field of random lasing in collaboration with Gian Luca Lippi at INPHYNI laboratory.

8.1.2 Time-domain numerical modeling of semiconductor devices

Participants: Eric Guichard [Silvaco Inc., Santa Clars, CA, USA], Stéphane Lanteri, Massimiliano Montone, Claire Scheid.

In the field of semiconductor physics modeling, charge carrier transport is the starring phenomenon that needs to be predicted in order to build a mathematical model, based on higher-level quantities (e.g. electric current and voltage), that can be practically used for device simulation. Charge carrier transport is generally described by a drift-diffusion model. This yields a system of coupled partial differential equations which can be solved at two levels: (1) quasistatic approximation: the external force applied to the crystal is electrostatic, and drift-diffusion equations are coupled to a Poisson equation for the electrostatic potential. The goal is to determine the spatial distribution of carrier concentrations and the electric field (deduced from the potential); (2) fullwave model: the crystal is subject to an applied electromagnetic field, and Maxwell equations are coupled with transport equations for carrier dynamics. The goal is to determine the space-time evolution of carrier concentrations and the electromagnetic field. The quasistatic approximation is rigorous when the steady state of the semiconductor has to be calculated. For example, this could be a preliminary step to the fullwave simulation of a device that is biased prior to responding to a (time-varying) electromagnetic excitation. The fullwave model is particularly relevant to electro-optics, i.e. when light-matter interaction is investigated. Indeed, such study is essential to understanding and accurately modeling the operation of photonic devices for light generation, modulation, absorption. In the context of the PhD of Massimiliano Montone (defended in March 2023), we have a designed a DGTD method for solving the coupled system of Maxwell equations and drift-diffusion equations in the fullwave setting. The method has been formulated in the general three-dimensional case, and a computer implementation has been realized in a one dimensional and two-dimensional setting. Furthermore a 1D theoretical stability study has been completed. A preprint gathering the first academical results has been submitted 32. Another paper is in preparation containing more applied results.

8.1.3 Time-domain numerical modeling of plasmonic-based nanoscale heating

Participants: Yves D'Angelo [LJAD, Université Côte d'Azur], Thibault Laufroy, Claire Scheid.

Due to the various scales and phenomena that come into play in realistic thermoplasmonics problems, accurate numerical modeling is challenging. Laser illumination first excites a plasmon oscillation (reaction of the electrons of the metal) that relaxes to a thermal equilibrium and in turn excites the metal lattice (phonons). The latter is then responsible for heating the surroundings. A relevant modeling approach thus consists in describing the electron-phonon coupling through the evolution of their respective temperature. Maxwell's equations are then coupled to a set of coupled nonlinear hyperbolic (or parabolic) equations for the temperatures of respectively electrons, phonons and environment. The nonlinearities and the different time scales at which each thermalization occurs make the numerical approximation of these equations quite challenging. In the context of the PhD of Thibault Laufroy, which has started in October 2020, we propose to develop a suitable numerical framework for studying thermoplasmonics. As a first step, we have reviewed the models used in thermoplasmonics that are most often based on strong or weak (nonlinear) couplings of Maxwell's equations with nonlinear equations modeling heat transfer (hyperbolic or parabolic). We first especially targeted the hyperbolic version of the model and proposed an implementation in 2D, based on a Discontinuous Galerkin approximation in space. We used specific strategies for time integration to account for the multiple time scales of the problem. This has been validated on academical test cases, but also on more concrete cases. A theoretical stability study has also been achieved. A preprint with these first results will soon be submitted for publication. Finally, in view of studying more concrete situations, we have initiated discussions with Stefan Dilhaire (professor at University of Bordeaux and Laboratoire Ondes et matières d'Aquitaine) on one side, and Leonidas Agiotis (postdoctoral researcher, Polytechnique Montréal) on the other side.

8.1.4 Time-domain numerical modeling of liquid crystal materials

Participants: Mahmoud Elsawy, Stéphane Descombes, Stéphane Lanteri, Claire Scheid.

Liquid crystal (LC)-based reconfigurable metasurfaces offer significant potential for advancing active metasurface technologies. This potential stems from their cost-efficiency, ease of fabrication, and ability to operate across a wide frequency spectrum. Among the various types of LCs, nematic liquid crystals are particularly prominent due to their favorable properties for such applications. Traditional LC modeling typically focuses on simulating the static response of the anisotropic permittivity tensor, often assuming that the permittivity simply transitions between two distinct states. However, this static approach neglects the dynamic time-dependent behavior of LCs, a critical factor that is overlooked in the majority of existing studies. Such neglect can lead to inaccuracies in predicting modulation times. Moreover, when LCs are integrated into highly resonant structures, the strong optical confinement within these structures can further influence the LC response time, necessitating more sophisticated modeling. To address these challenges, we have initiated in 2024 a study to develop a comprehensive dynamic model of LC behavior. By coupling the differential equations governing LC orientation under time-varying applied voltages with Maxwell's equations, the proposed model provides an accurate representation of the time-dependent transitions in LC orientation. This approach should surpass conventional odelin approaches by capturing the intricate dynamics of LC responses under varying excitation conditions. Consequently, the proposed model enables precise temporal control of unit cell responses, making it particularly well-suited for the design of reflective and transmissive multiresonant metasurfaces in advanced technological applications. As a next step, we will devise an appropriate discretization of this dynamic model of LC behavior.

8.1.5 Numerical modeling of time-modulated metasurfaces

Participants: Mahmoud Elsawy, Roman Gelly, Stéphane Lanteri.

