RESEARCH CENTRE

Inria Centre
at Université Côte d’Azur

IN PARTNERSHIP WITH:

CNRS, Université Côte d’Azur

2023
ACTIVITY REPORT

Project-Team

ATLANTIS

modeling and numerical methods for
computATionaL wave-mAtter iNteracTIons
at the nanoScale

IN COLLABORATION WITH: Laboratoire Jean-Alexandre Dieudonné (JAD)

DOMAIN

Applied Mathematics, Computation and
Simulation

THEME

Numerical schemes and simulations

Contents

Project-Team ATLANTIS

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

3.1 Driving physical fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Research agenda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Core research topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Complementary topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Application domains

4.1 Nanostructures for sunlight harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Metasurfaces for light shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 THz wave generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Plasmonic nanostructures for nanoscale sensing . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Plasmonic nanostructures for photothermal effects . . . . . . . . . . . . . . . . . . . . . . . .

5 Social and environmental responsibility

5.1 Impact of research results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 New software, platforms, open data

6.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 DIOGENeS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 New results

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7.1 High order methods for coupled problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7.1.1 Time-domain numerical modeling of gain media . . . . . . . . . . . . . . . . . . . . . 10
7.1.2 Time-domain numerical modeling of semiconductor devices . . . . . . . . . . . . . . 10
7.1.3 A posteriori error estimates for time-dependant wave propagation problems
. . . . 11
7.1.4 Efficient approximation of high-frequency Helmholtz problems . . . . . . . . . . . . 11
7.2 Data-driven reduced-order modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
7.2.1 Non-intrusive ROM for parameterized electromagnetic problems . . . . . . . . . . . 12
7.2.2 ROM using matrix decomposition and deep neural networks . . . . . . . . . . . . . . 13
7.2.3 ROM via dynamic mode decomposition and radial basis functions
. . . . . . . . . . 13
7.2.4 Nonlinear ROM with Graph Convolutional Autoencoder . . . . . . . . . . . . . . . . . 13
7.3 Dealing with complex models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
7.3.1 Toward thermoplasmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
7.4 Deep Learning methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
. . . . . . . . . . . . . . . 14
15

7.4.1 Physics-Informed Neural Networks for Maxwell equations
7.4.2 Interplay of Physics-Informed Neural Networks and multiscale numerical methods
7.4.3 Back-propagation optimization and multi-valued artificial neural networks for highly

vivid structural color filter metasurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7.5 Discovering novel nanoscale structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
7.5.1 Universal active metasurfaces for ultimate wavefront molding by manipulating the

reflection singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7.5.2 Advancing wavefront shaping with resonant nonlocal metasurfaces: beyond the

limitations of lookup tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.6 Software developments in DIOGENeS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7.7.1 Advanced modeling of nanostructured CMOS imagers based on DG methods . . . . 20
7.7.2 Nanoimprint color filter metasurface for imaging devices . . . . . . . . . . . . . . . . 21
7.7.3 Optimization of light trapping in nanostructured solar cells . . . . . . . . . . . . . . . 21
7.7.4 Plasmonic sensing with nanocubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7.7.5 Multiple scattering in random media . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
7.7.6 Nonlinear wavefront shaping with optical metasurfaces . . . . . . . . . . . . . . . . . 23
7.7.7 Biosensor metasurface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

8 Bilateral contracts and grants with industry

25
8.1 Bilateral contracts with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
8.2 Grants with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

9 Partnerships and cooperations

9.2 International research visitors

9.1.1 STIC/MATH/CLIMAT AmSud projects

27
9.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
9.2.1 Visits of international scientists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
9.4 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
9.4.1 ANR project
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
9.4.2 DGA/AID RAPID project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

9.3 European initiatives

9.3.1 H2020 projects

10 Dissemination

30
10.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10.1.2 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10.1.3 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
10.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

11 Scientific production

32
11.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
11.2 Publications of the year
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
11.3 Cited publications

Project ATLANTIS

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Project-Team ATLANTIS

Creation of the Project-Team: 2020 February 01

Keywords

Computer sciences and digital sciences

A6. – Modeling, simulation and control

A6.2. – Scientific computing, Numerical Analysis & Optimization

A6.2.1. – Numerical analysis of PDE and ODE

A6.2.7. – High performance computing

Other research topics and application domains

B4. – Energy

B4.3.4. – Solar Energy

B5.3. – Nanotechnology

B5.5. – Materials

B8. – Smart Cities and Territories

B8.2. – Connected city

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Stéphane Lanteri [Team leader, INRIA, Senior Researcher, HDR]

• Theophile Chaumont-Frelet [INRIA, Researcher, until Sep 2023]

• Mahmoud Elsawy [INRIA, ISFP]

• Frédéric Valentin [LNCC-PETROPOLIS, Senior Researcher, until Feb 2023, Inria International Chair]

Faculty Members

• Yves D Angelo [UNIV COTE D’AZUR, Professor, HDR]

• Stéphane Descombes [UNIV COTE D’AZUR, Professor, HDR]

• Claire Scheid [UNIV COTE D’AZUR, Associate Professor, HDR]

Post-Doctoral Fellow

• Ayoub Bellouch [INRIA, Post-Doctoral Fellow, from Oct 2023]

PhD Students

• Arthur Clini De Souza [SOLNIL, CIFRE, until Apr 2023]

• Jérémy Grebot [STMICROELECTRONICS, CIFRE, until Feb 2023]

• Enzo Isnard [THALES, CIFRE]

• Thibault Laufroy [UNIV COTE D’AZUR]

• Cedric Legrand [INRIA]

• Martin Lepers [STMICROELECTRONICS, CIFRE, with CEA LETI and CRHEA]

• Larissa Miguez Da Silva [LNCC-PETROPOLIS, from Mar 2023]

• Massimiliano Montone [INRIA, until Mar 2023]

• Florentin Proust [INRIA]

Technical Staff

• Alexis Gobe [INRIA, Engineer]

• Guillaume Leroy [INRIA, Engineer]

• Alan Youssef [INRIA, Engineer, from Oct 2023]

Interns and Apprentices

• Gaspard Brunelle [INRIA, Intern, from May 2023 until Aug 2023]

• Carlotta Filippin [INRIA, Intern, from Oct 2023]

• Roman Gelly [INRIA, Apprentice, from Sep 2023]

• Oussama Hajji [INRIA, Intern, from Jun 2023 until Sep 2023]

• Alexandre Pugin [INRIA, Intern, from Sep 2023]

Project ATLANTIS

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Administrative Assistant

• Delphine Robache [INRIA]

Visiting Scientist

• Christophe Geuzaine [UNIV GAND, from Apr 2023 until May 2023]

2 Overall objectives

Nanostructuring of materials has paved the way for manipulating and enhancing wave-matter interac-
tions, thereby opening the door for the full control of these interactions at the nanoscale. In particular,
the interaction of light waves (or more general optical waves) with matter is a subject of rapidly increasing
scientific importance and technological relevance. Indeed, the corresponding science, referred to as
nanophotonics [55], aims at using nanoscale light-matter interactions to achieve an unprecedented level
of control on light. Nanophotonics encompasses a wide variety of topics, including metamaterials, plas-
monics, high resolution imaging, quantum nanophotonics and functional photonic materials. Previously
viewed as a largely academic field, nanophotonics is now entering the mainstream, and will play a major
role in the development of exciting new products, ranging from high efficiency solar cells, to personalized
health monitoring devices able to detect the chemical composition of molecules at ultralow concentra-
tions. Plasmonics [60] is a field closely related to nanophotonics. Metallic nanostructures whose optical
scattering is dominated by the response of the conduction electrons are considered as plasmonic media.
If the metallic structure presents an interface with a positive dielectric permittivity, collective oscillations
of surface electrons create waves (called surface plasmons) that are guided along the interface, with the
unique characteristic of subwavelength-scale confinement. Nanofabricated systems that exploit these
plasmon waves offer fascinating opportunities for crafting and controlling the propagation of light in
matter. In particular, it can be used to channel light efficiently into nanometer-scale volumes. As light
is squeezed down into nanoscale volumes, field enhancement effects occur resulting in new optical
phenomena that can be exploited to challenge existing technological limits and deliver superior photonic
devices. The resulting enhanced sensitivity of light to external parameters (for example, an applied
electric field or the dielectric constant of an adsorbed molecular layer) shows also great promises for
applications in sensing and switching.

In ATLANTIS, our research activities aim at studying and impacting some scientific and technological
challenges raised by physical problems involving optical waves in interaction with nanostructured matter.
A crucial component in the implementation of this scientific endeavor lies in a close networking with
physicists who bring the experimental counterpart of the proposed research. Driven by a number of
nanophotonics-related physical drivers, our overall objectives are to design and develop innovative
numerical methodologies for the simulation of nanoscale light-matter interactions and to demonstrate
their capabilities by studying challenging applications in close collaboration with our physicist partners.
On the methodological side, the Discontinous Galerkin (DG) family of methods is a cornerstone of our
contributions. In particular, we study various variants of DG methods that can deal with complex material
models and coupled PDE systems that are relevant to the study of nanoscale light-matter interactions.
Moreover, mathematical modeling is a central activity of the team, in particular for shaping initial and
boundary value problems in view of devising accurate, efficient and robust numerical methods in the
presence of multiple space and time scales or/and geometrical singularities. Additional methodological
topics that are considered in close collaboration with colleagues from other Inria teams or external
applied mathematics research groups are model order reduction, inverse design. Novel methodological
contributions on these topics in the context of the physical problems studied in ATLANTIS are even-
tually implemented in the DIOGENeS software suite, which is a unique software plaform dedicated to
computational nanophotonics.

