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We present a method based on the scattering $\mathbb{T}$ operator, andconservation of net real and reactive power, to provide physical bounds on anyelectromagnetic design objective that can be framed as a net radiativeemission, scattering or absorption process. Application of this approach toplanewave scattering from an arbitrarily shaped, compact body of homogeneouselectric susceptibility $\chi$ is found to predictively quantify anddifferentiate the relative performance of dielectric and metallic materialsacross all optical length scales. When the size of a device is restricted to bemuch smaller than the wavelength (a subwavelength cavity, antenna,nanoparticle, etc.), the maximum cross section enhancement that may be achievedvia material structuring is found to be much weaker than prior predictions: theresponse of strong metals ($\mathrm{Re}[\chi] < 0$) exhibits a diluted(homogenized) effective medium scaling $\propto |\chi| / \mathrm{Im}[\chi]$;below a threshold size inversely proportional to the index of refraction(consistent with the half-wavelength resonance condition), the maximum crosssection enhancement possible with dielectrics ($\mathrm{Re}[\chi] > 0$) showsthe same material dependence as Rayleigh scattering. In the limit of a boundingvolume much larger than the wavelength in all dimensions, achievable scatteringinteractions asymptote to the geometric area, as predicted by ray optics. Forrepresentative metal and dielectric materials, geometries capable of scatteringpower from an incident plane wave within an order of magnitude (typically afactor of two) of the bound are discovered by inverse design. The basis of themethod rests entirely on scattering theory, and can thus likely be applied toacoustics, quantum mechanics, and other wave physics.

Global $\mathbb{T}$ operator bounds on electromagnetic scattering: Upper bounds on far-field cross sections