Active metasurfaces represent a transformative platform for the dynamic modulation of electromagnetic wavefronts, achieved through precise spatial control of the phase and amplitude of scattered light by leveraging arrays of subwavelength scatterers under external stimuli. This spatial modulation imparts tailored momentum to the outgoing light, enabling advanced functionalities such as beam steering, focusing, and holography. Yet, the periodic temporal modulation of these metasurfaces offers the ability to manipulate the frequency content of the scattered light, adding a new dimension of control and unlocking novel possibilities in optical signal processing and frequency-domain applications. However, the accurate numerical modeling of time-modulated metasurfaces poses significant challenges. Temporal modulation introduces dynamic variations in the electromagnetic properties of the metasurface, specifically in the permittivity, which must be seamlessly integrated into Maxwell's equations to account for the interplay between spatial and temporal effects. Such modeling is crucial to predict and optimize the metasurface performance, particularly for applications involving complex temporal waveforms or high-speed modulation. In our work we rely on the Discontinuous Galerkin Time-Domain (DGTD)to address these challenges. In this context, the DGTD approach allows for the discretization of Maxwell's equations in both space and time, enabling accurate modeling of the temporal modulation effects while maintaining the spatial fidelity required to capture subwavelength features. By exploiting DGTD, it is possible to capture the full dynamics of time-modulated metasurfaces, including the generation of frequency sidebands and their spatial diffraction. This capability is essential for designing metasurfaces that integrate both spatial and temporal modulation, enabling functionalities such as frequency mixing, harmonic beam steering, and the controlled breaking of Lorentz reciprocity. Furthermore, the DGTD approach is well-equipped to handle the computational demands of large-scale metasurfaces operating at high frequencies, ensuring accurate predictions and facilitating experimental validation. We have started by the 2D implemntation and we are currently preparing the compariosn with state-of-the art results. The next step is to integrate our 2D code with advanced optimization algorithm to design realistic time-modulated metasurface that can be fabricated and characerized experimentally. This work is carried out in the context of the PhD thesis of Roman Gelly.

8.1.6 Efficient approximation of high-frequency Helmholtz problems

Participants: Théophile Chaumont-Frelet, Victorita Dolean [TU Eindhoven, The Netherlands], Maxime Ingremeau [LJAD, Université Côte d'Azur], Florentin Proust.

Helmholtz problems describe the time-harmonic solutions of the wave equation (possibly in a heterogeneous medium, in a bounded medium, with boundary conditions, etc.). In general, there is no explicit solution to such an equation, and an approximate solution of the equation must be computed numerically. All the existing methods (finite elements, finite differences, etc.) have in common that they are more and more expensive when the frequency of the waves increases. In 35, we study new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients. These discretization spaces are spanned by Gaussian coherent states, that have the key property to be localized in phase space. We carefully select the Gaussian coherent states spanning the approximation space by exploiting the (known) micro-localization properties of the solution. This work is conducted in the context of the Inria POPEG Exploratory Research Action and the topic is also at the heart of the PhD thesis of Florentin Proust.

In the beginning of this thesis, such a method had been implemented for a simple one-dimensional problem. Even in this very simple case, it became clear that Gaussian coherent states could not be used in practice because they were strongly ill-conditioned. However, if the discretization spaces are now spanned by some particular linear combinations of Gaussian coherent states forming a so-called Wilson basis, then this problem disappears. In 35, it had been mathematically proved that using Gaussian coherent states to solve high-frequency Helmholtz problems had some advantages. In 2023, we had started to prove similar - and even broader - results about Wilson basis. In 2024, we continued to work on these theoretical aspects. We also developed a Python code to solve one-dimensional Helmholtz problems with Gaussian coherent states or with a Wilson basis. More precisely, we first focused on a one-dimensional equation with constant coefficients, and then we started to generalize to one-dimensional equations with variable coefficients. This one-dimensional code should be finished by the end of next February. Afterwards, we plan to come back to the theoretical part of the PhD. Finally, in June 2024, Florentin Proust went to the ECCOMAS conference, in Lisbon. He gave a talk in which he introduced the topic of his PhD 26.

8.2.1 POD-based ROM methods for parameterized electromagnetic problems

Participants: Xiao-Feng He [UESTC, Chengdu, China], Stéphane Lanteri, Kun Li [SUFEC, Chengdu, China], Liang Li [UESTC, Chengdu, China], Yixin Li [UESTC, Chengdu, China], Ying Zhao [UESTC, Chengdu, China].

In collaboration with researchers at the University of Electronic Science and Technology of China (UESTC) and the Southwestern University of Finance (SUFEC) and Economics, which are both located in Chengdu, we study ROM for time-domain electromagnetics and nanophotonics. More precisely, we have considered the applicability of the proper orthogonal decomposition (POD) technique for the system of time-domain Maxwell equations, possibly coupled to a Drude dispersion model, which is employed to describe the interaction of light with nanometer scale metallic structures. Our first contributions are described in 10-12 where we have proposed POD approach for building a reduced subspace with a significantly smaller dimension given a set of space-time snapshots that are extracted from simulations with a high order DGTD method. Then, a POD-based ROM is established by projecting (Galerkin projection) the global semi-discrete DG scheme onto the low-dimensional space spanned by the POD basis functions.