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Inria Annual Report 2023

3 Research program

3.1 Driving physical fields

Our research activities eventually materialize as innovative computational techniques for studying
concrete questions and applications that are tightly linked to specific physical fields (driving physical
fields) related to nanophotonics and plasmonics. In most cases, these scientific topics and applications
are addressed in close collaboration with physicists.
Quantum plasmonics. The physical phenomena involved in the deep confinement of light when inter-
acting with matter opens a major route for novel nanoscale devices design. Indeed, the recent progress
of fabrication at the nanoscale makes it possible to conceive metallic structures with increasingly large
size mismatch, in which microscale devices can be characterized by sub-nanometer features [48]. These
advances have also allowed to achieve spatial separation between metallic elements of only few nano-
meters [47]. At such sizes quantum effects become non-negligible, producing huge variations in the
macroscopic optical response. Following this evolution, the quantum plasmonics field has emerged, and
with it the possibility of building quantum-controled devices, such as single photon sources, transistors
and ultra-compact circuitry at the nanoscale. In ATLANTIS, we study novel numerical modeling methods
for solving some semi-classical models of quantum plasmonic effects such as in the context of the PhD
work of Nikolkai Schmitt [69]-[18].
Planar optics. Nanostructuring of matter can be tailored to shape, control wavefront and achieve unusual
device operations. Recent years have seen tremendous advances in the fabrication and understanding
of two-dimensional (2D) materials, giving rise to the field of planar optics. In particular, the concept
of quasi-2D metasurfaces has started to develop into an exciting research area, where nanostructured
surfaces are designed for novel functionalities [56]-[46]-[51]. Metasurfaces are planar metamaterials with
subwavelength thickness, consisting of single-layer or few-layer stacks of nanostructures. They can be
readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave
propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying
optical response (e.g. scattering amplitude, phase, and polarization). They mold optical wavefronts into
shapes that can be designed at will, and facilitate the integration of functional materials to accomplish
active control and greatly enhanced nonlinear response. Our first contributions on this topic have been
obtained in the context of the ANR OPERA project (completed in September 2022) and are concerned
with numerical modeling methods for the inverge design of metasurfaces [9]-[7] and metalenses [8].
Thermoplasmonics. Plasmonic resonances can be exploited for many applications [60]. In particular,
the strong local field enhancement associated with the plasmonic resonances of a metallic nanostructure,
together with the absorption properties of the metal, induce a photo-thermal energy conversion. Thus, in
the vicinity of the nanostructure, the temperature increases. These effects, viewed as ohmic losses, have
been for a long time considered as a severe drawback for the realization of efficient devices. However,
the possibility to control this temperature rise with the illumination wavelength or polarization has
gathered strong interest in the nano-optics community, establishing the basis of thermoplasmonics [44].
By increasing temperature in their surroundings, metal nanostructures can be used as integrated heat
nanosources. Decisive advances are foreseen in nanomedicine with applications in photothermal cancer
therapy, nano-surgery, drug delivery, photothermal imaging, protein tracking, photoacoustic imaging,
but also in nano-chemistry, optofluidics, solar and thermal energy harvesting (thermophotovoltaics).
Optoelectronics and nanoelectronics. Semiconductors also play a major role in leveraging nanoscale
light-matter interactions. Emission or absorption of light by a semiconductor is at the heart of opto-
electronics, which is concerned with devices that source, detect or control light. Photodiodes, solar
cells, light emitting diodes (LEDs), optical fibers and semiconductor lasers are some typical examples of
optoelectronic devices. The attractive properties of these devices is based on their efficiency in converting
light into electrical signals (or vice versa). Using a structuration with low dimensional materials and
carrier-photons interaction, optoelectronics aims at improving the quality of these systems. A closeby
field is nanoelectronics [61], i.e., the physical field that, while incorporating manufacturing constraints,
tries to describe and understand the influence of the nanostructuration of electronic devices on their
electronic properties. This area has quickly evolved with the increasing fabrication capabilities. One
striking motivating example is the drastic increase of the number of transistors (of a few nanometer
size) per chip on integrated circuits. At the achieved nanostructuration scales, inter-atomic forces, tun-

Project ATLANTIS

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neling or quantum mechanical properties have a non-negligible impact. A full understanding of these
effects is mandatory for exploiting them in the design of electronic components, thereby improving their
characteristics.

3.2 Research agenda

The processes that underly the above-described physical fields raise a number of modeling challenges
that motivate our research agenda:

• They exhibit multiple space and time scales;

• They are highly sensitive to exquisite geometrical features of nanostructures and matter nanostruc-

turing;

• They impose dealing with unconventional material models;

• They may require to leave the comfortable setting of linear differential models;

• Some of them are inherently multiphysics processes.

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 vari-
ants, 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.

Multiscale modeling. The physical models that we consider may feature three different space scales.
First, the size of the computational domain is fixed by the nanostructure under consideration and
the required observables. Second, the solution wavelength depends on the operating frequency and
on the light velocity in the constitutive materials. Finally, the finest scale involved corresponds to
the nanostructuring length. These three space scales can differ by orders of magnitude, leading to
unaffordable computational costs, if the discretization scheme must resolve the nanostructure details. We
thus aim at designing multiscale numerical schemes, that can embed fine scale information into a coarser
mesh. Such methodologies lead to embarrassingly parallel two-level algorithms, that are especially suited
for HPC environments and produce accurate numerical approximations. These multiscale schemes are
designed in the framework of MHM (Multiscale Hybrid-Mixed) formulations that we study in the context
of a long-term collaboration with the research group of Frédéric Valentin at LNCC, Petropolis, Brazil. In
the MHM framework, the inherent upscaling procedure that is at the heart of the approach, allows to
incorporate more physics in the numerical schemes themselves, as the upscaling principle is used to
construct physical basis functions that resolve the fine scales. At the second level, one defines a set of
boundary value problems, whose solutions call for adapted versions of classical finite element or DG
methods, and yield the upscaled basis functions.

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

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Inria Annual Report 2023

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 time-domain electromagnetics has been more scarce. We study
POD-based reduced-order modeling strategies in the context of a long-term collaboration with the
research group of Liang Li at the School of Mathematical Sciences of the University of Electronic Science
and Technology of China in Chengdu [13]-[11]-[12]. Alternatively, several works in the recent years have
promoted highly efficient surrogate modeling approaches based on Deep Neural Networks (DNNs) but
most of these approaches rely on the availability of large data set of solutions for training. We initiated
in 2022 a new research direction on a particular family of DNNs referred as Physics-Informed Neural
Networks (PINNs) [67] 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 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 con-
sidered 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.

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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 [62]. Artificial Intelligence (AI) techniques
are also increasingly investigated within this context [71]. 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 [52]-[53] and fluid-structure
interaction problems [68].

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 [57]. 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 [16]. 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 [43], or low-rank compression techniques [66].
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.

4 Application domains

Nanoscale wave-matter interactions find many applications of industrial and societal relevance. The
applications discussed in this section are those that we address in the first place in the short- to medium-
term. Our general goal is to impact scientific discovery and technological development in these applic-
ation topics by leveraging our methodological contributions for the numerical modeling of nanoscale
wave-matter interactions, and working in close collaboration with external partners either from the
academic or the industrial world. Each of these applications is linked to one or more of the driving
physical fields described in section 3.1 except nanoelectronics that we consider as a more prospective,
hence long-term application.

4.1 Nanostructures for sunlight harvesting

Photovoltaics (PV) converts photon energy from the sun into electric energy. One of the major challenges
of the PV sector is to achieve high conversion efficiencies at low cost. Indeed, the ultimate success of
PV cell technology requires substantial progress in both cost reduction and efficiency improvement. An
actively studied approach to simultaneously achieve both objectives is to exploit light trapping schemes.
Light trapping enables solar cells absorption using an active material layer much thinner than the material
intrinsic absorption length. This then reduces the amount of materials used in PV cells, cuts cell cost,

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facilitates mass production of these cells that are based on less abundant material and moreover can
improve cell efficiency (due to better collection of photo- generated charge carriers). Enhancing the light
absorption in ultrathin film silicon solar cells is thus of paramount importance for improving efficiency
and reducing costs. Our activities in relation with this application field aim at precisely studying light
absorption in nanostructured solar cell structures with the help of an adapted numerical procedure.
We consider both the characterization of light trapping for a given texturing of material layers, and the
goal-oriented inverse design of the nanostructuring.

4.2 Metasurfaces for light shaping

Metasurfaces produce abrupt changes over the scale of the free-space wavelength in the phase, amplitude
and/or polarization of a light beam. Metasurfaces are generally created by assembling arrays of miniature,
anisotropic light scatterers (i.e. resonators such as optical antennas). The spacing between antennas
and their dimensions are much smaller than the wavelength. As a result the metasurfaces, on account
of Huygens principle, are able to mould optical wavefronts into arbitrary shapes with subwavelength
resolution by introducing spatial variations in the optical response of the light scatterers. Designing
metasurfaces for realistic applications such as metalenses [70] is a challenging inverse problem. In this
context, the ultimate goal of our activities is to develop numerical methodologies for the inverse design
of large-area metasurfaces [65].

4.3 THz wave generation

Recent research on the interaction of short optical pulses with semiconductors has stimulated the devel-
opment of low power terahertz (THz) radiation transmitters. The THz spectral range of electromagnetic
waves (0.1 to 10 THz) is of great interest. In particular, it includes the excitation frequencies of semi-
conductors and dielectrics, as well as rotational and vibrational resonances of complex molecules. As
a result, THz waves have many applications in areas ranging from the detection of dangerous or illicit
substances and biological sensing to diagnosis and diseases treatment in medicine. The most common
mecanism of THz generation is based on the use of THz photoconductive antennas (PCA), consisting of
two electrodes spaced by a given gap and placed onto a semiconductor surface. The excitation of the gap
by a femtosecond optical pulse induces a sharp increase of the concentration of charge carriers for a short
period of time, and a THz pulse is generated. Computer simulation plays a central role in understanding
and mastering these phenomena in order to improve the design of PCA devices. The numerical modeling
of a general 3D PCA configuration is a challenging task. Indeed, it requires the simultaneous solution
of charge transport in the semiconductor substrate and the electromagnetic wave radiation from the
antenna [64]-[72]. The recently-introduced concept of hybrid photoconductive antennas leveraging
plasmonic effects is even more challenging [59]. So far, existing simulation approaches are based on the
Finite Difference Time-Domain (FDTD) method, and are only able to deal with classical PCAs. In relation
with the design of photonic devices for THz waves generation and manipulation, we intend to develop a
multiscale numerical modeling strategy for solving the system of Maxwell equations coupled to various
models of charge carrier dynamics in semiconductors.

4.4 Plasmonic nanostructures for nanoscale sensing

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. Nanocubes
are extensively studied in this context and have been shown to support such gap plasmon modes. At
visible frequencies, the lossy behavior of metals will cause the progressive absorption of the trapped
electromagnetic field, turning the metallic nanocubes into efficient absorbers. The frequencies at which
this absorption occurs can be tuned by adjusting the dimensions of the nanocube and the spacer. Such
metallic nanocubes can be used for a broad range of applications including plasmonic sensing, surface
enhanced Raman scattering (SERS), metamaterials, catalysis, and bionanotechnology. We aim at devising

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a numerical methodology for characterizing the impact of geometrical parameters such as the dimensions
of the cube, the rounding of nanocube corners or the size of the slit separating the cube and the substrate,
on the overall performance of these absorbers. In practice, this leads us to address two main modeling
issues. First, as the size of the slit is decreased, spatial dispersion effects [50] have to be taken into account
when dealing with plasmonic structures. For this purpose, we consider a fluid model in the form of a
nonlocal hydrodynamic Drude model [49], which materializes as a system of PDEs coupled to Maxwell’s
equations [18]-[17]. The second issue is concerned with the assessment of geometrical uncertainties and
their role in the development of spatial dispersion effects.

