Multiobjective statistical learning optimization for large-scale RGB metalens

Mahmoud M R Elsawy (1) , Mickaël Binois (2) , Régis Duvigneau (2) , Samira Khadir (3) , Anthony Gourdin (3) , Patrice Genevet (3) , Stéphane Lanteri (1)

1 ATLANTIS - Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
3 CRHEA - Centre de recherche sur l'hétéroepitaxie et ses applications

Designing highly efficient multiwavelength metalens has witnessed rapid growth in the past few years owing to their fascinating and peculiar applications. The conventional modelling technique relies on optimizing the individual nanoresonators in a periodic array and synthesizing the required phase profile. Generally speaking, the traditional procedure neglects the near-field coupling between the resonators and leads to a dramatic reduction of the efficiency, particularly at the visible regime, and notably for high numerical aperture lenses. Another alternative way is to combine a numerical optimization technique with full-wave simulations to mitigate this problem and optimize the full lens. Nonetheless, this process has been frequently applied to gradient-based techniques with/without freeform shapes which generally converge to a local solution. In this work, we present for the first time a global multiobjective optimization technique based on statistical learning to optimize RGB spherical metalenses at the visible regime. The optimization procedure is coupled to our high-order fullwave solver to capture the strong near field coupling between the resonators. The first 1 RGB optimized lens has 8µm diameter and NA= 0.47 and yields an average focusing efficiency of 55%. The second optimized lens has 10µm diameter and NA= 0.56 with 45% average efficiency. Furthermore, we obtained an average focusing error as small as 6% for the RGB colors. The optimized lenses have been fabricated and characterized experimentally, where a good agreement is attained between the numerical and the experimental results. The measured average focusing efficiency are approximately, 45% and 33%, for the first and the second design, respectively. To the best of our knowledge, this is the highest focusing efficiency obtained so far for such spherical metalens with classical cylindrical pillars with NA>0.5 at the visible regime.

Domaines: Optique / photonique; Optique [physics.optics]; Optimisation et contrôle [math.OC]

Mahmoud M R Elsawy, Mickaël Binois, Régis Duvigneau, Samira Khadir, Anthony Gourdin, et al.. Multiobjective statistical learning optimization for large-scale RGB metalens. 2021. ⟨hal-03212349v1⟩