Fundamental Limits on Electromagnetic Scattering in Nanostructured Materials: Upper Bounds on Extinction, Purcell Enhancement, and Absorption*

Advances in computational optimization (inverse design) and experimental fabrication techniques suggest the possibility of approaching the fundamental limits of optical control, which remain largely unknown. Through algebraic analysis of the scattering properties of Maxwell's equations, we formulate new constraints on various optical scattering processes, such as extinction and absorption, and apply these to establish upper bounds on thermal emission, radiative heat transfer, and Purcell enhancement in nanostructured materials. These bounds are general and useful in that they apply to arbitrary structures while incorporating the most relevant aspects of any photonic design problem: the material a given structure will be made of and the volume it will occupy. In particular, the bounds demonstrate the degree to which large metallic response and nanostructuring can be exploited to enhance light-matter interactions, with applications to single-photon extraction, photovoltaics, LEDs, and Raman scattering. They also reveal a transition from quasistatic (subwavelength) to ray optics behavior, and are shown to be nearly tight by comparison with structures discovered through inverse design.