4.5 Plasmonic nanostructures for photothermal effects

The field of thermoplasmonics has developed an extensive toolbox to produce, control and monitor
heat at the nanometer scale. Nanoparticles are promising nano-sensing and nano-manipulating tools,
and recent studies yielded remarkable advances in design, synthesis, and implementation of lumines-
cent nanoparticles. Some applications deal with bio-imaging and bio-sensing, like e.g. luminescent
nanothermometers, nanoparticles capable of providing contactless thermal reading through their light
emission properties [58]. Also, bio-functionalized gold nanorods are promising candidates for light-
induced hyperthermia [63], to cause local and selective damage in malignant tissue. At the same time,
laser pulse interaction with plasmonic nanostructures can also be exploited for cell nanosurgery [45],
including plasmonic enhanced cell transfection, molecular surgery and drug delivery. In parallel to all
these bio-oriented applications, plasmonic nanoparticles can also be thought of as prototypic systems
for understanding fundamental aspects of nanoscale material as well as light-matter interaction. Specific
numerical modeling tools are essential to provide a good insight in this understanding.

5 Social and environmental responsibility

5.1 Impact of research results

The parts of our research activities that are addressing the design of nanostructures for sunlight harvesting
on one hand, and of nanostructures for photothermal effects on the other hand, target applications con-
cerned with production of renewable energy and biomedical engineering (ranging from light controlled
drug-release to the ongoing battle against Covid-19).

6 New software, platforms, open data

6.1 New software

6.1.1 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 numer-
ical 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/

Authors: Stéphane Lanteri, Nikolai Schmitt, Alexis Gobe, Jonathan Viquerat, Guillaume Leroy

Contact: Stéphane Lanteri

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7 New results

7.1 High order methods for coupled problems

In this section, we present ongoing studies aiming at designing, analyzing and developing novel high
order methods for solving electromagnetic wave propagation problems in general on one hand, and for
differential systems modeling nanoscale light-matter interactions with complex media on the other hand.
We focus on the family of Discontinuous Galerkin (DG) methods. In the time-domain setting, the starting
point of these works is the DGTD (Discontinuous Galerkin Time-Domain) method introduced in [10].
In the frequency-domain setting, the HDGFD (Hybridized Discontinuous Galerkin Frequency-Domain)
method [1] is considered as the basis of our works.

7.1.1 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 [54]. 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.

7.1.2 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

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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 [35]) 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 first 1D theoretical stability study has been completed. A
preprint is in finalization.

7.1.3 A posteriori error estimates for time-dependant wave propagation problems

Participants:

Théophile Chaumont-Frelet.

The goal of this research line is to rigorously estimate the error incured by numerical approximation

for time-dependent wave propagation problems.

In [2], we derive an equilibrated a posteriori error estimator for the space (semi) discretization of the
scalar wave equation by finite elements. In the idealized setting where time discretization is ignored
and the simulation time is large, we provide fully-guaranteed upper bounds that are asymptotically
constant-free and show that the proposed estimator is efficient and polynomial-degree-robust, meaning
that the efficiency constant does not deteriorate as the approximation order is increased. To the best
of our knowledge, this work is the first to propose an estimator for the wave equation that is provably
reliable and efficient in the same norm. We also explain, without analysis, how the estimator is adapted
to cover time discretization by an explicit time integration scheme. Numerical examples illustrate the
theory and suggest that it is sharp.

The work published in [2] is also the starting point of the ANR project APOWA, where other aspects of
the a posteriori error estimation for time-dependent wave propagation problems will be be studied in
depth.

7.1.4 Efficient approximation of high-frequency Helmholtz problems

Participants:

Théophile Chaumont-Frelet, Victorita Dolean (LJAD, Université
Côte d’Azur), 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, ...). 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...) have in common that they
are more and more expensive when the frequency of the waves increases. In [37], 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 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 [3], it had been mathematically proved that using Gaussian

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coherent states to solve high-frequency Helmholtz problems had some advantages. In 2023, we started to
prove similar - and even broader - results about Wilson basis.

7.2 Data-driven reduced-order modeling

In short, reduced order modeling (ROM) allows to construct simplifications of high fidelity, complex
models. The resulting lower fidelity (also referred as surrogate) models capture the salient features of the
source models so that one can quickly study a system’s dominant effects using minimal computational
resources. 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 [11]-[13] 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.

7.2.1 Non-intrusive ROM for parameterized electromagnetic problems

Participants:

Stéphane Lanteri, Kun Li (SUFEC, Chengdu, China), Liang Li (UESTC,
Chengdu, China), Ying Zhao (UESTC, Chengdu, China).

In [12], we have introduced a non-intrusive variant of the POD-based ROM initially introduced
in [11]-[13], in the context of parameterized time-domain electromagnetic scattering problems. The
considered parameters are the dielctric 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.

More recently, in [24]-[14], we have designed an improved versions of the POD-CSI method [12]. During
the offline stage, the training parameters are chosen by using a Smolyak sparse grid method with a fixed
approximation level L over a target parameterized space. For each selected parameter, the snapshot
vectors are first produced by a high order DGTD method. In order to minimize the overall computational
cost in the offline stage and to improve the accuracy of the Non-Intrusive MOR (NIMOR) method, a
radial basis function (RBF) interpolation method is then used to construct more snapshot vectors at the
sparse grid with approximation level L+1, which includes the sparse grids from approximation level L.
Moreover, a Gaussian process regression (GPR) method is proposed to approximate the dominating time-
and parameter-modes of the reduced coefficient matrices. During the online stage, the reduced-order
solutions for new time and parameter values can be rapidly recovered via outputs from the regression
models without using the DGTD method.

Finally, in [15], we study the simulation of the interaction of light with 3D metallic nanostructures using
an adapted version of the method initially introduced in [11]-[13].

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7.2.2 ROM using matrix decomposition and deep neural networks

Participants:

Xiao-Feng He (UESTC, Chengdu, China), Stéphane Lanteri, Kun Li (SU-
FEC, Chengdu, China), Liang Li (UESTC, Chengdu, China).

In [23], we propose a non-intrusive ROM method for solving parameterized electromagnetic scattering
problems. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized
time-domain Maxwell equations for some values of the material parameters using a fullwave solver based
on a high order discontinuous Galerkin time-domain (DGTD) method. To perform a prior dimensionality
reduction, a set of reduced basis (RB) functions are extracted from the database via a two-step proper
orthogonal decomposition (POD) method. Intrinsic coordinates of the high-fidelity solutions are further
compressed through a convolutional autoencoder (CAE) network. Singular value decomposition (SVD) is
then used to extract the principal components of the low dimensional coding matrices generated by CAE,
and a cubic spline interpolation-based (CSI) approach is employed for approximating the dominating
time- and parameter-modes of these matrices. The generation of the reduced basis and the training of the
CAE and CSI are accomplished in the offline stage, thus the RB solution for given time/parameter values
can be quickly recovered via outputs of the interpolation model and decoder network. In particular, the
offline and online stages of the proposed RB method are completely decoupled, which ensures the validity
of the method. The performance of the proposed CAE-CSI ROM is illustrated with numerical experiments
for scattering of a plane wave by a 2-D dielectric disk and a multi-layer heterogeneous medium.

7.2.3 ROM via dynamic mode decomposition and radial basis functions

Participants:

Stéphane Lanteri, Kun Li (SUFEC, Chengdu, China), Liang Li (UESTC,
Chengdu, China), Yixin Li (UESTC, Chengdu, China).

In [25], we study another variant of a non-intrusive model order reduction (NIMOR) method for
surrogate modeling of time-domain electromagnetic wave propagation. The nested POD method, as a
prior dimensionality reduction technique, is employed to extract the time- and parameter-independent
reduced basis (RB) functions from a collection of high-fidelity solutions (or snapshots) on a properly
chosen training parameter set. A dynamic mode decomposition (DMD) method, resulting in a further
dimension reduction of the NIMOR method, is then used to predict the reduced-order coefficient vectors
for future time instants on the previous training parameter set. The radial basis function (RBF) is employed
for approximating the reduced-order coefficient vectors at a given untrained parameter in the future time
instants, leading to the applicability of DMD method to parameterized problems. A main advantage of the
proposed method is the use of a multi-step procedure consisting of the POD, DMD and RBF techniques to
accurately and quickly recover field solutions from a few large-scale simulations. Numerical experiments
for the scattering of a plane wave by a dielectric disk, by a multi-layer disk, and by a 3-D dielectric sphere
nicely illustrate the performance of the NIMOR method.

7.2.4 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 [12] 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 quations. More precisely, we study the

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approach recently proposed in [42], 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).

7.3 Dealing with complex models

7.3.1 Toward thermoplasmonics

Participants:

Yves D’Angelo, Thibault Laufroy, Claire Scheid.

Although losses in metal are viewed as a serious drawback in many plasmonics experiments, ther-
moplasmonics is the field of physics that tries to take advantage of the latter. Indeed, the strong field
enhancement obtained in nanometallic structures lead to a localized temperature increase in its vicinity,
leading to interesting photothermal effects. Therefore, metallic nanoparticles may be used as heat
sources that can be easily integrated in various environments. This is especially appealing in the field of
nanomedecine and can for example be used for diagnosis purposes or nanosurgery to cite but just a few.
Due to the various scales and phenomena that come into play, 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. For the latter, we began an interdisciplinary collaboration with Stefan
Dilhaire (Professor, Laboratoire Ondes et matières d’Aquitaine, Bordeaux, France). A preprint with these
first results is in preparation. Moreover, to make the picture complete and investigate the parabolic limit
of the hyperbolic approximation, we also considered the numerical modeling of the parabolic version of
the model in a similar discrete framework. This will in particular allow us to assess the potential of an
hyperbolic approach. Finally a theoretical stability study is also in progress.

7.4 Deep Learning methods

We initiated in 2022 a prospective research direction on alternative numerical modeling methods based
on Neural Networks (NN). We investigate both data-driven and model-driven approaches for dealing
with the system of Maxwell equations possibly coupled with various material models of interest to
nanophotonics. One first question that we want to address is wether DL methods can yield highly
efficient surrogate models of 3D time-domain electromagnetic wave propagation problems. Beside, we
are also interested in devising DL-based methods for dealing with problems which are more difficult to
handle with traditional numerical methods such as electromagnetic wave interaction with space-time
adaptive materials or nonlinear media.

7.4.1 Physics-Informed Neural Networks for Maxwell equations

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Participants: Oussama Hajji, Stéphane Lanteri, Alexandre Pugin.