Subsequently, we have designed several fully data-driven non-intrusive POD-based ROM approaches. In 11, we have proposed the POD-CSI method in the context of parameterized time-domain electromagnetic scattering problems. The considered parameters are the dielectric electric permittivity and the temporal variable. The snapshot vectors are produced by a high order DGTD method formulated on an unstructured simplicial mesh. Because the second dimension of the snapshots matrix is large, a two-step or nested POD method is employed to extract time- and parameter-independent POD basis functions. By using the singular value decomposition (SVD) method, the principal components of the projection coefficient matrices (also referred to as the reduced coefficient matrices) of full-order solutions onto the reduced-basis (RB) subspace are extracted. A cubic spline interpolation-based (CSI) approach is proposed to approximate the dominating time- and parameter-modes of the reduced coefficient matrices without resorting to Galerkin projection. The generation of snapshot vectors, the construction of POD basis functions and the approximation of reduced coefficient matrices based on the CSI method are completed during the offline stage. The RB solutions for new time and parameter values can be rapidly recovered via outputs from the interpolation models in the online stage. In particular, the offline and online stages of the proposed POD-CSI method are completely decoupled, which ensures the computational validity of the method. Moreover, a surrogate error model is constructed as an efficient error estimator for the POD-CSI method. Then in 7-16 we have designed improved versions of the POD-CSI method respectively refererred as POD-CSI-CAE and POD-DMD-RBF.

8.2.2 Nonlinear ROM with Graph Convolutional Autoencoder

Participants: Carlotta Filippin, Stéphane Lanteri, Federico Pichi [EPFL, Switzerland], Maria Strazzullo [Politecnico di Torino, Italy].

Although this POD-CSI method introduced in 11 provides encouraging results, it is not as efficient and robust as one would expect from a ROM perspective. Indeed, 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. One possible path to address this problem, which is currently investigated by several groups worldwide, relies on nonlinear reduction techniques. We initiated this year a study on nonlinear ROM for the time-domain Maxwell equations. More precisely, we study the approach recently proposed in 49, which proposes a nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). This preliminary study aims at realizing a first adaptation and evaluation of the GCA-ROM in the modeling context of time-domain electromagnetics. This study is at the heart of the Master thesis of Carlotta Filippin, and it is conducted in collaboration with Federico Pichi (EPFL, Switzerland) and Maria Strazzullo (Politecnico di Torino, Italy).

8.4.1 PINNs for the parametric Maxwell equations

Participants: Stéphane Lanteri, Nawfal Maghraoui, Alexandre Pugin, Mathieu Riou [Thales Research & Technology, Palaiseau, France].

Numerical simulations of electromagnetic wave propagation problems primarily rely on discretization of the system of time-domain Maxwell equations using finite difference or finite element type methods. For complex and realistic three-dimensional situations, such a process can be computationally prohibitive, especially in view of many-query analyses (e.g., optimization design and uncertainty quantification). Therefore, developing cost-effective surrogate models is of great practical significance. Among the different possible approaches for building a surrogate model of a given PDE system in a non-intrusive way (i.e., with minimal modifications to an existing discretization-based simulation methodology), approaches based on neural networks and Deep Learning (DL) has recently shown new promises due to their capability of handling nonlinear or/and high dimensional problems. In the present study, we propose to focus on the particular case of Physics-Informed Neural Networks (PINNs) introduced in 51. PINNs are neural networks trained to solve supervised learning tasks while respecting any given laws of physics described by a general (possibly nonlinear) PDE system. They seamlessly integrate the information from both the measurements and partial differential equations (PDEs) by embedding the PDEs into the loss function of a neural network using automatic differentiation. In 2022, we have initiated a study dedicated to the applicability of PINNs for building efficient surrogate models of the parametric Maxwell equations. We have progressed on this obejctive this year in the context of the Master internships of Nawfal Maghraoui (frequency-domain Maxwell equations) and Alexandre Pugin (time-domain Maxwell equations). Both settings are now at the heart of the PhD project of Alexandre Pugin, which has started on October 2024.

8.4.2 Multilevel and distributed PINNs for the Helmholtz equation

Participants: Victorita Dolean [TU Eindhoven, The Netherlands], Daria Hrebenshchykova, Stéphane Lanteri, Victor Michel-Dansac [MACARON project-team, Centre Inria de l'Université de Lorraine].

In the context of the Master intersnhip of Daria Hrebenshchykova 31, we investigate recently proposed extensions of PINNs, namely Finite Basis PINNs (FBPINNs) and Multilevel Finite Basis PINNs (MFBPINNs), for solving the Helmholtz equation in one and two dimensions. Through numerical simulations, we compare the efficiency, accuracy, and scalability of these methods. While FBPINNs exhibit good performance for low-frequency problems, the multilevel method outperforms the FBPIN method for high-frequency problems. This work also introduces neural network architectures and training schemes, including architectures based on single and multiple optimizers, integrated into the ScimBa library developed by the MACARON project-team of Centre Inria de l'Université de Lorraine. The results demonstrate the advantages of the multilevel approach for solving complex frequency-domain acoustic and electromagnetic wave propagation problems, which will be the objective of the PhD project of Daria Hrebenshchykova that has started on November 2024.

8.4.3 Efficient deep learning methodology for large-scale metalens

Participants: Marco Abbarchi [Solnil, Marseille, France], Arthur Clini de Souza, Mahmoud Elsawy, Hugo Enrique Hernandez-Figueroa [University of Campinas (Unicamp), Campinas, Sao Paulo, Brazil], Badre Kerzabi [Solnil, Marseille, France], Stéphane Lanteri, Plaoma Pellegrini [University of Campinas (Unicamp), Campinas, Sao Paulo, Brazil].

