  The classical adjoint-based topology optimization (TO) method, based on the
use of a random continuous dielectric function as an adjoint variable
distribution, is known to be one of the most efficient optimization methods
that enable the design of optical devices with outstanding performances.
However, the strategy for selecting the optimal solution requires a very fine
pixelation of the permittivity function of the profile under optimization.
Typically, at least 28 pixels are needed while optimizing a one wavelength wide
1D metagrating. This makes it very difficult to extend TO methods to
large-scale optimization problems. In this paper, we introduce a new concept of
adjoint-based topology optimization that enables fast and efficient geometry
based design of both periodic and aperiodic metasurfaces. The structures are
built from nano-rods whose widths and positions are to be adjusted. Our new
approach requires a very low number of design parameters, thus leading to a
drastic reduction in the computational time: about an order of magnitude.
Hence, this concept makes it possible to address the optimization of
large-scale structures in record time. As a proof-of-concept we apply this
method to the design of (i) a periodic metagrating, optimized to have a
specific response into a particular direction, and (ii) a dielectric metalens
(aperiodic metasurface), enabling a high energy focusing into a well-defined
focal spot.
