T-Operator Limits on Electromagnetic Scattering: Bounds on Extinguished, Absorbed, and Scattered Power from Arbitrary Sources

We present a scheme for obtaining physical bounds on any electromagnetic scattering problem that can be framed as a net emission, scattering or absorption process. The method requires only a high level description of the design problem---the material the device will be made of, a boundary for the volume the device may occupy, and a description of the incident field or excitation current source---to simultaneously consider all structuring possibilities. Both surprising and anticipated characteristics related to material and geometric properties are observed. For the canonical case of a propagating planewave interacting with an arbitrarily designable object contained in a spherical bounding domain of radius, the scattering cross sections in the small radii (quasi-static) limit display a material dependence on the electric susceptibility for metals corresponding to a diluted (homogenized) material response, achievable via nanostructuring, such that for the same material loss, the performance of strong metals is found to be significantly weaker than that of resonant spherical nanoparticles satisfying the localized plasmon-polariton condition. For large radii, achievable scattering interactions asymptote to the geometric cross section of the ball, as predicted by ray optics. Bounds on the maximum power radiated by a dipole located a distance above the spherical bounding domain are also investigated and found to be reduced compared to prior analyses, with strong metals and dielectrics exhibiting the expected scaling with respect to separation in the deep near field regime but a more muted dependence on the real part of the susceptibility. The basis of the proposed method rests entirely on the applicability of scattering theory, and can thus likely be applied to acoustics, quantum mechanics, and other wave physics.