Metasurfaces are the 2D equivalent of metamaterials, having wavelength-sized elements that leverage various physical phenomena to control the wavefront of the transmitted and reflected beams. Building on our recent advancements in deep learning (DL) 2, we develop an efficient deep learning strategy for designing large-scale metalenses in reflection 21-24. Our strategy is based on optimizing several beam deflectors for a wide range of diffracted angles. This eliminates the need for individual optimization for each angle, similar to our earlier work on color filter designs in 2. The proposed structure consists of supercells with two distinct ridges made of TiO${}_2$ (see Fig. 6). The widths, height and spacing between these ridges are optimized parameters, ensuring enhanced performance of the diffracted beams. We simulated 10 000 different unit cells configurations to build a dataset. Afterwards, we trained a deep neural network surrogate model, which defines two functions. Firstly, it can be exploited as a fast solver to replace costly fullwave simulations. Secondly, it represents a differentiable solver, enabling efficient gradient optimization. The next step is training a Multi-Valued Artificial Neural Network (MVANN) to predict the possible designs responsible for generating a target response. The last step is using a network, hereby called the condenser, to filter out the spurious solutions of the MVANN and post-process the geometrical parameters, such as uniforming the height across all solutions and applying hard constraints. This approach allowed precise selection of the period and corresponding deflection angles. Several metalenses with different diameters have been optimized ranging from 50 µm to 1 mm demonstrating scalability of our approach. Our academic partner in Brazil is in the process of fabricating the optimized metalens structures. The results of this study are expected to be published in early 2025.

Show image description

(a) shows the representation of the considered structure with the optimization parameters. (b) presents the gathering technique to form highly perfroamnce metalens in reflection. (c): numerical simulation of a metalens with numerical aperture in the range of 0.5 with a diameter of 50 $\mu$m.

8.5.1 Trimer metasurfaces for highly sensitive biomedical sensors

Participants: Haogang Cai [Department of Biomedical Engineering, New York University, USA], Mahmoud Elsawy, Stéphane Lanteri, Hao Wang [Department of Biomedical Engineering, New York University, USA].

In this work, we design a highly sensitive metasurface for biomedical sensing relying on toroidal dipoles. Through numerical simulations (see Fig. 7) and experimental validation, we unveil that these metasurfaces offer remarkable sensitivity, especially across the visible spectrum. This high sensitivity enables the detection of refractive index variations with high precision, which would have great value in many biomedical applications. The fabrication and the experimental characterization have been done and showed a very good agreement with our numerical simulations. We are preparing a paper to be submitted in early 2025.

Show image description

(a) shows the transmission response of the trimer metasurface. (b) presents the sensitivity analysis of the three main modes together the field profile of the toridal mode.

8.7.1 Modeling of centimeter-scale metasurfaces in imaging systems

Participants: Mahmoud Elsawy, Sébastien Héron [Thales Research & Technology, Palaiseau, France], Enzo Isnard, Stéphane Lanteri.

Metasurfaces are 2D optical components structured at sub-wavelength scale that locally control the properties of incident light. They can perform various functions such as beam steering, polarization control and focusing. However, metasurfaces are still difficult to incorporate into imaging systems due to the difficulty of modeling their behavior together with other components. For a traditional optical system composed of mirrors or refractive lenses, ray-tracing tools are used to predict the imaging performances. For metasurfaces, one cannot use these tools, as geometrical optics is no longer valid for describing the interactions of light with sub-wavelength elements. To accurately simulate them, Maxwell's equations have to be solved using finite difference or finite element methods. These methods are computionally expensive and are only adapted for components of size around ten wavelengths. Thus, they are of no practical use to simulate metasurfaces inside imaging optical systems (see Fig. 9), which are in the centimeter scale for industrial applications in imaging. Beyond this size limitation, one may need to integrate a metasurface neither at the entrance nor at the output of the system. This positionning often leads to smaller incident angle and/or to decrease of the component area because of its relative position with respect to the system stop and pupils. Besides, this also leads to modeling issues: a) the incidents fields are not plane waves anymore, and b) computed electromagnetic fields after the metasurface need to be recast as rays. To address these issues, we develop a novel numerical methodology to couple a fullwave solver with a ray tracing tool in order to simulate a whole system containing mesurfaces and refractive components 22. The main objective is to fully simulate and optimize the whole system including the metasurface to achieve various functionality. This work is implemented in the frame of the PhD of Enzo Isnard. We are preparing a manuscript to be submitted soon to Optics Express journal in early 2025.

Show image description

Example of an imaging system containing a metasurface. To simulate the whole system, we need to convert rays into electromagnetic fields and vice versa. As the metasurface lies in the middle of the system, the incident wavefront is not necessarily planar.

8.7.2 Advanced modeling of nanostructured CMOS imagers based on DG methods

Participants: Stéphane Lanteri, Denis Rideau [STMicroelectronics, Crolles].

The exploitation of nanostructuring to improve the performance of CMOS (Complementary Metal-Oxide-Semiconductor) imagers based on microlens grids is a very promising avenue. In this perspective, numerical modeling is a key component to accurately characterize the absorption properties of these complex imaging structures, which are intrinsically multiscale (from the micrometer scale of the lenses to the nanometric characteristics of the nanostructured material layers). The FDTD (Finite Difference Time-Domain) method is the solution adopted in the first instance for the simulation of the interaction of light with this type of structure. However, because FDTD is based on a Cartesian mesh, this method shows limitations when it comes to accurately account for complex geometric features such as the curvature of microlenses or the texturing of material layer surfaces. In this context of the PhD of Jérémy Grebot, our main objectives are (1) to leverage locally refined meshes with a high order DGTD method for modeling the propagation of light in a nanostructured CMOS imager and, (2) to study and optimize the impact of nanostructuring for improving light absorption. In particular, with respect to the second objective, an inverse design methodology combining a high order DGTD method with a statistical learning-based global optimization algorithm is developed for studying various nanostructuring patterns of the surface of the absorbing semiconductor material such as one- and two-dimensional gratings.

