  We show that topology optimization (TO) of metallic resonators can lead to
$\sim 10^2\times$ improvement in surface-enhanced Raman scattering (SERS)
efficiency compared to traditional resonant structures such as bowtie antennas.
TO inverse design leads to surprising structures very different from
conventional designs, which simultaneously optimize focusing of the incident
wave and emission from the Raman dipole. We consider isolated metallic
particles as well as more complicated configurations such as periodic surfaces
or resonators coupled to dielectric waveguides, and the benefits of TO are even
greater in the latter case. Our results are motivated by recent rigorous upper
bounds to Raman scattering enhancement, and shed light on the extent to which
these bounds are achievable.
