Nanostructuring of materials has paved the way for manipulating and
enhancing wave-matter interactions, 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 nanophotonics56,
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, plasmonics, 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
concentrations. Plasmonics 61 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 permittivity dielectric, 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 promise 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 eventually implemented in the DIOGENeS software suite, which is a unique software plaform dedicated to computationl nanophotonics.

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 clos collaboration with physicists.

Quantum plasmonics. The physical phenomena involved in
the deep confinement of light when interacting 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
49. These advances have also allowed to
achieve spatial separation between metallic elements of only few
nanometers 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
70-14.

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
57- 48- 52.
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) are
are concerned with numerical modeling methods for the inverge design
of metasurfaces
7-5 and
metalenses 6.

Thermoplasmonics. Plasmonic resonances can be
exploited for many applications 61. 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 45. 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 optoelectronics, 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 62, 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, tunneling 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.

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

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

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
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 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
11-9-10.
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) 68
that we plan to investigate for PDE models relevant nanophotonics with
the goal of designing non-intrusive surrogate modeling approaches that
require a minimal amount of data.

Error estimation and adaptivity. While standard theory
ensures the convergence of the discrete approximation to the correct
solution, it does not permit to quantitatively estimate the
discretization error in actual applications. As a result, the
selection of the discretization parameters is often carried out by the
practitioners themselves, based on their experience and hence manual
approaches to guarantee a sufficient accuracy level. We aim at
providing reliable measurements of the discretization error and
devising a more systematic and rigorous procedure to select and adapt
discretization parameters — in particular the mesh size and the
discretization order — through the use of a posteriori estimators. On
the one hand, we propose to design a posteriori error estimators for
the wave-matter interaction problems we consider in ATLANTIS, able to
provide a fully reliable error estimation. On the other hand, such
estimators can be employed to drive hp-adaptive algorithms, where the
mesh and discretization order are iteratively improved to fit the
complicated structure of the solution.

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 quantuum 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 equations (again
at significantly different time and space scales) is a possible
relevant scenario. In the optoelectronics field, the accurate
prediction of semiconductors optical properties is a major concern. A
possible strategy may require to solve both the electromagnetic and
the drift-diffusion equations. In all these aforementioned examples,
difficulties mainly arise both from the differences in physical nature
as well as in the time/space scales at which each physical phenomenon
occurs. Accurately modeling/solving their coupled interactions remains
a formidable challenge.

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

Beside the above-discussed core reserach 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 63.
Artificial Intelligence (AI) techniques are also increasingly
investigated within this context 72. 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
53- 54
and fluid-structure interaction problems 69.

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 58. 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
12. 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
44, or low-rank compression techniques
67. 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.

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 application 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.

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, 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.

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 71 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 66.

Recent research on the interaction of short optical pulses with semiconductors has stimulated the development 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 semiconductors 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 65- 73. The recently-introduced concept of hybrid photoconductive antennas leveraging plasmonic effects is even more challenging 60. So far, existing simulation approaches are based on the FDTD method, and are only able to deal with classical PCAs. In relation with the design of photonic devices for THz waves generation and manioulation, we intend to a multiscale numerical modeling strategy for solving the system of Maxwell equations coupled to various models of charge carrier dynamics in semiconductors.

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 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 51 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 50, which materializes as a system of PDEs coupled to Maxwell's equations 14-13. The second issue is concerned with the assessment of geometrical uncertainties and their role in the development of spatial dispersion 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 luminescent 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
59. Also, bio-functionalized gold nanorods
are promising candidates for light-induced hyperthermia
64, 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
46, 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.

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 concerned with production of renewable energy and biomedical engineering (ranging from light controlled drug-release to the ongoing battle against Covid-19).

This year, thanks to the innovative computational and inverse design methods that we develop in the team, we have investigated for the first time a novel active metasurface design that relies on the position of topological singularities, namely zeros and poles of the reflection coefficient, to address full phase modulation of light reflected off the metasurface with almost unity efficiency (see section 8.6 for more details).

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 8. In the frequency-domain setting, the HDGFD (Hybridized Discontinuous Galerkin Frequency-Domain) method 1 is considered as the basis of our works.

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 55. 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.