8.7.3 Nanoimprint color filter metasurface for imaging devices

Participants: David Grosso [Institut Matériaux Microélectronique Nanosciences de Provence (IM2NP) Aix-Marseille Université and Solnil], Marco Abbarchi [Institut Matériaux Microélectronique Nanosciences de Provence (IM2NP) Aix-Marseille Université and Solnil], Badre Kerzabi [Solnil], Mahmoud Elsawy, Alexis Gobé, Stéphane Lanteri.

Due to the rapid growth of metasurface applications, several manufacturing techniques have been developed in the past few years. Among them, NanoImprint Lithography (NIL) has been considered as a promising fabrication possibility for metasurface. NIL can achieve features below 100 nm without the need for complex and expensive optics and light sources needed to achieve similar resolutions in advanced photolithography. Yet, despite the advantages of this fabrication procedure, it has some limitations related to the dimensions of the single nanoresonators. In other words, the fabrication constraints related to the aspect ratio (ratio between height and width) is important. Typically, a maximum aspect ratio of 2 can be considered in such a technique. In this work, together with our collaborators from IM2NP, Aix-Marseille Université and the Solnil startup who are specialists in nanoimprint technology, we aim at optimizing a low cost color filtering metasurface for imaging applications taking into account all the fabrication constraints. The main goal of this study is to rely on inverse design strategies to unveil the geometrical characteristics and topological arrangement of meta-atoms to maximize the efficiency of several metasurface configurations. Various shapes with different physical mechanisms have been investigated. It is worth mentioning that, in this study, various shapes have been optimized and studied numerically, yet, as a starting point for the fabrication, the cylindrical pillars will be considered as a first illustration for the nanoimprint fabrication.

8.7.4 Optimization of light trapping in nanostructured solar cells

Participants: Stéphane Collin [Sunlit team, C2N-CNRS, Paris-Saclay, France], Alexis Gobé, Henning Helmers [Fraunhofer-Institut für Solare Energiesysteme ISE, Freiburg, Germany], Oliver Höhn [Fraunhofer-Institut für Solare Energiesysteme ISE, Freiburg, Germany], Stéphane Lanteri, Guillaume Leroy, Ines Revol [LAAS, Toulouse, France].

There is significant recent interest in designing ultrathin crystalline silicon solar cells with active layer thickness of a few micrometers. Efficient light absorption in such thin films requires both broadband antireflection coatings and effective light trapping techniques, which often have different design considerations. In collaboration with physicists from the Sunlit team at C2N-CNRS, we exploit statistical learning methods for the inverse design of material nanostructuring with the goal of optimizing light trapping properties of ultraphin solar cells. This objective is challenging because the underlying electromagnetic wave problems exhibit multiple resonances, while the geometrical settings are non-trivial. Such multi-resonant solar cell structures are attractive for maximizing light absorption for the full solar light spectrum as illustrated in Fig. 10. We exploit statistical learning methods for the inverse design of material nanostructuring with the goal of optimizing light trapping properties of ultraphin solar cells. This study is conducted in collaboration with physicists from C2N (Centre for Nanosciences and Nanotechnology) in Campus Paris-Saclay), LAAS (Laboratoire d'Analyse et d'Architecture des Systèmes) in Toulouse and the Fraunhofer-Institut für Solare Energiesysteme ISE in Freiburg, Germany.

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Optimization of light absorption in a solar cell based on a pyramidal grating. Top figures: geometrical model. Bottom: absorption spectra.

8.7.5 Plasmonic sensing with nanocubes

Participants: Antoine Moreau [Institut Pascal, Clermont-Ferrand, France], Stéphane Lanteri, Guillaume Leroy, Claire Scheid.

The propagation of light in a slit between metals is known to give rise to guided modes. When the slit is of nanometric size, plasmonic effects must be taken into account, since most of the mode propagates inside the metal. Indeed, light experiences an important slowing-down in the slit, the resulting mode being called gap-plasmon. Hence, a metallic structure presenting a nanometric slit can act as a light trap, i.e. light will accumulate in a reduced space and lead to very intense, localized fields. We study the generation of gap plasmons by various configurations of silver nanocubes separated from a gold substrate by a dielectric layer, thus forming a narrow slit under the cube. When excited from above, this configuration is able to support gap-plasmon modes which, once trapped, will keep bouncing back and forth inside the cavity. We exploit statistical learning methods for the goal-oriented inverse design of cube size, dielectric and gold layer thickness, as well as gap size between cubes in a dimer configuration (see Fig. 11). This study is conducted in collaboration with Antoine Moreau at Institut Pascal (CNRS). Starting in January 2024, we will continue this study in the context of the ANR SWAG-P project, which is coordinated by Antoine Moreau from Institut Pascal, Clermont-Ferrand, France.

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Optimization of a plasmonic nanocube dimer setting for the generation of Fano resonances.

8.7.6 Multiple scattering in random media

Participants: Stéphane Descombes, Stéphane Lanteri, Guillaume Leroy, Cédric Legrand, Gian Luca Lippi [INPHYNI laboratory, Nice].