Numerical simulations of electromagnetic wave propagation problems primarily rely on discretiz-
ation 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 quanti-
fication). 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), ap-
proaches 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
[67]. 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 system
Maxwell equations. We have continued this study this year in the context of the internships of Oussama
Hajji (frequency-domain Maxwell equations) and Alexandre Pugin (time-domain Maxwell equations).

7.4.2 Interplay of Physics-Informed Neural Networks and multiscale numerical methods

Participants:

Antonio Tadeu Gomes (LNCC, Petropolis, Brazil), Stéphane Lan-
Larissa Miguez Da Silva (LNCC, Petropolis, Brazil),
teri,
Frédéric Valentin (LNCC, Petropolis, Brazil).

This study is concerned with multiscale modeling using the family of Multiscale Hybrid-Mixed (MHM)
algorithms. and aims at improving the accuracy and computational efficiency of MHM methods for wave
propagation PDE models. For that purpose, we adopted numerical analysis tools based on hybridization
techniques as usual, and in a more innovative way investigating the interaction between multiscale
methods and the new field of Scientific Artificial Intelligence (SciIA). Specifically, we investigate alternat-
ives to the current computational cost of the MHM method, notably associated with the calculation of
multiscale basis functions. In fact, it can become particularly prohibitive in time-dependent or nonlinear
3D problems. We foresee the strategies to resolve such a drawback by proposing a hybrid strategy to
adapt the MHM methodology to incorporate scientific physics-driven machine learning techniques
(PINNs-Physical-Informed Neural Network, for example). We believe that such a methodology will be
at the forefront of the next wave of data-driven scientific discoveries in the physical and engineering
sciences.

7.4.3 Back-propagation optimization and multi-valued artificial neural networks for highly vivid

structural color filter metasurfaces

Participants: Hugo Enirique Hernández-Figueroa (Laboratory of Applied and Com-
putational Electromagnetism (LEMAC), University of Campinas, Sao
Paulo, Brazil), , David Grosso (CNRS-IM2NP, Université Aix Marseille,
France), Badre Kerzabi (Solnil, Marseille, France), Marco Abbarchi (),
Arthur Clini de Souza, Mahmoud Elsawy, Stéphane Lanteri.

In this work, we introduce a novel technique for designing color filter metasurfaces using a data-driven
approach based on deep learning. Our innovative approach employs inverse design principles to identify
highly efficient designs that outperform all the configurations in the dataset in terms of color filtering

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Inria Annual Report 2023

properties, which consists of 585 distinct geometries solely. By combining Multi-Valued Artificial Neural
Networks and back-propagation optimization, we overcome the limitations of previous approaches, such
as poor performance due to extrapolation and undesired local minima. The numerical tool developed
in this study enables the cost-effective fabrication of structural color filters by exploring a wide range
of narrow line shapes that exhibit high-quality resonances, aligning with desired spectral reflection
responses. Notably, our methodology expands the color gamut beyond the conventional RGB colors,
offering unprecedented versatility in color generation (see Fig. 1). Furthermore, our Deep Learning
approach successfully respects fabrication constraints, ensuring practical feasibility. The achievements
of our research significantly contribute to the field of optical device design. By pushing the boundaries of
metasurface optimization, we open up new possibilities for the development of advanced optical devices.
The proposed methodology holds promise for various applications, such as display technologies, data
encoding, and artistic expression. These notable advancements not only enhance the understanding
of metasurface design principles but also provide valuable insights for future research endeavors. The
paper has been published recently in Scientific Reports journal [21]

Figure 1: (a) Chromaticity diagram depicting the outcomes of the 100 optimization results. The arrows
in the diagram indicate the corresponding designs showcased in (b). The gray line represents the
calculated perceived color corresponding to the target spectrum. (b) Detailed examination of 6 different
optimizations, displaying their dimensions (in nm) of each geometrical parameter and the corresponding
sRGB color representation of the simulated spectrum.

7.5 Discovering novel nanoscale structures

At the creation of the team in February 2020, our collaborations with physicists from the nanophotonics
domain aimed at leveraging our developed numerical modeling methodologies in order to study specific
topics in relation with concrete applications (see Section 7.7 for more details). An evolution that started
in 2022 was our will to adapt and exploit these numerical methodologies to discover nanostructure
organizations exhibiting behaviors and performances opening the road to new application perspectives.

7.5.1 Universal active metasurfaces for ultimate wavefront molding by manipulating the reflection

singularities

Project ATLANTIS

Participants:

(CRHEA

laboratory,

Colom (CRHEA

Antipolis),
Patrice Genevet
Antipolis),
Rémi
Antipolis),
Christina
Elena Mikheeva (CRHEA laboratory, Sophia Antipolis),
Jean-
Yves Duboz (CRHEA laboratory, Sophia Antipolis), Mahmoud Elsawy,
Stéphane Lanteri.

Sophia
Sophia
Sophia

laboratory,

laboratory,

(CRHEA

Kyrou

17

Optical metasurfaces have become increasingly prevalent as key components for manipulating light
properties. Nevertheless, the majority of these devices remain passive and lack the capability to adapt to
changing environmental conditions. Here, we propose an innovative design approach using asymmetric
Gires–Tournois resonators to achieve comprehensive phase modulation of light with near-unity efficiency.
The active metasurface resonators filled with either silicon or hetero-structured materials. These choices
allow for the utilization of thermo-optical or electro-optical effects, respectively. Remarkably, in both
cases, complete phase modulation, combined with a 100% reflection amplitude, is observed, even when
dealing with exceedingly low refractive index changes on the order of 0.01. To account for the strong
nonlocal effect and enhance deflection efficiencies for each deflection angle, a sophisticated statistical
learning optimization methodology is employed to optimize the refractive index modulation profile
within the extended unit cell. As a result, active beam steering designs, leveraging the active thermo-
optical effect, have been optimized to achieve exceptional performance exceeding 90% (see Fig. 2).
Additionally, optimization efforts have been directed towards active wavefront splitting using electro-
optic materials, leading to ultimate modulation performance levels with nearly 92% efficiency. The
realization of highly efficient active beam shaping at high frequencies holds the potential for significant
applications in areas such as imaging microscopy and three-dimensional light detection and ranging
(LiDAR). The paper is published in Laser and Photonics Review [22].

7.5.2 Advancing wavefront shaping with resonant nonlocal metasurfaces: beyond the limitations of

lookup tables

Participants:

Sébastien Héron (Thales Research & Technology, Palaiseau, France),
Enzo Isnard, Mahmoud Elsawy, Stéphane Lanteri.

Resonant metasurfaces are of paramount importance in addressing the growing demand for reduced
thickness and complexity, while ensuring high optical efficiency. This becomes particularly crucial in
overcoming fabrication challenges associated with high aspect ratio structures, thereby enabling seam-
less integration of metasurfaces with electronic components at an advanced level. However, traditional
design approaches relying on lookup tables and local field approximations often fail to achieve optimal
performance, especially for nonlocal resonant metasurfaces. In this study, we investigate the use of
statistical learning optimization techniques for nonlocal resonant metasurfaces, with a specific emphasis
on the role of near-field coupling in wavefront shaping beyond single unit cell simulations. Indeed,
state-of-the art optimization algorithms as evolutionary algorithm and local gradient can be utilized, but
to the extent of requiring prohibitive number of simulations, getting stuck in a local design or requiring a
careful starting point. Three different resonant metasurfaces were considered in this study (see Fig. 3).
The first one operates in transmission and utilizes the properties of resonant Huygens metasurfaces.
Numerical results indicate that a beam steering metasurface achieved an efficiency of 80%, surpassing the
classical design with only 23% efficiency. Additionally, an extended depth-of-focus (EDOF) metalens was
optimized, resulting in a five-fold increase in focal depth and a four-fold enhancement in focusing power
compared to classical designs. Furthermore, the performance of wavelength-selected metagratings in
reflection was investigated based on asymmetric cavity considerations. Notably, non-intuitive designs
were obtained, surpassing 85% efficiency, which far exceeds the efficiency achieved with classical gradient
phase distribution. The presence of nonlocal effects arising from the interaction between neighboring
unit cells significantly alters the behavior of the fields. A comprehensive understanding of this phe-
nomenon is crucial for designing high-performance resonant metasurfaces. This knowledge empowers
researchers and engineers to create metasurfaces with enhanced performance, opening avenues for novel

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Inria Annual Report 2023

Figure 2: Active beam steering using an array of active G-T Si nanoresonators. Periodic electrical activation
of six (a) and four (d) unit cells with pixel-by-pixel refractive index modulation. The optimization results
for each case are depicted in (b) and (e), respectively. The beam steering responses after the optimized
refractive index distribution in the sequential pixels are shown in panels (c) and (f) for six- and four- pixels
configuration, respectively, with the corresponding field map at the design wavelength λ = 1500 nm. The
optimization parameters represent the refractive index distribution in each pixel represented by different
colors in (a) and (d).

Project ATLANTIS

19

applications in various domains. This work has been accepted for publication in Scientific Reports early
2024.

Figure 3: Optimization results for the EDOF nonlocal metalens. (a) Objective function values as a function
of the number of simulations. The insight represents the geometry of half of the metalens in the x
direction. (b) Field maps of ∥E∥2 at 1064 nm of the optimized design with fixed and varying h, the
parabolic designs and of the log-asphere design. The green rectangle represents the region in which
we try to increase the DOF (c) Plot of the minimum and maximum focus efficiency over 20 equally
spaced rectangles in the target region. The focus efficiency is defined as the part the incident power that
is transmitted in a focus plane. The focus efficiency for the optimized design with a varying h varies
from 26% to 35% while for the parabolic designs it varies between 0.05% and 27%. (d) Optical Transfer
Functions (OTFs) of each designs at f , f + 2.5 DOF and f + 5 DOF. Optimized designs preserve spatial
frequencies up to 600 cycle/mm at the three locations whereas the classical ones both fail at f + 5 DOF.

7.6 Software developments in DIOGENeS

Participants:

Alexis Gobé, Guillaume Leroy, Stéphane Lanteri.

In order to maximize the impact of our research activities described in section 3, a modern software
platform is necessary. For that purpose, the team develops the DIOGENeS (DIscOntinuous GalErkin Nano-
scale Solvers) software suite, which is dedicated to the numerical modeling of nanoscale wave-matter
interactions in the 3D case. The initial (and current) version of this software concentrates on light-matter
interactions with nanometer scale structures, for applications to nanophotonics and nanoplasmon-
ics. DIOGENeS is a unique numerical framework leveraging the capabilities of discontinuous Galerkin
methods for the simulation of multiscale problems relevant to nanophotonics and nanoplasmonics.
DIOGENeS is a major asset in our strategy to demonstrate that the methodological contributions that we
produce can be successfully applied to problems addressed by physicists and engineers trying to exploit
specific features of nanoscale wave-matter interactions for scientific and technological applications.

