For applications from optical sensing to photoemission spectroscopy, it is desirable to pattern a plasmonic surface and enhance, over a large area, the field intensity near the surface. What is the largest possible large-area field enhancement? Here, we show a simple semi-analytical bound, based primarily on power-conservation principles, that dictates the fundamental limits to large-area plasmonic field enhancements. Our bounds depend only on the material permittivity and the angle of incidence. Our theory predicts that > 1000X field enhancements are possible with patterned silver metasurfaces. Through numerical optimization, we discover structures that achieve enhancements over 97% of the fundamental limit, for designable wavelengths across the visible and near-infrared.
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