Fluorescence signals emitted by probes, used to characterize the expression of biological markers in tissues or cells, can be very hard to detect due to a small amount of molecules of interest (proteins, nucleic sequences), to specific genes expressed at the cellular level, or to the limited number of cells expressing these markers in an organ or a tissue. Access to information coming from weaker emitters can only come from strengthening the signal, since electronic post-amplification raises the noise floor as well. Molecule-specific biochemical processes are being developed for this purpose, and a new mechanism based on the simultaneous action of stimulated emission and multiple scattering induced by nanoparticles suspended in the sample has been recently demonstrated to effectively amplify weak fluorescence signals. A precise assessment of the signal fluorescence amplification that can be achieved by such a scattering medium requires an electromagnetic wave propagation modeling approach capable of accurately and efficiently coping with multiple space and time scales, as well as with non-trivial geometrical features (shape and topological organization of scatterers in the medium). In the context of a collaboration with physicists from the Institut de Physique de Nice INPHYNI (Gian Luca Lippi from the complex photonic systems and materials group), we initiated this year a study on the simultaneous action of stimulated emission and multiple scattering by randomly distributed nanospheres in a bulk medium (see Fig. 12). From the numerical modeling point of view, our short term goal is to develop a time-domain numerical methodology for the simulation of random lasing in a gain medium.

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Multiple scattering by randomly distributed nanospheres in a bulk medium.

8.7.7 Nonlinear wavefront shaping with optical metasurfaces

Participants: Giuseppe Leo [CNRS-MPQ, Université Paris Cité, France], Jean-Michel Gerard [PHELIQS, CEA and Université Grenoble Alpes, France], Mahmoud Elsawy, Stéphane Lanteri.

In recent years, the control of sub-wavelength light-matter interactions has enabled the observation of new linear optical phenomena, further establishing a new class of ultra-thin devices for real-world applications. To extend metasurface functionality and implement nonlinear manipulations, the scientific community has considered optical metasurfaces for harmonic emission field control. However, the performance of nonlinear metasurfaces is still modest. Flat optics have also shown their potential in the nonlinear optics with wavefront shaping in far-harmonic fields. There is currently a related effort by the nonlinear nanophotonics community to seek higher conversion efficiencies across narrow resonances of the quasi-bound states of the continuum (qBIC) associated with strong near-field coupling and nonlocal resonance modes. However, the overall performance is relatively weak as most of the current studies ignore the strong near-field coupling between neighboring cells. In this collaboration, we exploit the specific advantages of 'thin' resonators that behave like phased-array antennas, unlike photonic crystals with strong localized energies, to develop highly efficient nonlinear metasurfaces for nonlinear wavefront shaping. Within this strategy, we improve the performance of nonlinear wavefront shaping by inverse design optimization of both meta-atoms and meta-molecules. In addition, we consider long-term design options for nonlinear metasurfaces based on perfect nonlocal responses and long-range near-field coupling, and rigorous computational methods to address nonlinearities in terms of nonlocal configurations. Our preliminary results (see Fig. 13) show the ability to improve the second harmonic generation signal by almost a factor of seven. Fabrication and characterization of the structure is currently underway, and the results will be published in a prominent journal. Since October 2024, we continue this study in the context of the ANR NO-RESTRAIN project, which is coordinated by Giuseppe Leo from the MPQ (Matériaux et Phénomènes Quantiques) at Université Paris Cité, France.

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Optimized second-harmonic generation (SHG) from an asymmetric nanochair (inset). The left column represent the comparison of SHG response as a function of the pump wavelength for three different designs (classical denote the design without optimization). The right column refers to the field profiles at the two frequencies $2\omega$ and $\omega$ for the optimal design.

10.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program

10.1.2 STIC/MATH/CLIMAT AmSud projects

• Claire Scheid is member of the MatAmSud (between Chile, Uruguay, Argentina and France) project entitled NoLoCE (Nonlocal and Local Coupled Equations: Analysis, Computation, and Probability), PI: Juan Pablo Borthagaray (Associate Professor at the Instituto de Matemática y Estadística, Facultad de Ingeniería, Universidad de la República, Uruguay).

10.2.1 ANR projects

10.2.2 DGA/AID RAPID project

11.1.1 Scientific events: organisation

11.1.2 Journal

• Stéphane Lanteri is the Lead Editor of a feature issue of Journal of the Optical Society of America B dedicated to recent research results on inverse design in photonics 27.

11.1.3 Invited talks

• Mahmoud Elsawy, September 26, 2024, INSP - Sorbonne Université, Paris.
• Mahmoud Elsawy, November 8, 2024, Laboratory of Applied and Computational Electromagnetics (LEMAC), Universidade Estadual de Campinas, Brazil.
• Claire Scheid, Oberwolfach workshop on "Nonlinear Optics: Physics, Analysis, and Numerics", March 11-15, 2024, MFO center, Germany.
• Stéphane Lanteri was a plenary speaker at the 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation - Waves 202423, June 30-Jyly 5, 2025, Berlin, Germany.
• Stéphane Lanteri, April 30, 2024, CEA SPEC - IRAMIS, Gif-sur-Yvette, France.
• Stéphane Lanteri, October 10, 2024, Thales Research & Technology, Palaiseau, France.
• Stéphane Lanteri, November 8, 2024, Laboratory of Applied and Computational Electromagnetics (LEMAC), Universidade Estadual de Campinas Campinas, Brazil.
• Stéphane Lanteri, December 5, 2024, Barcelona Supercomputing Center, Spain.

11.1.4 Leadership within the scientific community

• Since July 2023, Claire Scheid is member of the Scientific Committee of the "Maison de la simulation et des interactions" of Université Côte d'Azur.
• Since October 2024, Claire Scheid is an elected CNU (Comité National des Universités) member of the 26th section (applied mathematics).
• Since June 2024, Stéphane Lanteri is a member of the Scientific Council of the 3iA Côte d'Azur.