This suite is organized around the following components:

• A core library containing all the basic building blocks for the construction of high order discontinu-

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Inria Annual Report 2023

ous Galerkin methods formulated on tetrahedral, orthogonal hexahedral and hybrid tetrahedral-
hexahedral meshes;

• Fullwave solvers implementing high order discontinuous Galerkin methods for the discretization of
time domain (DGTD - Discontinuous Galerkin Time-Domain) and in frequency domain (HDGFD -
Hybridized Discontinuous Galerkin Frequency-Domain) coupled to a generalized model of physical
dispersion in metallic or semiconductor materials;

• A library of geometric modeling modules for the definition of simulation configurations involving
nanostructures or nanostructured materials. This library exploits the Python API of the GMSH
solver;

• A bridge component between fullwave solvers, geometric modeling modules and numerical op-
timization algorithms for the inverse design of nanostructures. This component integrates shape
parameterization modules, but also scripts defining optimization workflows driving the use of
statistical learning-based global optimization algorithms from the Triese toolbox, which is built on
TensorFlow and is dedicated to Bayesian optimization;

• A library of core modules for allowing users to define their own physical observables, e.g., total
transmittance, volumic absorptance, scattering parameters, etc., from results of fullwave simula-
tions.

The core library and the fullwave solvers are based on an object-oriented architecture implemented in
Fortran 2008. The DGTD and HDGFD solvers are adapted to high performance computing platforms. Two
levels of parallelization are currently exploited: a coarse-grained parallelization in distributed memory
(between SMP computation nodes) combining a partitioning of the computation mesh and a parallel
programming based on the message exchange model using the MPI standard.

This year several novel features have been developed that are concerned with the GFactory and Observer
components (see Fig. 4).

Figure 4: Architecture of the DIOGENeS software suite. DGTD and HDGFD are the high order DG-based
fullwave solvers for time-domain and frequency-domain modeling settings. GFactory is the geometrical
modeling component that exploits the Python API of the GMSH mesh generation tool. Observer is the base
component for developing post-processing scripts of simulation results. Optim is the base component
for developing inverse design workflows in Python by using statistical learning global optimization
algorithms from external frameworks such as Trieste.

7.7 Applications

7.7.1 Advanced modeling of nanostructured CMOS imagers based on DG methods

Project ATLANTIS

21

Participants:

Jérémy Grebot, Stéphane Lanteri, Denis Rideau (STMicroelectronics,
Crolles).

The exploitation of nanostructuring to improve the performance of CMOS imagers based on mi-
crolens 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, for what concern 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.

7.7.2 Nanoimprint color filter metasurface for imaging devices

Participants: David Grosso (Institut Matériaux Microélectronique Nanosciences de
Provence (IM2NP) Aix-Marseille Université and Solnil), Marco Abbar-
chi (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 deploy our optimization methodology
to maximize the efficiency of such metasurface configuration. 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.

7.7.3 Optimization of light trapping in nanostructured solar cells

Participants:

Stéphane Collin (Sunlit team, C2N-CNRS, Paris-Saclay), Alexis Gobé,
Stéphane Lanteri.

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 con-
siderations. In collaboration with physicists from the Sunlit team at C2N-CNRS, we exploit statistical

22

Inria Annual Report 2023

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 electro-
magnetic 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. 5. 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 the Sunlit headed by Stéphane Collin at the Center for Nanoscience
and Nanotechnology (C2N, CNRS).

Figure 5: Optimization of light absorption in a solar cell based on a nanocone grating.

7.7.4 Plasmonic sensing with nanocubes

Participants:

Antoine Moreau (Institut Pascal, Clermont-Ferrand), 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. 6). 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, which is coordinated by
Antoine Moreau.

7.7.5 Multiple scattering in random media

Participants:

Stéphane Descombes, Stéphane Lanteri, Guillaume Leroy, Cédric Le-
grand, Gian Luca Lippi (INPHYNI laboratory, Sophia Antipolis).

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

Project ATLANTIS

23

Figure 6: Optimization of a plasmonic nanocube dimer setting for the generation of Fano resonances.

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. 7). From the
numerical modeling point of view, or short term goal is to develop a time-domain numerical methodology
for the simulation of random lasing in a gain medium.

Figure 7: Multiple scattering by randomly distributed nanospheres in a bulk medium.

7.7.6 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

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Inria Annual Report 2023

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. 8)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.

Figure 8: 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 2ω and ω for the optimal design.

7.7.7 Biosensor metasurface

Participants: Haogang Cai (Department of Biomedical Engineering, New York Uni-

versity, USA), Mahmoud Elsawy, Stéphane Lanteri.

Over the last decades, the domain of nanophotonic biosensors has witnessed an expansion from
extensively investigated plasmonic platforms to dielectric metasurfaces. In contrast to plasmonic reson-
ance, dielectric metasurfaces operate on the basis of Mie resonances, yielding sensitivity comparable to
plasmonic counterparts while exhibiting superior resonance bandwidth, Q factor among others figures
of merit. While the plasmonic photothermal effect has proven advantageous in various biomedical
applications, it presents an inherent constraint in biosensing. Dielectric metasurfaces address issues
associated with ohmic loss and heating, thereby enhancing repeatability, stability, and biocompatibility.
However the overall performance is less than the plasmoic counterparts. In this collaboration, we exploit
innovative metasurface configurations characterized by high-Q resonances, providing insight into a range
of physical phenomena customized through the geometric designs of meta-atoms. Specifically, we engin-
eer a single-unit cell based on trimmer silicon meta-atoms, capitalizing on robust near-field coupling
by introducing symmetry breaking to the unit cell. This novel design facilitates the creation of a highly

Project ATLANTIS

25

efficient biosensor dielectric metasurface that surpasses the performance of conventional configurations.
The structure has been successfully fabricated and is presently undergoing characterization.

Figure 9: Optimized biosensor metasurface based on trimmer silicon meta-atoms.

8 Bilateral contracts and grants with industry

8.1 Bilateral contracts with industry

Nom: Simulation of photonic pigments

Participants:

Alexis Gobé, Stéphane Lanteri.

• Duration: Jun 2023 - Dec 2023

• Local coordinator: Stéphane Lanteri

• Participants: Valérie Alard [LVMH], Nicolas Benoot [LVMH]

• To manufacture a colored material, one normally use a dye or pigment. But another approach
to producing color is to fabricate a nanostructure that reflects or scatters light so that waves of
certain frequencies can interfere constructively. These nanostructured materials are said to have
structural colors. Unlike traditional traditional colors, which comes from light-absorbing dyes
or pigments that absorb light, structural colors can be made resistant to fading. In this context,
it is desirable to obtain a structural color that is independent of angle, i.e., the color is the same
regardless of the orientation of the material, and whatever the angle between the light source and
the eyes. There are many structurally colored materials that, like an opal stone, are iridescent, which
means that the color changes depending on viewing angle and orientation. The reason for this is
that the nanostructure of these materials is well-ordered (or crystalline), as in photonic crystals.
To manufacture materials whose color is independent of angle, we need to create disordered
nanostructures. These materials are called photonic glasses. The aim is to study how the optical
properties of these glasses are linked to their structure and the particles. This type of study is
primarily based on experiment. In this project, we relied on numerical modeling to study the
optical properties of photonic pigments.

Nom: SEASIDE - numerical Study of mEtasurfAceS by Inverse DEsign

Participants: Mahmoud Elsawy, Alexis Gobé, Guillaume Leroy, Stéphane Lanteri.

26

Inria Annual Report 2023

• Duration: Sep 2022 - Aug 2023

• Local coordinator: Stéphane Lanteri

• Participants: Abbarchi, David Grosso and Badre Kerzabi [Solnil, Marseille]

• Solnil is a startup company launched in 2020. Its activities are concerned with the design, develop-
ment, operation and provision of products, hardware, software services, automatons or complex
machines, implementing innovative technologies resulting from research on processes for the
nano-fabrication of sol-gel materials and in particular, the direct nano-printing of such materials
for various applications in the fields of optics and optoelectronics. Solnil carries out research and
development operations, as well as scientific and technical studies. The company’s ambition is to
exploit and industrialize a low-cost nano-fabrication process for optical applications. This process
is an evolution of an existing technology, referred as nanoimprinting, which can be described as a
molding process at sub-micrometer resolutions. The industrial applications of nanoimprinting
are numerous today numerous: 3D measurements for recognition, DNA sequencing augmented
reality glasses, anti-reflection films, LED sources etc. In the present project, which is a first step
toward a longer term partnership, we resort to numerical modeling for the optimal design of
metasurface-based multispectral sensors.

Nom: DGTD solvers for semiconductor device modeling

Participants:

Stéphane Lanteri, Massimiliano Montone, Claire Scheid.

• Duration: Nov 2019-Jan 2023

• Local coordinator: Stéphane Lanteri

• Participants: Eric Guichard [Silvaco Inc., Santa Clara, USA], Massimiliano Montone, Claire Scheid,
Slim Chourou [Silvaco Inc., Santa Clara, USA], Mark Townsend [Silvaco Inc., Santa Clara, USA]

• This contract with the TCAD division of Silvaco Inc. is closely linked to the PhD project of Massimili-
ano Montone and is concerned with the numerical modeling of semiconductor-based photonic
devices using high order DGTD methods. More precisely, the main methodological objective of
the PhD project is to design, analyze and develop DG-based approaches for solving the system
of time-domain Maxwell equations coupled to the unsteady drift-diffusion equations in 3D. On
the application side, in close collaboration with Silvaco Inc., microLEDs and CMOS image sensors
will constitute the driving technologies for the application of the methodological developments
achieved in the PhD work; moreover, nanostructured solar cells and photoconductive antennas
(including hybrid photoconductive antennas leveraging plasmonic effects) will serve as more
prospective applications that will possibly be considered in collaboration with physicists from
academic groups, which are partners of the ATLANTIS project-team.

8.2 Grants with industry

Nom: DGTD solvers for modeling light absorption in CMOS imagers

Participants:

Alexis Gobé, Jérémy Grebot, Guillaume Leroy, Stéphane Lanteri.