In the field of semiconductor physics modeling, charge carrier transport is the starring phenomenon that needs to be predicted in order to build a mathematical model, based on higher-level quantities (e.g. electric current and voltage), that can be practically used for device simulation. Charge carrier transport is generally described by a drift-diffusion model. This yields a system of coupled partial differential equations which can be solved at two levels: (1) quasistatic approximation: the external force applied to the crystal is electrostatic, and drift-diffusion equations are coupled to a Poisson equation for the electrostatic potential. The goal is to determine the spatial distribution of carrier concentrations and the electric field (deduced from the potential); (2) fullwave model: the crystal is subject to an applied electromagnetic field, and Maxwell equations are coupled with transport equations for carrier dynamics. The goal is to determine the space-time evolution of carrier concentrations and the electromagnetic field. The quasistatic approximation is rigorous when the steady state of the semiconductor has to be calculated. For example, this could be a preliminary step to the fullwave simulation of a device that is biased prior to responding to a (time-varying) electromagnetic excitation. The fullwave model is particularly relevant to electro-optics, i.e. when light-matter interaction is investigated. Indeed, such study is essential to understanding and accurately modeling the operation of photonic devices for light generation, modulation, absorption. In the context of the PhD of Massimiliano Montone 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 two-dimensional setting.

The limiting amplitude principle predicts the asymptotic harmonic
regime of a structure that is monochromatically illuminated. This
makes a frequency-domain approach relevant, viewed as a long time
asymptotic of a monochromatic time-domain simulation setting.
Besides, it means that a time-domain solver may be used to solve
frequency-domain problems, avoiding an explicit linear system solve.
In this context, we investigate a modeling approach that allows to
build bridges between the frequency- and time-domain approaches. This
works heavily relies on the possibility of having reliable, accurate
and high order discretization strategies for approximating time-domain
problems. In collaboration with Marcus J. Grote and Jet Tang,
University of Basel, Switzerland, we consider the use of time-domain
solvers to efficiently solve frequency-domain problems in non
dispersive materials. Specifically, we consider an approach called
conjugate gradient controlability method that we study
theoretically in 3D and numerically in 2D and 3D
18. We have shown that the proposed
method converges toward the time-harmonic solution, and numerical
examples suggest that the method is robust in the high-frequency
regime and/or in the presence of trapped waves in complex geometries.

Helmholtz problems describe the periodic 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 32, 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 localised in phase space. We carefully select the Gaussian coherent states spanning the approximation space by exploiting the (known) micro-localisation properties of the solution. This work in 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 has been implemented for a simple one-dimensional problem.

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 9-11 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.

In 10, we have introduced a non-intrusive variant of the POD-based ROM initially introduced in 9-11, in the context of parameterized time-domain electromagnetic scattering problems. The considered parameters are the 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 23, we have designed an improved version of the POD-CSI method 10. 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 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 22, we study the simulation of the interaction of light with 3D metallic nanostructures using an adapted version of the method initially introduced in 9-11.

Linear reduction methods such as POD hardly capture the complex dynamics of highly nonlinear systems, therefore nonlinear manifold learning methods such as kernel principal component analysis (PCA) and Hessian feature maps have recieved much attention in the recent years. Assuming that data points lie in a low dimensional manifold embedded in an higher dimensional Euclidean space, manifold learning aims to identify the intrinsic dimensionality equal to the number of parameters that describe the system, and thus obtain low dimensional representations of the data points. Although kernel PCA and Hessian feature maps are effective in providing low dimensional representations for high dimensional data points, their main drawback is that they do not provide an analytical formula to decode the compressed data back to their high dimensional representation in the original space. An autoencoder (AE) overcomes this disadvantage by learning how to compress (encode) a high dimensional data to a low dimensional code and then reconstruct (decode) the code to a representation as close to the original input as possible. The encoder and decoder parts of an autoencoder are trained simultaneously but can be used separately, which provides an opportunity to build a mapping between the input time/parameter and encoded representation. Directly applying large-scale simulation data (snapshots) to a fully-connected autoencoder is not only computationally prohibitive, but also ignores the opportunity to exploit the structure of features in high dimensional. As an extension of ordinary AEs, convolutional autoencoders (CAEs) are characterized by shared parameters and local connectivity which help to reduce the memory as well as computational costs. This study is concerned with a non-intrusive ROM that combines matrix decomposition and deep neural networks for parameterized electromagnetic scattering problems 37. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized time-domain Maxwell equations with a high order DGTD method. To perform a prior dimensionality reduction, a set of RB functions are extracted from the database via a two-step POD method. Projection coefficients of RB functions are further compressed through a convolutional autoencoder (CAE) network. SVD is then used to extract the principal components of the reduced-order matrices generated by CAE, and a CSI approach is employed for approximating the dominating time- and parameter-modes of the reduced-order matrices. The generation of the RB 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.

