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 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.

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

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.

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.