• Duration: Jan 2019-Jun 2023

• Local coordinator: Stéphane Lanteri

Project ATLANTIS

27

• Participants: Alexis Gobé, Valentin Goblot [STMicroelectronics, Crolles], Jérémy Grebot, Denis

Rideau [STMicroelectronics, Crolles], Guillaume Leroy, Claire Scheid

• This grant is part of the Nano 2022 IPCEI (Important Projects of Common European Interest) pro-
gram, which involves several European industrial groups and companies in the microelectronics
field. The team is involved in a subproject conducted in close collaboration with STMicrolectron-
ics (CMOS Imagers division of the Technology for Optical Sensors department) in Crolles. The
exploitation of nanostructuring to improve the performance of CMOS imagers based on microlens
grids is a very promising path. In this perspective, numerical modeling is a key component to
accurately characterize the absorption properties of these complex imager structures that are
intrinsically multiscale (from the micrometer scale of lenses to the nanometric characteristics of
nanostructured layers of materials). The FDTD method (for Finite Difference Time-Domain) is the
solution adopted in the first instance for the numerical simulation of the interaction of light with
this type of structure. However, because it is based on a Cartesian mesh (mostly uniform structured
mesh), this method has limitations when it comes to accurately account for complex geometrical
features such as microlens curvature or texturing of material layer surfaces. In this context, the
main objective of our study is to take advantage of the possibilities offered by the DGTD method
with realistic geometric models of complex imager structures based on locally refined tetrahedral
meshes.

9 Partnerships and cooperations

9.1 International initiatives

9.1.1 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 Probabil-
ity), PI: Juan Pablo Borthagaray (Associate Professor at the Instituto de Matemática y Estadística,
Facultad de Ingeniería, Universidad de la República, Uruguay).

9.2 International research visitors

9.2.1 Visits of international scientists

Inria International Chair

• Frédéric Valentin from LNCC, Petropolis, Brasil, is holding an Inria International Chair from January

2018 until May 2023. He has visited the team between January and February 2023.

Other international visits to the team

• Haogang Cai from the Health Technology and Engineering Institute (Tech4Health) at New York

University Grossman School of Medicine, USA, has visited the team on July 24-25 2023.

• Hugo Hernandez Figueroa who is the head of the Laboratory of Applied and Computational
Electromagnetism (LEMAC) at Universidade Estadual de Campinas, Brasil, has visited the team on
November 2nd-3rd 2023.

9.3 European initiatives

9.3.1 H2020 projects

RISC2 (A network for supporting the coordination of High-Performance Computing research between
Europe and Latin America)

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Inria Annual Report 2023

Participants:

Luc Giraud (HIEPACS project-team, Inria Bordeaux - Sud-Ouest),
Stéphane Lanteri, Patrick Valduriez (ZENITH project-team).

• Type: H2020 (Coordinated Support Action)

• Link.

• Duration: Jan 2021 - Jun 2023

• Coordinator: Barcelona Supercomputing Center

• Partners:

– Forschungzentrum Julich GMBH (Germany)

– Inria (France)

– Bull SAS (France)

– INESC TEC (Portugal)

– Universidade de Coimbra (Portugal)

– CIEMAT (Spain)

– CINECA (Italy)

– Universidad de Buenos Aires (Argentina)

– Universidad Industrial de Santander (Columbia)

– Universidad de le Republica (Uruguay)

– Laboratorio Nacional de Computacao Cientifica (Brazil)

– Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional (Mexico)

– Universidad de Chile (Chile)

– Fundacao Coordenacao de Projetos Pesquisas e Estudos Tecnologicos COPPETEC (Brazil)

– Fundacion Centro de Alta Tecnologia (Costa Rica)

• Inria contact: Stéphane Lanteri

• Recent advances in AI and the Internet of things allow high performance computing (HPC) to
surpass its limited use in science and defence and extend its benefits to industry, healthcare and the
economy. Since all regions intensely invest in HPC, coordination and capacity sharing are needed.
The EU-funded RISC2 project connects eight important European HPC actors with the main HPC
actors from Argentina, Brazil, Chile, Colombia, Costa Rica, Mexico and Uruguay to enhance cooper-
ation between their research and industrial communities on HPC application and infrastructure
development. The project will deliver a cooperation roadmap addressing policymakers and the
scientific and industrial communities to identify central application areas, HPC infrastructure and
policy needs.

9.4 National initiatives

9.4.1 ANR project

SWEET (Sub-WavelEngth Electro-optic sysTems)

Participants: Henri Camon (CNRS-LAAS),

Jean-Yves Duboz (CNRS-CRHEA),
Mahmoud
(CNRS-LAAS),
Samira Khadir (CNRS-CRHEA), Stéphane Lanteri, Daniel Tur-
over (NAPA Technologies).

Olivier Gauthier-Lafaye

Elsawy,

Project ATLANTIS

• Type: ANR

• Duration: Jan 2023 to Dec 2026

• Coordinator: CNRS-LAAS (Toulouse)

29

• Partner: Inria (ATLANTIS project-team), CNRS-CRHEA (Sophia Atipolis), NAPA Technologies

(Archamps)

• Inria contact: Stéphane Lanteri

• Beam steering is a key enabling photonic technology that would improve the performance of light
detection and ranging modules (LiDAR). A typical LiDAR component consists of a light source for
illumination, a light modulating device to scan the scene and finally a fast detection system to
recover the optical information received from the scene. The operation principle of conventional
LiDARs relies on the Time-of-Flight (ToF) measurement, where a pulsed laser directed toward a
distant reflective object measures the propagation round-trip time (ToF) of light pulses propagating
from the laser to the scene and back to the detection module. The LiDAR sector is currently ongoing
important research and development efforts to enable real-time sensing of the distance of fast-
moving objects, with applications in robotics, autonomous vehicles and future augmented reality
devices. Dynamic beam steering with competitive performances requires the deflection of a light
beam along any arbitrary direction to spatially scan a large angular field-of-view (FoV) with high
speed and high efficiency. SWEET addresses several drawbacks of current LiDAR technologies
by proposing innovative ultrafast beam steering systems, their combinations and integration
into demonstrator. We propose to realize an ultrafast 2D beam steering system using innovative
transparent tunable MS using LC and III-nitride materials. Our motivation is to develop a generic
technology to meet the market needs of LiDAR applications in terms of operation speed, FoV,
angular resolution, manufacturability. As indicators, we consider the most stringent requirements
for LiDAR integration in the automotive industry. In this context, the general objective of our
contribution to the SWEET project is to design active metasurface components for synamic beam
steering.

9.4.2 DGA/AID RAPID project

AEROCOM (Ultra-flat and low-cost antennas)

Participants:

Ayoub Bellouch, Guillaume Bouchet, Guillaume de Calan (NANOE),
Mahmoud Elsawy, Van Hoang (Thales Research & Technology), Guil-
laume Leroy, Stéphane Lanteri, Julien Sourice (NANOE), Erika Van-
delle (Thales Research & Technology).

• Type: RAPID

• Duration: Jan 2023 to Dec 2024

• Coordinator: NANOE (Palaiseau)

• Partner: Inria (ATLANTIS project-team), Thales Research & Technology (Palaiseau)

• Inria contact: Stéphane Lanteri

• The development of agile, ultra-flat and low-cost Ka-band antennas is a major challenge to enable
Internet accessibility in mobility, in particular on board of public land and air transport (trains,
buses, airliners), and to secure communication servers (for combat aircraft, military vehicles, etc.).
A possible antenna architecture to address this challenge is composed of a radiating source and
a deflection system consisting of two deflectors. The compactness and the moderate cost of the
de-pointing system could be obtained thanks to the sub-wavelength structuring technique, and
to the shaping by additive manufacturing. Indeed, the sub-wavelength patterning technique has

30

Inria Annual Report 2023

recently shown the possibility to realize antenna components much thinner than a homogeneous
bulk material, with equivalent or even better radio frequency performance. In this context, the
general objective of our contribution to the AEROCOM project is to develop an advanced numerical
methodology for the virtual design of subwavelength structured deflectors and their cascading to
achieve an ultra-flat Ka-band antenna system consisting of two such metadeflectors.

10 Dissemination

Participants:

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

10.1 Promoting scientific activities

10.1.1 Scientific events: organisation

General chair, scientific chair

• Stéphane Lanteri was a member of the Scientific Committee of the 3rd Inria-DFKI European

Summer School on AI (IDESSAI 2023), Sophia Antipolis, Setember 4-8, 2023.

Member of the organizing committees

• Stéphane Descombes was a member of the steering committee of the 6th edition of the SophI.A

Summit, 22-24 November, Sophia Antipolis.

• Claire Scheid and Stéphane Lanteri have co-organized a minisymposium on "Advances in numer-
ical methods for nonlinear optics", at the ICIAM 2023 conference, Tokyo, Japan, August 20-25, 2023,
with Camille Carvalho (Université de Lyon, INSA Lyon, UJM, UCBL, ECL, CNRS) and Vrushali A.
Bokil (Department of Mathematics, College of Science, Oregon State University, USA).

10.1.2 Scientific expertise

• Claire Scheid was a member of the Maître de Conférence selection committee for Centrale Méditer-

ranée (spring 2023).

• Since July 2023, Claire Scheid is a member of the Scientific Committee of the "Maison de la simula-

tion et des interactions" of Université Côte d’Azur (https ://msi.univ-cotedazur.fr/).

10.1.3 Research administration

• Stéphane Lanteri: member of the Project-team Committee’s Bureau of the Inria research center at

Université Côte d’Azur

• Stéphane Lanteri: Deputy Head of Science of Inria Research Center at Université Côte d’Azur (since

September 2022)

• Stéphane Lanteri: member of Evaluation Committee of Inria (since September 2022)

• Stéphane Lanteri: member of the “Comité de Chercheurs Calculant au CINES”

10.2 Teaching - Supervision - Juries

10.2.1 Teaching

• Claire Scheid, EDP et Différences finies, Practical works, Master 1 MPA, 18h, Université Côte d’Azur

Project ATLANTIS

31

• 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. Lec-

ture, L3, 56h, Université Côte d’Azur

• Yves D’Angelo, Modélisation Simulation Numérique, Master 1 IM/MPA, 50 h, Université Côte d’Azur

• Yves D’Angelo, Modélisation de la Turbulence dans l’Industrie, Master 1 MPA and IM, 16 h, Université

Côte d’Azur

• Stéphane Descombes, Mathematics practical works, L1 Eco, 40 h, Université Côte d’Azur,

• Engineering: Stéphane Descombes, Scientific Machine Learning, 12 h, MAM5, Polytech Nice Sophia

- Université Côte d’Azur,

• Stéphane Descombes, Approximation Numérique des fonctions, intégrales et équations différenti-

elles, practical works, L3, 28h, Université Côte d’Azur,

• Engineering: Stéphane Lanteri, High performance scientific computing, 24 h, MAM5, Polytech Nice