Recently, semi-analytical methods became quite popular to solve Maxwell’s equations. These methods are based on the derivation of optical resonances also called quasi-normal modes (QNM). Locating optical resonant frequencies within the complex plane provides precious information. Indeed, the real and imaginary parts of complex resonant frequencies provide the excitation frequency and the quality factor of each quasinormal mode. In addition, the symmetries and hotspots occuring in the field distribution associated to each resonance indicates how each resonance can be excited and where the density of electromagnetic energy will be the highiest. Such information is already enough to draw useful conclusions, i.e., identify where sharp features will occur in the transmission and reflection spectra, which resonance will contribute the most to the scattering process or which part of a nanostructure will be subject to high absorption and nonlinear phenomena. Thus, quasi-normal modes give access to the value of many observable at any frequencies whithout the necessity to solve Maxwell’s equations more than the few times that are necessary to derive the needed optical resonances. Additionnally, the knowledge of the resonant frequencies and fields of a structure is enought to predict the optical characteristics of other structures presenting structural changes with respect to the originally known system. This approach is known as the resonant state expansion, which offer powerfull tools particularily in the scope of optimisation algorithms. Another and not the least advantage of this approach is that it can be implemented on top of many frequency domain solvers such as Fourier modal methods, finite element methods (FEM) solvers or discontinuous Garlekin methods (DG). Efficient algorithms to derive swiftly and accurately quasi-normal modes is more and more needed. In this context, we have conductive a comparative study in the 2D case about the efficiency of two contour integral methods to derive optical resonances, known as the FEAST and Beyn methods. This is a fisrt step toward the development of a scalable QNM solver for 3D problems in the framework of the DIOGENeS software suite.

To reduce the computational cost related to the use of high-fidelity simulations when evaluating the cost function, we investigate the construction of multi-fidelity auto-regressive Gaussian Process models, that can rely on different physical models (e.g. inviscid or viscous flows) or numerical accuracy (e.g. coarse or fine meshes). The objective is to construct a model that is accurate regarding the high-fidelity evaluations, but mostly based on low-fidelity simulations. Of particular interest is the definition of an efficient acquisition function, that selects both the next design point to evaluate and the corresponding fidelity level to use. This work is achieved in collaboration with SecondMind company and was the topic of Maha Ouali's internship.

In this section, we present ongoing studies aiming at designing, analyzing and developing novel numerical methods for dealing with multiscale problems. The corresponding works are concerned with the multiscale schemes that are designed in the framework of MHM (Multiscale Hybrid-Mixed) formulations. They are conducted in the context of a long-term collaboration with the research group of Frédéric Valentin at LNCC, Petropolis, Brazil.

The flux variable determines the approximation quality of numerical methods based on hybridization. We prove that the approximation of flux variables in discontinuous polynomial spaces from the L2 orthogonal projection is superconvergent in meshes that are not aligned with jump coefficient interfaces. The results only assume the local regularity of exact solutions on physical partitions. Based on the proposed flow approximation, we demonstrate that MHM method is superconvergent on non-aligned grids, supporting the numerical results presented in seminal MHM works. Such results are sufficiently generic to be used to prove the superconvergence of the MHM method when applied to other operators. This work is described in the preprint 33.

The robustness of MHM discretizations of Helmholtz problems with
respect to the frequency parameter

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 vicin- ity, 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 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 also layed the foundations of the numerical approximation framework and provided a first stability study.

