Eddie Wadbro: Design optimization of plasmonic nano-antennas

The material distribution approach to topology optimization was originally developed for the optimization of linearly elastic structures. During the last decade much work has been focused on adapting this method to design devices that control acoustic as well as electromagnetic wave propagation. Here, we focus on the problem of analyzing and designing a plasmonic nano-antenna with the source being a planar TE-polarized wave. Nano-antennas are used to concentrate the energy in light into regions that are much smaller than the wavelength. The design problem is to place silver and air in a 100x100 nm² design region to maximize the electric energy in a small  10x10 nm² target region. At optical frequencies, silver exhibits extreme dielectric properties, having a strictly negative real permittivity. The field can thus exhibit huge values at the interface between the silver and the air, which dramatically increases the computational effort necessary for the numerical device design. We prove existence and uniqueness of solutions to the governing non-standard Helmholtz equation with absorbing boundary conditions. To solve the design optimization problem, we develop a two-stage procedure, where the first step uses the material distribution with only a small penalty to find an initial guess for the second step that optimizes the design by using a domain-variation approach. The method of moving asymptotes solves the resulting optimization problems and the final designs perform very well and the electric energy in the target region is several orders of magnitude larger than when there is only air in the design region.