Segmented Bayesian optimization of meta-gratings for sub-wavelength light focusing

Abstract

Using inverse design tools to engineer functional photonic nanostructures has been a subject of great interest over the past several years. We report combining a segmented Bayesian optimization algorithm with the rigorous coupled wave analysis to design meta-gratings for sub-wavelength light focusing. Specifically, the meta-gratings comprise one-dimensional periodic arrays of supercells, each of which consists of dozens of dielectric bars. By optimizing geometry of the structure, we demonstrate two kinds of meta-gratings operating at single and double wavelengths, respectively. Both of them can focus the incoming light into periodic sub-wavelength spots with high energy density. The full width at half-maximum (FWHM) of the focusing spots for the single wavelength ($\lambda = 633\,\,{\rm nm}$) case can be as small as $0.36\lambda $, while FWHMs of the focusing spots at double wavelengths ($\lambda = 533\,\,{\rm nm}$ and 633 nm) are about $0.4\lambda $. This proposed approach provides an affordable method to tackle the problem of complex photonic structure design.