For centuries, optical design consisted in developing thin films and various coating to address light reflection, transmission and/or diffusion at interfaces. Developments in nanophotonics have strongly improved our ability to control light scattering processes with optically resonant nanostructures. Artificial optical materials, also dubbed metamaterials and metasurfaces, presenting unexpected light propagation effects have been realized, leading to cloacking, negative refraction, subwavelength focusing, generalized refraction and vectorial electromagnetic field control. These metamaterials and metasurfaces are realized by assembling subwavelength photonic structures. The study of the device’s optical response is generally complex and requires lengthy numerical simulations that describe in detail the effect of light interaction with a large number of nanophotonic building blocks. To avoid modeling thousands and billions of small geometrical features, homogenisation methods that approximate the complexity of an inhomogeneous material filed with nanoscale inclusions by its effective medium response, i.e., homogeneous artificial material, have been proposed. For the case of metasurfaces, consisting of a surfacic two-dimensional arrangement of nanostructures, equivalent transition conditions linking the values of the macroscopic field quantities on both sides of a thin homogenized layer have been derived. In fact, such transition conditions are well known in electromagnetics but also in acoustics and are commonly used to simplify physical interpretation or ease numerical simulations. Metasurfaces have thus been modeled using advanced effective transition conditions, called Generalized Sheet Transition Conditions (GSTCs). These transition conditions conceal in a tensorial form the equivalent response occurring on reflecting and transmitting fields at complex interfaces. Efforts to reproduce above-mentioned intriguing effects using GSTC formulation, including anomalous refraction, cloaking and vectorial electromagnetic field control have been realized recently But so far, most works dealing with GSTCs only considered layers manufactured on planar surfaces. In this work, we address theoretically the problem of electromagnetic field transition conditions at conformal interfaces to achieve surface topography-dependent transmitted and reflected fields. Our analysis, supported by 2D and 3D finite element simulations, provides a solid theoretical framework to design metasurfaces for cloaking, wearable optics and next generation of freeform imaging systems 21.

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.

Dynamic metasurface is an emerging concept for achieving a flexible control of electromagnetic waves. Generalized sheet transition conditions (GSTCs) can be used to model the relationship between the electromagnetic response and surface susceptibility parameters characterizing a metasurface. However, when it comes to the inverse problem of designing and controlling a metasurface in a space–time varying context based on GSTCs, the dynamic synthesis of the susceptibility parameters is a difficult and non-intuitive task. In this study, we transform the inverse problem of solving dynamic susceptibility parameters into a sequence of control problems. Based on FDTD numerical simulations, a Deep Reinforcement Learning (DRL) framework using a proximal policy optimization (PPO) algorithm and a fully connected neural network is designed to control the susceptibility parameters intelligently and efficiently, promoting the further expansion of the application range of metasurface and thus helping realize more flexible and effective control of electromagnetic waves. This work has been published in 24 where we provide numerical results in a 1D setting to show the applicability, correctness and effectiveness of the proposed approach.

Numerical simulations of electromagnetic wave propagation problems primarily rely on spatially and temporally discretization of the system of time-domain Maxwell equations using finite difference or finite element type methods. For complex and realistic three-dimensional situations, such a process can be computationally prohibitive, especially in view of many-query analyses (e.g., optimization design and uncertainty quantification). Therefore, developing cost-effective surrogate models is of great practical significance. Among the different possible approaches for building a surrogate model of a given PDE system in a non-intrusive way (i.e., with minimal modifications to an existing discretization-based simulation methodology), approaches based on neural networks and Deep Learning (DL) has recently shown new promises due to their capability of handling nonlinear or/and high dimensional problems. In the present study, we propose to focus on the particular case of Physics-Informed Neural Networks (PINNs) introduced in 68. PINNs are neural networks trained to solve supervised learning tasks while respecting any given1q 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 in 2D. Our first results have been presented in the workshop entitled "HPC and Data Sciences meet Scientific Computing" that was organized in the context of the CARLA 2022 conference.

Hybrid-Mixed (MHM) algorithms to improve accuracy and make MHM methods more cost-effective. For that, 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 alternatives to the current computational cost of the MHM method 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.

