High-efficiency, large-area, topology-optimized metasurfaces

Abstract

Metasurfaces are ultrathin optical elements that are highly promising for constructing lightweight and compact optical systems. For their practical implementation, it is imperative to maximize the metasurface efficiency. Topology optimization provides a pathway for pushing the limits of metasurface efficiency; however, topology optimization methods have been limited to the design of microscale devices due to the extensive computational resources that are required. We introduce a new strategy for optimizing large-area metasurfaces in a computationally efficient manner. By stitching together individually optimized sections of the metasurface, we can reduce the computational complexity of the optimization from high-polynomial to linear. As a proof of concept, we design and experimentally demonstrate large-area, high-numerical-aperture silicon metasurface lenses with focusing efficiencies exceeding 90%. These concepts can be generalized to the design of multifunctional, broadband diffractive optical devices and will enable the implementation of large-area, high-performance metasurfaces in practical optical systems.

Keywords: Metamaterials; Microresonators.

Fig. 1. Strategies for metasurface design.

a Conventional approaches sample the desired phase profile at discrete points and specify phase shifting elements to form a nanoscale phased array. b Our approach is to divide the desired phase profile into wavelength-scale, linear sections and use topology optimization to design each section individually. c Computation time versus device size for topology-optimized metasurfaces that are designed using two approaches: direct optimization of the entire metasurface (orange) and optimization of the metasurface after division into 3λ-wide sections (green)

Fig. 2. Impact of phase profile linearization on the cylindrical lens performance.

a Cylindrical lenses of focal length 36λ and NA of 0.7 are constructed using linear sections of length d for various values of d. b Line scans of the field intensity at the focal planes of the lenses. Lenses that are linearized with sections that are smaller than 4λ have peak intensities that are within 1% of that of the ideal lens

Fig. 3. Metasurface element optimization.

a At the beginning of the optimization process, the initial dielectric distribution is a random dielectric continuum. The dashed lines indicate the desired scattering angle of 20° and phase of π/2. After 10 iterations, the scattering profile is already highly directional. After 100 iterations, the optimization is complete and the metasurface section is a binary structure of silicon and air that supports the desired scattering metrics. b An intensity plot that shows the scattered fields of the optimized metasurface element

Fig. 4. Simulation results of optimized metalenses.

a Relative and absolute efficiencies for metalenses that were designed with various numerical apertures. b A full-field simulation of a metalens with an NA of 0.9

Fig. 5. Experimental characterization of fabricated metalenses.

a Scanning electron micrographs of the metalenses with tilted and top-down views. b Relative and absolute efficiencies of the fabricated metalenses, along with their simulated values. c–e Intensity line scans at the focal planes of the metalenses with NAs of 0.2, 0.5, and 0.8, respectively, along with comparisons with the simulated lenses. f–h Efficiencies of the fabricated metalenses as a function of the wavelength, along with their simulated values. These metalenses have the same design but were fabricated on a different sample than those that were measured in (a–e)