Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers

Various scatterers such as rough surfaces or nanostructures are typically used to enhance the low efficiency of Raman spectroscopy (surface-enhanced Raman scattering). In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterers, depending only on its material constants and the separation distance from the molecule. According to our metric, silver is optimal in visible wavelengths while aluminum is better in the near-UV region. Our general analytical bound scales as the volume of the scatterer and the inverse sixth power of the distance to the active molecule. For periodic scatterers, a second bound with surface-area scaling is presented. Simple geometries such as spheres and bowties are shown to fall short of the bounds. However, using topology optimization based inverse design, we obtain surprising structures maximizing the Raman enhancement. These optimization results shed light to what extent our bounds are achievable.