We have initiated this year a study to develop accurate and efficient DL-based surrogate models for the numerical characterization of light-matter interactions with nanostructured materials, more particularly for metasurfaces. Metasurfaces are an evolution of artificially structured materials on a smaller scale than the wavelength, known as metamaterials. The latter derive their optical properties not only from the intrinsic properties of the base materials, but above all from the precise geometry, size, orientation and arrangement of their structural elements. In this way, materials with unexpected and sometimes specific optical properties can be designed, exceeding the limits of what can be achieved with existing materials. In this preliminary study during the internship of Arthur Clini De Souza, we consider convolutional autoencoder and variational convolutional autoencoder NNs and compare their relative performance for the inverse design of a single nanoresonator, which is a base meta-atom for a Huygens metasurface. This study is conducted in collaboration with Hugo Enrique Hernandez Figueroa who is the head of the Laboratory of Applied and Computational Electromagnetics (LEMAC), which is part of the School of Electrical and Computer Engineering (FEEC) at the University of Campinas (UNICAMP).

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 8.8 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.

Optical metasurfaces are becoming ubiquitous optical components to
mold the amplitude, phase, and polarization of light. So far, most of
these devices are passive in essence, that is, they cannot be
arbitrarily reconfigured or optimized according to the user's interest
and/or change in the surrounding environment. In this work, we
propose an innovative design strategy relying on the position of
topological singularities, namely zeros and poles of the reflection
coefficient, to address full phase modulation of light reflected off
an active metasurface with almost unity efficiency. The active
metasurface unit cells, consisting of asymmetric Gires-Tournois
resonators filled with either silicon or hetero-structured materials
to leverage on the thermo-optical or electro-optical effects,
respectively. In both cases, a full phase modulation associated with

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 Nanoscale 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 nanoplasmonics. 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:

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 Fog. 2).

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

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 colour 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.

There is significant recent interest in designing ultrathin crystalline silicon solar cells with active layer thickness of a few micrometers. Efficient light absorption in such thin films requires both broadband antireflection coatings and effective light trapping techniques, which often have different design considerations. In collaboration with physicists from the Sunlit team at C2N-CNRS, We exploit statistical learning methods for the inverse design of material nanostructuring with the goal of optimizing light trapping properties of ultraphin solar cells. This objective is challenging because the underlying electromagnetic wave problems exhibit multiple resonances, while the geometrical settings are non-trivial. Such multi-resonant solar cell structures are attractive for maximizing light absorption for the full solar light spectrum as illustrated in Fig. 3. 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).

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. This study is conducted in collaboration with Antoine Moreau at Institut Pascal (CNRS).

Fluorescence signals emitted by probes, used to characterize the expression of biological markers in tissues or cells, can be very hard to detect due to a small amount of molecules of interest (proteins, nucleic sequences), to specific genes expressed at the cellular level, or to the limited number of cells expressing these markers in an organ or a tissue. Access to information coming from weaker emitters can only come from strengthening the signal, since electronic post-amplification raises the noise floor as well. While costly and molecule-specific biochemical processes are being developed for this purpose, 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 a 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. 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.

In recent years, the control of subwavelength light-matter
interactions has enabled the observation of new linear optical
phenomena, further establishing a new class of ultra-thin devices for
real-world applications. To extend metasurface functionality and
implement nonlinear manipulations, the scientific community has
considered optical metasurfaces for harmonic emission field
control. However, the performance of nonlinear metasurfaces is still
modest. Flat optics have also shown their potential in the nonlinear
optics with wavefront shaping in far-harmonic fields. There is
currently a related effort by the nonlinear nanophotonics community to
seek higher conversion efficiencies across narrow resonances of the
quasi-bound states of the continuum (qBIC) associated with strong
near-field coupling and nonlocal resonance modes. However, the overall
performance is relatively weak as most of the current studies ignore
the strong near-field coupling between neighboring cells. In the
context of a collaboration that has started in 2022 with the groups of
Giuseppe Leo at the MPQ laboratory (Matériaux et Phénomènes
Quantiques, CNRS UMR 7162, Université Paris Cité) and Jean-Michel
Gerard at the PHELIQS laboratory (PHotonique, ELectronique et
Ingénierie QuantiqueS, UMR-E of CEA and Université Grenoble
Alpes), 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 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.

Nom: SEASIDE - numerical Study of mEtasurfAceS by Inverse DEsign

Nom: DGTD solvers for semiconductor device modeling

Nom: DGTD solvers for modeling light absorption in CMOS imagers