Optimization of metasurfaces under geometrical uncertainty using statistical learning.

The performance of metasurfaces measured experimentally often discords with expected values from numerical optimization. These discrepancies are attributed to the poor tolerance of metasurface building blocks with respect to fabrication uncertainties and nanoscale imperfections. Quantifying their efficiency drop according to geometry variation are crucial to improve the range of application of this technology. Here, we present a novel optimization methodology to account for the manufacturing errors related to metasurface designs. In this approach, accurate results using probabilistic surrogate models are used to reduce the number of costly numerical simulations. We employ our procedure to optimize the classical beam steering metasurface made of cylindrical nanopillars. Our numerical results yield a design that is twice more robust compared to the deterministic case.

Global optimization of metasurface designs using statistical learning methods.

Optimization of the performance of flat optical components, also dubbed metasurfaces, is a crucial step towards their implementation in realistic optical systems. Yet, most of the design techniques, which rely on large parameter search to calculate the optical scattering response of elementary building blocks, do not account for near-field interactions that strongly influence the device performance. In this work, we exploit two advanced optimization techniques based on statistical learning and evolutionary strategies together with a fullwave high order Discontinuous Galerkin Time-Domain (DGTD) solver to optimize phase gradient metasurfaces. We first review the main features of these optimization techniques and then show that they can outperform most of the available designs proposed in the literature. Statistical learning is particularly interesting for optimizing complex problems containing several global minima/maxima. We then demonstrate optimal designs for GaN semiconductor phase gradient metasurfaces operating at visible wavelengths. Our numerical results reveal that rectangular and cylindrical nanopillar arrays can achieve more than respectively 88% and 85% of diffraction efficiency for TM polarization and both TM and TE polarization respectively, using only 150 fullwave simulations. To the best of our knowledge, this is the highest blazed diffraction efficiency reported so far at visible wavelength using such metasurface architectures.

Exact calculation of the nonlinear characteristics of 2D isotropic and anisotropic waveguides.

We use our vector Maxwell's nonlinear eigenmode solver to study the stationary solutions in 2D cross-section plasmonic slot waveguides with isotropic Kerr nonlinear codes and anisotropic Kerr nonlinear cores. First, for the isotropic case, we demonstrate that, even in the low-power regime, 1D studies may not provide accurate and meaningful results compared to 2D ones. Second, we study, including at high powers, the link between the nonlinear parameter γnl and the change of the nonlinear propagation constant Δß. Third, we demonstrate that our approach is also valid for anisotropic waveguides, and we show how to improve by, a factor of 2, the figure of merit of nonlinear plasmonic slot waveguides using realistic materials.

Improved nonlinear slot waveguides using dielectric buffer layers: properties of TM waves.

We propose an improved version of the symmetric metal slot waveguides with a Kerr-type nonlinear dielectric core adding linear dielectric buffer layers between the metal regions and the core. Using a finite element method to compute the stationary nonlinear modes, we provide the full phase diagrams of its main transverse magnetic modes as a function of the total power, buffer layer, and core thicknesses that are more complex than the ones of the simple nonlinear metal slot. We show that these modes can exhibit spatial transitions toward specific modes of the new structure as a function of power. We also demonstrate that, for the main modes, the losses are reduced compared to the previous structures, and that they can now decrease with power. Finally, we describe the stability properties of the main stationary solutions using nonlinear FDTD simulations.