11.1.5 Research administration

• Stéphane Lanteri is a member of the Project-team Committee's Bureau of the Inria research center at Université Côte d'Azur.
• Stéphane Lanteri is the Deputy Head of Science of Inria Research Center at Université Côte d'Azur (since September 2022).
• Stéphane Lanteri is a member of Evaluation Committee of Inria (since September 2022).
• Since September 2024, Claire Scheid is responsible (maths side) of the Mathematics-Physics double degree program (for the 3 years) at Université Côte d'Azur.

11.2.1 Teaching

• Mahmoud Elsawy, Resolution of linear and nonlinear systems, 24h TP, L3, Université Côte d'Azur.
• Claire Scheid, Optimisation et éléments finis. Lecture, practical works, M1 MPA and IM, 72h eq.TD, Université Côte d'Azur.
• Claire Scheid, Option modélisation. Lectures and practical works, M2 Agrégation, 45h eq.TD, Université Côte d'Azur.
• Claire Scheid, Approximation Numérique des fonctions, intégrales et équations différentielles. Lecture, L3, 56h, Université Côte d'Azur.
• Stéphane Descombes, Scientific Machine Learning, 15 h, MAM5, Polytech Nice Sophia - Université Côte d'Azur.
• Stéphane Descombes, Approximation Numérique des fonctions, intégrales et équations différentielles, practical works, L3, 28h, Université Côte d'Azur.
• Stéphane Descombes, Introduction aux équations aux dérivées partielles, M1, 30h, Université Côte d'Azur.
• Stéphane Descombes, Calcul scientifique, M1, 30h, Université Côte d'Azur
• Stéphane Lanteri, Scientific Machine Learning, 24 h, MAM5, Polytech Nice Sophia - Université Côte d'Azur.

11.2.2 Supervision

• PhD in progress: Arthur Clini De Souza. (Cifre PhD grant with Solnil, Marseille), Deep neural networks for the design of large-scale photonic devices for active beam steering, co-supervised by Mahmoud Elsawy and Stéphane Lanteri.
• PhD in progress: Daria Hrebenshchykova (PEPR NumPEx PhD fellowship), Building physics-based multilevel substitution models from neural networks. Application to electromagnetic wave propagation, co-supervised by Victor Michel-Dansac (MACARON project-team, Centre Inria de l'Université de Lorraine), Victorita Dolean (Eindhoven University of Technology, The Netherlands) and Stéphane Lanteri.
• PhD in progress: Enzo Isnard (Cifre PhD grant with Thales Research & Technology, Palaiseau), Modeling and optimization of freeform optical metasurfaces integrated into an imaging system, co-supervised by Mahmoud Elsawy and Stéphane Lanteri.
• PhD in progress: Carlotta Filippin (ANR SWAG-P PhD fellowship), Reduced-order modeling and global optimization for the robust design of Gap Plasmon Resonators, co-supervised by Claire Scheid, Antoine Moreau (Institut Pascal, Universi†é Clermont-Auvergene) and Stéphane Lanteri.
• PhD in progress: Roman Gelly (PhD fellowship from Université Côte d'Azur), Advanced numerical modeling of time-modulated metasurfaces, co-supervised by Mahmoud Elsawy and Stéphane Lanteri.
• PhD defended: Jérémy Grebot (Cifre PhD grant with STMicroelectronics), Advanced modeling of nanostructured CMOS imagers28, Université Côte d'Azur, May 2024, co-supervised by Stéphane Lanteri and Claire Scheid.
• PhD in progress: Thibault Laufroy (PhD fellowship from Université Côte d'Azur), High order finite element type solvers for thermoplamonics, co-supervised by Yves d'Angelo and Claire Scheid.
• PhD in progress: Cédric Legrand (DGA-Inria PhD fellowship), High order finite element type solvers for modeling gain media, co-supervised by Stéphane Descombes and Stéphane Lanteri.
• PhD in progress: Florentin Proust, Novel finite element methods for dealing with high frequency wave propagation problems, co-supervised by Maxime Ingremeau (Université Côte d'Azur, LJAD) and Théophile Chaumont-Frelet.
• PhD in progress: Alexandre Pugin (DGA-Inria PhD fellowship), Physically informed neural networks for building surrogate models in numerical electromagnetics, co-supervised by Stéphane Descombes and Stéphane Lanteri.
• Apprenticeship in progress: Julien Noël (MAM5, Polytech Nice Sophia - Université Côte d'Azur), Numerical study of Maxwell-Schrödinger equations, co-supervised by Stéphane Descombes and Claire Scheid.
• Postdoc in progress: Ayoub Bellouch (AEROCOM RAPID project), Advanced computational design of cascaded metadeflectors for an ultra-flat antenna system Lanteri Stéphane, co-supervised by Mahmoud Elsawy and Stéphane Lanteri.
• Postdoc in progress: Alemayehu Getahun Kumela (Inria Exploratory Action META4PIQ), Metasurfaces for quantum information processing, supervised by Mahmoud Elsawy.