Sophia - Université Côte d’Azur

10.2.2 Supervision

• PhD defended: Théophile Chaumont-Frelet and Stéphane Lanteri have co-supervised the PhD of
Zakaria Kassali, Multiscale finite element simulations applied to the design of photovoltaic cells,
defended in January 2023

• PhD defended: Stéphane Lanteri and Claire Scheid have co-supervised the PhD of Massimiliano
Montone, High order finite element type solvers for the coupled Maxwell-semiconductor equations
in the time-domain, defended in March 2023

• PhD in progress: Arthur Clini De Souza, Deep neural networks for the design of large-scale photonic

devices for active beam steering, Mahmoud Elsawy and Stéphane Lanteri

• PhD in progress: Jérémy Grebot, Advanced modeling of nanostructured CMOS imagers, Stéphane

Lanteri and Claire Scheid

• PhD in progress: Enzo Isnard, Modeling and optimization of freeform optical metasurfaces integ-

rated to an imaging system, Mahmoud Elsawy and Stéphane Lanteri

• PhD in progress: Thibault Laufroy, High order finite element type solvers for thermoplamonics,

Yves d’Angelo and Claire Scheid

• PhD in progress: Cédric Legrand, High order finite element type solvers for modeling gain media,

Stéphane Descombes and Stéphane Lanteri

• PhD in progress: Martin Leppers, Microlenses based on metasurfaces for image sensor pixels,

Patrice Genevet (CRHEA, Sophia Antipolis) and Stéphane Lanteri

• PhD in progress: Florentin Proust, Novel finite element methods for dealing with high frequency
wave propagation problems, Maxime Ingremeau (Université Côte d’Azur, LJAD) and Théophile
Chaumont-Frelet

32

10.2.3 Juries

Inria Annual Report 2023

• Claire Scheid was a reviewer of the PhD and a member of the PhD committee of Maria Cabrera

Calvo, Sorbonne University, France, March 20, 2023

• Stéphane Lanteri was a reviewer of the PhD and a member of the PhD committee of Jayeeta Amboli,

Université d’Aix-Marseille, Institut Fresnel, France, December 18, 2023

• Stéphane Lanteri was a member of the PhD committee of Victoriya Kashtanova, Université Côte

d’Azur, Inria, Sophia Antipolis, June 14, 2023

11 Scientific production

11.1 Major publications

[1] 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’. In: International Journal
of Numerical Modelling: Electronic Networks, Devices and Fields (17th Oct. 2019). DOI: 10.1002/jn
m.2678. URL: https://hal.inria.fr/hal-02327982.

[2] T. Chaumont-Frelet. Asymptotically constant-free and polynomial-degree-robust a posteriori estim-
ates for space discretizations of the wave equation. 6th Apr. 2022. URL: https://inria.hal.scien
ce/hal-03632468.

[3] T. Chaumont-Frelet, V. Dolean and M. Ingremeau. Efficient approximation of high-frequency Helm-
holtz solutions by Gaussian coherent states. 8th Aug. 2022. URL: https://inria.hal.science/ha
l-03747290.

[4] T. Chaumont-Frelet, A. Ern and M. Vohralík. ‘On the derivation of guaranteed and p-robust a
posteriori error estimates for the Helmholtz equation’. working paper or preprint. Aug. 2020. URL:
https://hal.inria.fr/hal-02202233.

[5] S. Descombes, S. Lanteri and L. Moya. ‘Locally implicit discontinuous Galerkin time domain
method for electromagnetic wave propagation in dispersive media applied to numerical dosimetry
in biological tissues’. In: SIAM Journal on Scientific Computing 38.5 (2016), A2611–A2633. DOI:
10.1137/15M1010282. URL: https://hal.inria.fr/hal-01133694.

[6] S. Descombes, S. Lanteri and L. Moya. ‘Temporal convergence analysis of a locally implicit dis-
continuous galerkin time domain method for electromagnetic wave propagation in dispersive
media’. In: Journal of Computational and Applied Mathematics 316 (May 2017), pp. 122–132. DOI:
10.1016/j.cam.2016.09.038. URL: https://hal.archives-ouvertes.fr/hal-01244237.

[7] M. Elsawy, M. Binois, R. Duvigneau, S. Lanteri and P. Genevet. ‘Optimization of metasurfaces under
geometrical uncertainty using statistical learning’. In: Optics Express 29.19 (2021), p. 29887. DOI:
10.1364/OE.430409. URL: https://hal-unilim.archives-ouvertes.fr/hal-03356986.

[8] 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’. In: ACS photonics 8.8
(26th July 2021), pp. 2498–2508. DOI: 10.1021/acsphotonics.1c00753. URL: https://hal.arc
hives-ouvertes.fr/hal-03212349.

[9] 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’. In: Scientific Reports 9.1
(Nov. 2019). DOI: 10.1038/s41598-019-53878-9. URL: https://hal.archives-ouvertes.fr
/hal-02156881.

[10]

S. Lanteri, C. Scheid and J. Viquerat. ‘Analysis of a Generalized Dispersive Model Coupled to a DGTD
Method with Application to Nanophotonics’. In: SIAM Journal on Scientific Computing 39.3 (Jan.
2017), A831–A859. DOI: 10.1137/15M105207X. URL: https://hal.inria.fr/hal-01674031.

Project ATLANTIS

33

[11] K. Li, T.-Z. Huang, L. Li and S. Lanteri. ‘A reduced-order discontinuous Galerkin method based on a
Krylov subspace technique in nanophotonics’. In: Applied Mathematics and Computation 358 (Oct.
2019), pp. 128–145. DOI: 10.1016/j.amc.2019.04.031. URL: https://hal.inria.fr/hal-02
433050.

[12] K. Li, T.-Z. Huang, L. Li and S. Lanteri. ‘Non-intrusive reduced-order modeling of parameterized
electromagnetic scattering problems using cubic spline interpolation’. In: Journal of Scientific
Computing 87.2 (May 2021). DOI: 10.1007/s10915-021-01467-2. URL: https://hal.inria.f
r/hal-03437698.

[13] K. Li, T.-Z. Huang, L. Li and S. Lanteri. ‘POD-based model order reduction with an adaptive snapshot
selection for a discontinuous Galerkin approximation of the time-domain Maxwell’s equations’. In:
Journal of Computational Physics 396 (Nov. 2019), pp. 106–128. DOI: 10.1016/j.jcp.2019.05.0
51. URL: https://hal.inria.fr/hal-02433048.

[14] K. Li, T.-Z. Huang, L. Li, Y. Zhao and S. Lanteri. ‘A non-intrusive model order reduction approach for
parameterized time-domain Maxwell’s equations’. In: Discrete and Continuous Dynamical Systems
- Series B 28.1 (26th Mar. 2022), pp. 449–473. DOI: 10.3934/dcdsb.2022084. URL: https://inri
a.hal.science/hal-03922914.

[15] K. Li, T.-z. Huang, L. Li and S. Lanteri. ‘Simulation of the interaction of light with 3-D metallic
nanostructures using a proper orthogonal decomposition-Galerkin reduced-order discontinuous
Galerkin time-domain method’. In: Numerical Methods for Partial Differential Equations (1st Sept.
2022). DOI: 10.1002/num.22911. URL: https://inria.hal.science/hal-03922856.

[16] L. Li, S. Lanteri and R. Perrussel. ‘A hybridizable discontinuous Galerkin method combined to
a Schwarz algorithm for the solution of 3d time-harmonic Maxwell’s equations’. In: Journal of
Computational Physics 256 (Jan. 2014), pp. 563–581. DOI: 10.1016/j.jcp.2013.09.003. URL:
https://hal.inria.fr/hal-00795125.

[17] N. Schmitt, C. Scheid, S. Lanteri, A. Moreau and J. Viquerat. ‘A DGTD method for the numerical
modeling of the interaction of light with nanometer scale metallic structures taking into account
non-local dispersion effects’. In: Journal of Computational Physics 316 (July 2016). DOI: 10.1016/j
.jcp.2016.04.020. URL: https://hal.archives-ouvertes.fr/hal-01334396.

[18] N. Schmitt, C. Scheid, J. Viquerat and S. Lanteri. ‘Simulation of three-dimensional nanoscale light
interaction with spatially dispersive metals using a high order curvilinear DGTD method’. In:
Journal of Computational Physics 373 (Nov. 2018), pp. 210–229. URL: https://hal.inria.fr/ha
l-01973550.

11.2 Publications of the year

International journals

[19] T. Chaumont-Frelet and M. Vohralík. ‘p-robust equilibrated flux reconstruction in H(curl) based
on local minimizations. Application to a posteriori analysis of the curl-curl problem’. In: SIAM
Journal on Numerical Analysis 61.4 (17th July 2023), pp. 1783–1818. DOI: 10.1137/21M141909X.
URL: https://inria.hal.science/hal-03227570.

[20] S. Christiansen, T. G. Halvorsen and C. Scheid. ‘Convergence of a discretization of the Maxwell-
Klein-Gordon equation based on Finite Element Methods and Lattice Gauge Theory’. In: Numerical
Methods for Partial Differential Equations 39.4 (8th Mar. 2023), pp. 3271–3308. DOI: 10.1002/num
.23008. URL: https://hal.science/hal-03513047.

[21] A. Clini de Souza, S. Lanteri, H. E. Hernández-Figueroa, M. Abbarchi, D. Grosso, B. Kerzabi and
M. Elsawy. ‘Back-Propagation Optimization and Multi-Valued Artificial Neural Networks for Highly
Vivid Structural Color Filter Metasurfaces’. In: Scientific Reports 13.1 (4th Dec. 2023), p. 21352. URL:
https://hal-iogs.archives-ouvertes.fr/hal-04169093.

[22] M. Elsawy, C. Kyrou, E. Mikheeva, R. Colom, J.-y. Duboz, K. Z. Kamali, S. Lanteri, D. Neshev and
P. Genevet. ‘Universal active metasurfaces for ultimate wavefront molding by manipulating the
reflection singularities’. In: Laser and Photonics Reviews 17.7 (9th Apr. 2023). DOI: 10.1002/lpor
.202200880. URL: https://unilim.hal.science/hal-03864817.

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Inria Annual Report 2023

[23] X.-F. He, L. Li, S. Lanteri and K. Li. ‘Model order reduction for parameterized electromagnetic
problems using matrix decomposition and deep neural networks’. In: Journal of Computational
and Applied Mathematics 431 (Oct. 2023), p. 115271. DOI: 10.1016/j.cam.2023.115271. URL:
https://hal.science/hal-03927379.

[24] X.-F. He, L. Li, S. Lanteri and K. Li. ‘Reduced Order Modeling for Parameterized Electromagnetic
Simulation Based on Tensor Decomposition’. In: IEEE Journal on Multiscale and Multiphysics
Computational Techniques 8 (4th Aug. 2023), pp. 296–305. DOI: 10.1109/JMMCT.2023.3301978.
URL: https://inria.hal.science/hal-04402221.

