Temporal coupled-mode theory for light scattering by an arbitrarily shaped object supporting a single resonance

We develop a temporal coupled-mode theory to describe the interaction of plane wave with an individual scatterer having an arbitrary shape. The theory involves the expansion of the fields on cylindrical or spherical wave basis for the two-dimensional and three-dimensional cases, respectively, and describes the scattering process in terms of a background scattering matrix and the resonant radiation coefficients into different cylindrical or spherical wave channels. This theory provides a general formula for the scattering and absorption cross sections. We show that for a subwavelength asymmetric scatterer with a single resonance, the scattering and absorption cross sections can exceed the single-resonance limit for some specific incident angles of illumination, but the sum of these cross sections over all angles has an upper limit. We validate the theory with numerical simulations of a metallic scatterer that does not have any rotation symmetry.