11.2.3 Juries

• Mahmoud Elsawy was an examiner for the PhD of Lucas Grosjean, entitled "Nanophotonique en niobate de lithium pour l'intelligence artificielle", Université Bourgogne Franche-Comté, France, December 16, 2024.
• Mahmoud Elsawy was an examiner for the PhD of Xingyu Yang entitled "Manipulating the inverse Faraday effect at the nanoscale", Sorbonne Université, France, September 27, 2024.
• Claire Scheid was an examiner for the PhD of Étienne Peillon entitled "Simulation and analysis of sign-changing Maxwell’s equations in cold plasma", ENSTA, Institut Polytechnique de Paris, France, April 4, 2024.
• Stéphane Lanteri was a reviever for the HDR (accreditation to supervise research) of Juliette Chabassier entitled "Modélisation physique et simulation numérique d’instruments de musique", Université de Pau et des Pays de l'Adour, France, June 26, 2024.
• Stéphane Lanteri was an examiner for the PhD of Francisco Orlandini entitled "A waveguide port boundary condition for the finite element analysis of optical devices", Universidade Estadual de Campinas Campinas, Brazil, October 7, 2024.
• Stéphane Lanteri was an examiner for the PhD of Valentin Ritzenthaler entitled "Stratégies de couplage des méthodes Compatible Discrete Operators appliquées aux équations de Maxwell dans le domaine temporel", ISAE-SUPAERO, Toulouse, France, December 10, 2024.

International journals

• 19 articleT.Théophile Chaumont-Frelet and P.Patrick Vega. Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations.SIAM Journal on Numerical Analysis621February 2024, 400-421HALDOI
• 20 articleE.Enzo Isnard, S.Sébastien Héron, S.Stéphane Lanteri and M.Mahmoud Elsawy. Advancing wavefront shaping with resonant nonlocal metasurfaces: beyond the limitations of lookup tables.Scientific Reports14January 2024, 1555HALDOI

International peer-reviewed conferences

• 21 inproceedingsA.Arthur Clini de Souza, S.Stéphane Lanteri, H. E.Hugo Enrique Hernandez-Figueroa, M.Marco Abbarchi, D.David Grosso, B.Badre Kerzabi and M.Mahmoud Elsawy. Inverse design of bright, dielectric metasurfaces color filters based on back-propagation and multi-valued artificial neural networks.SPIE digital libraryMachine Learning in Photonics13017Proceedings Volume 13017, Machine Learning in Photonics; 130170E (2024)Strasbourg, FranceSPIEJune 2024, 24HALDOIback to text
• 22 inproceedingsE.Enzo Isnard, S.Sébastien Héron, M.Mahmoud Elsawy and S.Stéphane Lanteri. Modeling of centimeter-scale metasurfaces in imaging systems.SPIE digital libraryComputational Optics 202413023Proceedings volume 13023 SPIE optical systems design: Computational Optics 2024Strasbourg, FranceSPIEApril 2024, 15HALDOIback to text
• 23 inproceedingsS.Stéphane Lanteri, T.-Z.Ting-Zhu Huang, K.Kun Li, L.Liang Li and A.Alan Youssef. Reduced-order modeling for time-domain electromagnetics.Waves 2024 - The 16th International Conference on Mathematical and Numerical Aspects of Wave PropagationBerlin, GermanyL. GizonJune 2024, 25-30HALDOIback to text
• 24 inproceedingsA. C.Arthur Clini de Souza, P. E.Paloma Elias da Silva Pellegrini, S. V.Silvia Vaz Guerra Nista, S.Stéphane Lanteri, H. E.Hugo Enrique Hernandez-Figueroa, M.Marco Abbarchi, B.Badre Kerzabi and M.Mahmoud Elsawy. Cost-efficient deep learning method for mass inverse design of photonic devices.IEEE Xplore2024 SBFoton International Optics and Photonics Conference (SBFoton IOPC)Salvador, BrazilIEEEDecember 2024, 3HALDOIback to text

Conferences without proceedings

• 25 inproceedingsA.Ayoub Bellouch, M.Mahmoud Elsawy, S.Stéphane Lanteri, E.Erika Vandelle and T. Q.Thi Quynh Van Hoang. Inverse design of sub-wavelength metadeflectors for an ultra-flat antenna system in Ka-Band.JNM 2024 - XXIIIèmes Journées Nationales MicroondesAntibes Juan-Les-Pins, FranceJune 2024HALback to text
• 26 inproceedingsT.Théophile Chaumont-Frelet, V.Victorita Dolean, M.M Ingremeau and F.Florentin Proust. A Galerkin method with microlocalised shape functions to solve high-frequency Helmholtz problems.ECCOMAS 2024Lisbonne, PortugalJune 2024HALback to text

Edition (books, proceedings, special issue of a journal)

• 27 periodicalInverse design in photonics.Journal of the Optical Society of America B41Inverse design in photonics2January 2024, IDP1HALDOIback to text

Doctoral dissertations and habilitation theses

• 28 thesisJ.Jérémy Grebot. Advanced modeling of CMOS imagers.Université Côte d'AzurMay 2024HALback to text

Reports & preprints

• 29 miscA.Ayoub Bellouch, M.Mahmoud Elsawy, S.Stéphane Lanteri, E.Erika Vandelle and T. Q.Thi Quynh Van Hoang. Advanced optimization based on Bayesian learning to design nonlocal metasurfaces deflectors for satellite communication.December 2024HAL
• 30 reportC.Carlotta Filippin, M.Maria Strazzullo, S.Stéphane Lanteri and F.Federico Pichi. Nonlinear reduced-order modeling with a Graph Convolutional Autoencoder for time-domain electromagnetics.RR-9565Universite Cote d'Azur; Politecnico di TorinoOctober 2024HAL
• 31 reportS.Stéphane Lanteri, D.Daria Hrebenshchykova, V.Victor Michel-Dansac and V.Victorita Dolean. Multilevel and Distributed Physics-Informed Neural Networks for the Helmholtz Equation.RR-9571Inria & Université Cote d'Azur, CNRS, I3S, Sophia Antipolis, FranceOctober 2024HALback to text
• 32 miscS.Stéphane Lanteri, M.Massimiliano Montone and C.Claire Scheid. A discontinuous time-domain fullwave approach for semiconductors.September 2024HALback to text