[25] K. Li, Y. Li, L. Li and S. Lanteri. ‘Surrogate modeling of time-domain electromagnetic wave propaga-
tion via dynamic mode decomposition and radial basis function’. In: Journal of Computational
Physics 491 (Oct. 2023), p. 112354. DOI: 10.1016/j.jcp.2023.112354. URL: https://inria.ha
l.science/hal-04401269.

[26] A. Modave and T. Chaumont-Frelet. ‘A hybridizable discontinuous Galerkin method with character-
istic variables for Helmholtz problems’. In: Journal of Computational Physics 493 (15th Nov. 2023),
p. 112459. DOI: 10.1016/j.jcp.2023.112459. URL: https://hal.science/hal-03909368.

[27] S. Nicaise and C. Scheid. ‘Stability properties for a problem of light scattering in a dispersive
metallic domain’. In: Evolution Equations and Control Theory 12.1 (2023), p. 20. DOI: 10.3934/eec
t.2022020. URL: https://hal.science/hal-03540550.

International peer-reviewed conferences

[28] M. Elsawy, A. Gobé, S. Lanteri, G. Leroy and C. Scheid. ‘Advanced computational design of complex
nanostructured photonic devices using high order discontinuous Galerkin methods and statistical
learning global optimization’. In: First International Conference Math 2 Product (M2P 2023) Emer-
ging Technologies in Computational Science for Industry, Sustainability and Innovation. Taormina
(Sicile), Italy, 30th May 2023. URL: https://inria.hal.science/hal-04405929.

[29] M. Elsawy, A. Gobé, G. Leroy, S. Lanteri and P. Genevet. ‘Advanced computational framework for
the design of ultimate performance metasurfaces’. In: SPIE digital library. Smart Photonic and
Optoelectronic Integrated Circuits 2023. Vol. 12425. Smart Photonic and Optoelectronic Integrated
Circuits 2023. San Francisco, United States: SPIE, 17th Mar. 2023, p. 17. DOI: 10.1117/12.2646681.
URL: https://hal.science/hal-04355009.

[30] M. Elsawy and S. Lanteri. ‘Nonlocal active metasurfaces with ultimate wavefront shaping per-
formance’. In: NANOP 2023 : Functional Nanophotonics - Nanophotonics and Micro/Nano Optics
International Conference 2023. Barcelona, Spain, 27th Nov. 2023. URL: https://hal.science/ha
l-04355059.

[31]

J. Grebot, R. Helleboid, G. Mugny, I. Nicholson, L.-H. F. Mouron, S. Lanteri and D. Rideau. ‘Bayesian
Optimization of Light Grating for High Performance Single-Photon Avalanche Diodes’. In: IEEE
Xplore. 2023 International Conference on Simulation of Semiconductor Processes and Devices
(SISPAD). Kobe, France: IEEE, 27th Sept. 2023, pp. 365–368. DOI: 10.23919/SISPAD57422.2023
.10319552. URL: https://inria.hal.science/hal-04405833.

Conferences without proceedings

[32] M. Elsawy, S. Lanteri and P. Genevet. ‘Achieving Ultimate Performance in Active Beam Steering:
Universal Approach with 100% Amplitude and 2π Phase Control’. In: ICMAT2023 - International
Conference on Materials for Advanced Technologies. Singapore (SG), Singapore, 29th June 2023.
URL: https://hal.science/hal-04355021.

[33] E. Isnard, S. Héron, S. Lanteri and M. Elsawy. ‘Advancing wavefront shaping with resonant metas-
urface’. In: Optical Wave & Waveguide Theory and Numerical Modelling (OWTNM 2023). Marseille,
France, 4th May 2023. URL: https://inria.hal.science/hal-04406187.

Project ATLANTIS

35

Doctoral dissertations and habilitation theses

[34] Z. Kassali. ‘Analysis of a multiscale finite element method applied to the design of photovoltaic
cells : a multiscale hybrid-mixed method for the Helmholtz equation with quasi-periodic boundary
conditions’. Université Côte d’Azur, 11th Jan. 2023. URL: https://theses.hal.science/tel-0
4056632.

[35] M. Montone. ‘Full-wave discontinuous Galerkin time-domain methods for semiconductor device
simulation’. Université Côte d’Azur, 30th Mar. 2023. URL: https://theses.hal.science/tel-0
4138766.

Reports & preprints

[36] T. Chaumont-Frelet. An equilibrated estimator for mixed finite element discretizations of the curl-

curl problem. 3rd Aug. 2023. URL: https://inria.hal.science/hal-04177080.

[37] T. Chaumont-Frelet and M. Ingremeau. Decay of coefficients and approximation rates in Gabor

Gaussian frames. Inria, 2023. URL: https://inria.hal.science/hal-03746979.

[38] T. Chaumont-Frelet, A. Moiola and E. A. Spence. Explicit bounds for the high-frequency time-
harmonic Maxwell equations in heterogeneous media. 17th Jan. 2023. URL: https://inria.hal.s
cience/hal-04001866.

[39] T. Chaumont-Frelet and M. Vohralík. Constrained and unconstrained stable discrete minimizations
for p-robust local reconstructions in vertex patches in the De Rham complex. 11th May 2023. URL:
https://inria.hal.science/hal-03749682.

Other scientific publications

[40] A. Clini de Souza, S. Lanteri, H. Enrique Hernandez-Figueroa, M. Abbarchi, D. Grosso, B. Kerzabi
and M. Elsawy. ‘Deep Learning Technique for Highly Vivid Structural Color Filter Metasurfaces’. In:
Nanophotonics and Micro/Nano Optics International Conference 2023. Barcelona (Spain), Spain,
27th Nov. 2023. URL: https://hal.science/hal-04355081.

[41] M. Elsawy, M. Binois, E. Isnard, R. Duvigneau, P. Genevet and S. Lanteri. ‘Advanced Optimization
Technique for Robust and Multiobjective Metasurface designs’. In: ICMAT2023 - International
Conference on Materials for Advanced Technologies. Singapore (SG), Singapore, 29th June 2023.
URL: https://hal.science/hal-04355037.

11.3 Cited publications

[42]

‘A graph convolutional autoencoder approach to model order reduction for parametrized PDEs’.
In: J. Comput. Phys. 501 (2024), p. 112762.

[43] E. Agullo, L. Giraud and Y. Jing. ‘Block GMRES method with ineact breackdowns and deflated

restarting’. In: SIAM J. Matrix Anal. Appl. 35.4 (2014), pp. 1625–1261.

[44] G. Baffou. Thermoplasmonics. Cambridge University Press, 2017.

[45] E. Boulais, R. Lachaine, A. Hatef and M. Meunier. ‘Plasmonics for pulsed-laser cell nanosurgery:
fundamentals and applications’. In: J. Photochem. Photobiol. C: Photochem. Rev. 17 (2013), pp. 26–
49.

[46] H. Chen, A. Taylor and N. Yu. ‘A review of metasurfaces: physics and applications’. In: Rep. Progr.

Phys. 79 (7 2016), p. 076401.

[47] X. Chen, H. Park, M. Pelton, X. Piao, N. Lindquist, H. Im, Y. Kim, J. Ahn, K. Ahn, N. Park, D. Kim
and S. Oh. ‘Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of
electromagnetic waves’. In: Nature Comm. 4 (2013), p. 2361.

[48] C. Ciracì, R. Hill, J. Mock, Y. Urzhumov, A. Fernández-Domínguez, S. Maier, J. Pendry, A. Chilkoti
and D. Smith. ‘Probing the ultimate limits of plasmonic enhancement’. In: Science 337.6098 (2012),
pp. 1072–1074.

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Inria Annual Report 2023

[49] C. Ciracì, J. Pendry and D. Smith. ‘Hydrodynamic model for plasmonics: a macroscopic approach

to a microscopic problem’. In: Chemphyschem 14 (6 2013), pp. 1109–1116.

[50] M. Dechaux, P.-H. Tichit, C. Ciracì, J. Benedicto, R. Pollès, E. Centeno, D. Smith and A. Moreau.
‘Influence of spatial dispersion in metals on the optical response of deeply subwavelength slit
arrays’. In: Phys. Rev. B 93.4 (2016), p. 045413.

[51] F. Ding, A. Pors and S. Bozhevolnyi. ‘Gradient metasurfaces: a review of fundamentals and applica-

tions’. In: Rep. Progr. Phys. 81 (2 2018), p. 026401.

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<scratchpad>
- Main topic: Research Centre at Inria, focusing on nanophotonics and plasmonics
- Key points:
  - Studying nanoscale light-matter interactions and developing innovative numerical methodologies
  - Investigating various physical fields, including quantum plasmonics, planar optics, and thermoplasmonics
  - Developing high-order DG methods for solving electromagnetic wave propagation problems
  - Exploring multiscale modeling, data-driven reduced-order modeling, and nonlinear ROM methods
  - Applying these methods to various application domains, including sunlight harvesting, metasurfaces, THz wave generation, and plasmonic sensing
- Structure: The document is organized into sections on Research Centre, Project ATLANTIS, Research Program, Application Domains, and Bilateral Contracts and Grants with Industry
- Potential artifacts to ignore: Links, HTML tags, and unnecessary web-related elements
</scratchpad>

<final_summary>
The document presents the Research Centre at Inria, focusing on nanophotonics and plasmonics. The centre is investigating various physical fields, including quantum plasmonics, planar optics, and thermoplasmonics, and developing innovative numerical methodologies to study nanoscale light-matter interactions. The centre is applying these methods to various application domains, including sunlight harvesting, metasurfaces, THz wave generation, and plasmonic sensing. The document also highlights the centre's research activities, including multiscale modeling, data-driven reduced-order modeling, and nonlinear ROM methods, and its collaborations with industry partners and external research groups. Overall, the document showcases the Research Centre's efforts to advance the field of nanophotonics and plasmonics through cutting-edge research and development.
The document presents the Research Centre at Inria, focusing on nanophotonics and plasmonics. The centre is investigating various physical fields, including quantum plasmonics, planar optics, and thermoplasmonics, and developing innovative numerical methodologies to study nanoscale light-matter interactions. The centre is applying these methods to various application domains, including sunlight harvesting, metasurfaces, THz wave generation, and plasmonic sensing. The document also highlights the centre's research activities, including multiscale modeling, data-driven reduced-order modeling, and nonlinear ROM methods, and its collaborations with industry partners and external research groups. Overall, the document showcases the Research Centre's efforts to advance the field of nanophotonics and plasmonics through cutting-edge research and development.