Abstract
We combine a statistical learning-based global optimization strategy with a high order 3D Discontinuous Galerkin Time-Domain (DGTD) solver to design a compact and highly efficient graded index photonic metalens. The metalens is composed of silicon (Si) strips of varying widths (in the transverse direction) and lengths (in the propagation direction) and operates at the telecommunication wavelength. In our work, we tackle the challenging Transverse Electric case (TE) where the incident electric field is polarized perpendicular to strips direction. We reveal that the focusing efficiency approaches 80% for the traditional design with fixed strip lengths and varying widths. Nevertheless, we demonstrate numerically that the efficiency is as high as 87% for a design with varying strip lengths along the propagation direction.
Highlights
Integrated photonics plays an indispensable role in optical communication, computing, and sensing
While nanophotonics devices exhibiting a single longitudinal or transversal period subwavelength pattern can be optimized with a parametric scanning, most of the optimization work in this domain rely on shape or topology optimization, known as inverse design techniques [5,6,7,8,9,10,11]
Contrary to the traditional common global optimization strategies like Genetic Algorithms (GAs) [20], Efficient Global Optimization (EGO) is not based on adaptive sampling, but on a surrogate model constructed on the basis of available objective function evaluations
Summary
Integrated photonics plays an indispensable role in optical communication, computing, and sensing. Contrary to the traditional common global optimization strategies like Genetic Algorithms (GAs) [20], EGO is not based on adaptive sampling, but on a surrogate model constructed on the basis of available objective function evaluations. In the second phase, using the data obtained from the DOE, a Gaussian Process (GP) model is constructed to fit these data This GP model allows us to predict the values of the cost function in the parameter space without the need to perform additional electromagnetic simulations. It is formulated on a fully unstructured tetrahedral mesh allowing for a local refinement of the mesh and the possibility of using curvilinear cells for a high order approximation of sophisticated geometry features with strong discontinuity These modelling features of the DGTD makes it an ideal electromagnetic solver for nanophotonic devices. For more details about our solver, the reader can refer to Refs. [26,27]
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