In recent years, metasurfaces have emerged as revolutionary tools to manipulate the behavior of light at the nanoscale. These devices consist of nanostructures defined within a single layer of metal or dielectric materials, and they offer unprecedented control over the optical properties of light, leading to previously unattainable applications in flat lenses, holographic imaging, polarimetry, and emission control, amongst others. The operation principles of metaoptics include complex light-matter interactions, often involving insidious near-field coupling effects that are far from being described by classical ray optics calculations, making advanced numerical modeling a requirement in the design process. In this contribution, recent optimization techniques used in the inverse design of high performance metasurfaces are reviewed. These methods rely on the iterative optimization of a Figure of Merit to produce a final device, leading to freeform layouts featuring complex and non-intuitive properties. The concepts in numerical inverse designs discussed herein will push this exciting field toward realistic and practical applications, ranging from laser wavefront engineering to innovative facial recognition and motion detection devices, including augmented reality retro-reflectors and related complex light field engineering.

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.

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.

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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 γ and the change of the nonlinear propagation constant Δβ. 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.

Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a nonlinear metamaterial core of Kerr-type embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assumed that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and the nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical, it is based on the finite-element method in which all the components of the electric field are considered in the Kerr-type nonlinearity with no presumptions on the nonlinear refractive index change. Our finite-element based model is valid beyond weak nonlinearity regime and generalize the well-known single-component fixed power algorithm that is usually used. Examples of the main cases are investigated including ones with strong spatial nonlinear effects at low powers. Loss issues are reduced through the use of gain medium in the nonlinear metamaterial core.

We study the main nonlinear solutions of plasmonic slot waveguides made from an anisotropic metamaterial core with a positive Kerr-type nonlinearity surrounded by two semi-infinite metal regions. First, we demonstrate that for a highly anisotropic diagonal elliptical core, the bifurcation threshold of the asymmetric mode is reduced from GW/m threshold for the isotropic case to 50 MW/m one indicating a strong enhancement of the spatial nonlinear effects, and that the slope of the dispersion curve of the asymmetric mode stays positive, at least near the bifurcation, suggesting a stable mode. Second, we show that for the hyperbolic case there is no physically meaningful asymmetric mode, and that the sign of the effective nonlinearity can become negative.