For what applications are plasmonic materials better than all-dielectric materials, and vice versa? Or 2D materials versus their bulk counterparts? How does the requisite bandwidth affect materials selection? Here, we use the complex-analytic properties of certain optical-response functions in conjunction with novel energy-conservation constraints to derive fundamental limits to near-field optical response for any material, over any bandwidth. We show that certain canonical geometries can approach the bounds at specific frequencies, while at many others there is significant opportunity for structured materials to surpass them by orders of magnitude. We map out a frequency-bandwidth phase space in which we identify optimal materials among plasmonic, all-dielectric, and 2D-material candidates, and we put forward a quantitative material figure of merit to stimulate new-materials discovery.
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