# Deep learning methodology for designing large scale matełenses in reflection

Arthur Clini de Souza, Stephane Lanteri, Hugo Enrique Hernandez-Figueroa, Marco Abbarchi, Badre Kerzabi, Paloma Elias da Silva Pellegrini, Silvia Vaz Guerra Nista, Mahmoud Elsawy

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► To cite this version:

Arthur Clini de Souza, Stephane Lanteri, Hugo Enrique Hernandez-Figueroa, Marco Abbarchi, Badre Kerzabi, et al. Deep learning methodology for designing large scale matełenses in reflection. NANOP 2025 - Nanophotonics and Micro/Nano Optics International Conference 2025, Oct 2025, Paris, France. hal-05285823

HAL Id: hal-05285823

https://inria.hal.science/hal-05285823v1

Submitted on 8 Oct 2025

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# Efficient Deep Learning Methodology for Designing Large Scale Metalenses

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UNICAMP

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**SOLNIL**
Nanoimprint your world

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Each deflector will be pointing to the focus. However, it is required hard constraints to provide full control over the deflection angle.

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The surrogate model. It is a fast differentiable solver and the pivotal point of this work. Will be used for inverse design

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However, each design is independent of the neighbors and therefore, cause abrupt changes in parameters, decreasing the deflection efficiency.

A Multi-Valued Artificial Neural Network (MVANN) is a Multilayer Perceptron (MLP) that has multiple solutions. The motivation to use a MVANN is that the inverse design process is multivalued, requiring multiple solutions rather than a single value.

We will use different order modes across the metalens. However, it can cause phase mismatches.

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Can be fixed by adding a separation between regions.

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$$L_{\text{MVANN}}(\mathbf{x}, \mathbf{y}) = \frac{1}{\sum_{i=1}^{N_{\text{outs}}} \frac{1}{\text{MSE}_i(\mathbf{x}, \mathbf{y})}}$$

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**Solution:** Pre-trained Tandem neural network with hard constraints. We start by condensing the solutions of the MVANN into a weighted average of the parameters based on their performance. Then, we train a tandem network to provide a smooth parameter transition. By altering the network hyperparameters, we control how fast the parameters are allowed to change.

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<figure><img src="image_17.png" /><figcaption>50 µm diameter</figcaption></figure>

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Arthur Clini de Souza<fnref n="1" />,², P. Elias da Silva Pellegrini<fnref n="3" />, S. Vaz Guerra Nista<fnref n="3" />, S. Lanteri<fnref n="1" />, H. E. Hernandez-Figueroa<fnref n="3" />, M. Abbarchi²,<fnref n="4" />, B. Kerzabi², M. Elsawy<fnref n="1" />

<figure><img src="image_20.png" /><figcaption>Previous work</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Team</figcaption></figure>

<footnote n="1">¹Université Côte d'Azur, Inria, CNRS, LJAD, Sophia Antipolis, France, ²Solnil, Marseille, France,</footnote>

<footnote n="3">³University of Campinas (UNICAMP) Campinas, São Paulo, Brazil,</footnote>

<footnote n="4">⁴Université Aix Marseille, CNRS, Université de Toulon, Marseille, France</footnote>