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 nanophotonics55,
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 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 eventually implemented in the DIOGENeS software suite, which is a unique software plaform dedicated to computational 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 close 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
48. These advances have also allowed to
achieve spatial separation between metallic elements of only few
nanometers 46. 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- 47- 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 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 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, 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, is a major objective of our
core research activities in ATLANTIS. We focus on the family of
Discontinuous Galerkin (DG) methods that has been extensively
developed for wave propagation problems during the last 15 years. We
investigate several variants, namely nodal DGTD for time-domain
problems, and HDG (Hybridized DG) for frequency-domain problems, with
the general goal of devising, analyzing and developing extensions of
these methods in order to deal with the above-mentioned physical
drivers: nonlinear features, in particular in relation with generation
of higher order harmonics in electromagnetic wave interaction with
nonlinear materials, and nonlinear models of electronic response in
metallic and semiconductor materials; multiphysic couplings such as
for instance when considering PDE models relevant to thermoplasmonics,
optoelectronics and nanoelectronics. There are to date very few works
promoting DG-type methods for these situations. Our methodological
contributions of these methods eventually materialize in the DIOGENeS
software suite.

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 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 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 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.

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 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.

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 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.

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 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.

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
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.

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).

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.

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.

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

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.

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 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.

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.

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 24-15, 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 14, 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.

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.

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.

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 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).

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.

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.

Numerical simulations of electromagnetic wave propagation problems primarily rely on discretization of the system of time-domain Maxwell equations using finite difference or finite element type methods. For complex and realistic three-dimensional situations, such a process can be computationally prohibitive, especially in view of many-query analyses (e.g., optimization design and uncertainty quantification). Therefore, developing cost-effective surrogate models is of great practical significance. Among the different possible approaches for building a surrogate model of a given PDE system in a non-intrusive way (i.e., with minimal modifications to an existing discretization-based simulation methodology), approaches based on neural networks and Deep Learning (DL) has recently shown new promises due to their capability of handling nonlinear or/and high dimensional problems. In the present study, we propose to focus on the particular case of Physics-Informed Neural Networks (PINNs) introduced in 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).

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 alternatives 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.

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 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

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.

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.

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 seamless 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 phenomenon is crucial for designing high-performance resonant metasurfaces. This knowledge empowers researchers and engineers to create metasurfaces with enhanced performance, opening avenues for novel applications in various domains. This work has been accepted for publication in Scientific Reports early 2024.

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 Fig. 4).

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 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.

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. 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).

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.

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

In recent years, the control of sub-wavelength light-matter interactions has enabled the observation of new linear optical phenomena, further establishing a new class of ultra-thin devices for real-world applications. To extend metasurface functionality and implement nonlinear manipulations, the scientific community has considered optical metasurfaces for harmonic emission field control. However, the performance of nonlinear metasurfaces is still modest. Flat optics have also shown their potential in the nonlinear optics with wavefront shaping in far-harmonic fields. There is currently a related effort by the nonlinear nanophotonics community to seek higher conversion efficiencies across narrow resonances of the quasi-bound states of the continuum (qBIC) associated with strong near-field coupling and nonlocal resonance modes. However, the overall performance is relatively weak as most of the current studies ignore the strong near-field coupling between neighboring cells. In this collaboration, we exploit the specific advantages of 'thin' resonators that behave like phased-array antennas, unlike photonic crystals with strong localized energies, to develop highly efficient nonlinear metasurfaces for nonlinear wavefront shaping. Within this strategy, we improve the performance of nonlinear wavefront shaping by inverse design optimization of both meta-atoms and meta-molecules. In addition, we consider long-term design options for nonlinear metasurfaces based on perfect nonlocal responses and long-range near-field coupling, and rigorous computational methods to address nonlinearities in terms of nonlocal configurations. Our preliminary results (see Fig. 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.

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

Nom: Simulation of photonic pigments

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