# Advanced numerical design methodologies for next-generation metasurface architectures

Mahmoud Elsawy, Arthur Clini de Souza, Enzo Isnard, Roman Gelly, Stéphane Lanteri

► To cite this version:

Mahmoud Elsawy, Arthur Clini de Souza, Enzo Isnard, Roman Gelly, Stéphane Lanteri. Advanced numerical design methodologies for next-generation metasurface architectures. GDR Ondes 2025 - 11ème Conférence Plénière du GDR ONDES SUPMICROTECH-ENSMM, Oct 2025, Besançon, France. hal-05363258

HAL Id: hal-05363258

https://hal.science/hal-05363258v1

Submitted on 13 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

Public Domain
Advanced numerical design methodologies for next-generation metasurface architectures

**M. Elsawy**, A. Clini de Souza, E. Isnard, R. Gelly, and S. Lanteri
Université Côte d'Azur, Inria, CNRS, LJAD, 06902 Sophia Antipolis Cedex, France
mahmoud.elsawy@inria.fr

Abstract

Metasurfaces [1-2], with their intricate subwavelength designs, provide precise level of control of the light properties. This peculiar control paves the way towards the realization of innovative applications ranging from broadband achromatic lenses to quantum photonics and modern AR/VR displays. Yet, each application has its own unique and demanding performance criteria, which necessitate precise management of dispersion, the ability to scale to larger sizes, and the integration of innovative, dynamic mechanisms such as time-varying and nonlinear responses. This presentation will tackle these challenges by examining the fundamental issues in modelling these complex behaviours beyond the traditional modelling aspects. Furthermore, classical design methodologies like lookup tables and parametric sweep fail to meet the requirements of such systems, given that the underlying design spaces are high-dimensional and the geometrical features interact with system performance in a complex manner. Thus, there is increasing demand to develop inverse design methods which are capable of directly deducing the optimal structural parameters given target performance requirements. Traditional inverse design methods can be very expensive in terms of computation, and they often struggle with fabrication imperfections. To address this, we exploited an innovative statistical learning-based optimization methods [3-5]. These methods are much more efficient at exploring sophisticated objective functions [6], can manage multiple objectives simultaneously, and more importantly, can take into account the fabrication tolerances [7].

In the second part of our discussion, we tackle a significant challenge: scalability. When it comes to designing large-scale metasurfaces, such as the metalenses used in virtual reality, traditional optimization algorithms can be a real challenge due to their high computational demands. To tackle this issue, we developed recently [8-9] an innovative deep learning-based approach that takes a "divide and conquer" strategy. We start by creating a library of compact, neural network-optimized beam-deflecting elements. Then, we use a sophisticated, physics-aware model that acts like a smart architect, piecing together these pre-optimized components into a complete lens while ensuring everything aligns perfectly in terms of phase and interaction. This comprehensive framework is highly efficient, allowing us to create metalenses with different apertures and focal lengths on demand, all without having to re-optimize from the ground up. This makes it naturally scalable for practical manufacturing.

In the third part, we move from static metasurfaces to reconfigurable ones. Most current devices are passive, meaning their optical response is fixed after fabrication, but future applications in communications and adaptive imaging will require real-time tunability. Modelling these systems is challenging because, unlike passive designs, the optimization depends on changes in the permittivity rather than geometry. This is particularly difficult since physical tuning mechanisms usually allow only small changes, especially for high-speed modulation. For example, electro-optic heterostructures with multi-quantum wells (MQWs) typically allow refractive index changes of only 0.01. We recently developed [10] a universal design methodology for active metasurfaces that achieves full phase modulation with nearly 100% amplitude modulation. However, high-Q resonances lead to strong nonlocal coupling, which can degrade performance. To address this, we designed active
metasurface supercells supporting strongly resonant field distributions and used a stochastic global optimization method (StoSOO) to explore the design space efficiently while accounting for nonlocal interactions. This approach has produced beam-forming designs with outstanding performance, achieving deflection efficiencies above 85% in realistic, fabricable devices.

Finally, I will discuss our recent activities in modelling space-time metasurface, a key step forward for the field of active metasurface. By combining temporal modulation with spatial structuring, these devices enable functions that static metasurfaces cannot achieve, such as nonreciprocal light transport, frequency conversion, and ultrafast optical control. Modelling them is a challenging task. In our case, we rely on a Discontinuous Galerkin Time-Domain (DGTD) framework, which can accurately capture the complex dynamics of time-modulated systems. We will present preliminary results showing how DGTD can be applied to realistic structures, providing a path for both studying and designing space-time metasurfaces for future adaptive and reconfigurable optics.

## References

1. P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, "Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings," *Opt. Lett.*, vol. 23, no. 14, pp. 1081-1083, 1998

2. Capasso, F., Genevet, P., Kats, M. A., Aieta, F., Tetienne, J.-P., & Gaburro, Z. (2011). Light propagation-with phase discontinuities: generalized laws of reflection and refraction. *Science*, 334(6054), 333-337

3. M. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, and P. Genevet, "Global optimization of metasurface designs using statistical learning methods," *Sci. Rep.*, vol. 9, p. 1-15, 2019.

4. M. Elsawy, S. Lanteri, R. Duvigneau, J. A. Fan, and P. Genevet, "Numerical optimization methods for metasurfaces," *Laser Photonics Rev.*, vol. 14, no. 10, p. 1900445, 2020.

5. E. Isnard, S. Héron, S. Lanteri, and M. Elsawy. Advancing wavefront shaping with resonant nonlocal metasurfaces: beyond the limitations of lookup tables. *Sci Rep* 14, 1555 (2024)

6. M. Elsawy, A. Gourdin, M. Binois, R. Duvigneau, D. Felbacq, S. Khadir, P. Genevet, and S. Lanteri, "Multiobjective statistical learning optimization of RGB metalens," *ACS Photonics*, vol. 8, no. 8, pp. 2498-2508, 2021.

7. M. Elsawy, M. Binois, R. Duvigneau, S. Lanteri, and P. Genevet, "Optimization of metasurfaces under-geometrical uncertainty using statistical learning," *Opt. Express*, vol. 29, pp. 29887-29898, 2021

8. C. de Souza, S. Lanteri, M. Elsawy, et al., "Deep learning for large-scale metalenses: design and fabrication," *Laser Photonics Rev.*, submitted, 2025.

9. A. C. de Souza, S. Lanteri, and M. Elsawy et al. Back-propagation optimization and multi-valued artificial neural networks for highly vivid structural color filter metasurfaces. *Sci Rep* 13, 21352 (2023)

10. M. Elsawy, C. Kyrou, E. Mikheeva, E. Colom, J.-Y. Duboz, K. Z. Kamali, S. Lanteri, D. Neshev, and P. Genevet, "Universal active metasurfaces for ultimate wavefront molding by manipulating the reflection singularities," *Laser Photonics Rev.*, vol. 17, p. 2200880, 2023.