  Anomalous resonances in properly shaped plasmonic nanostructures can in
principle lead to infinite absorption/gain efficiencies over broad bandwidths.
By developing a closed-form analytical solution for the fields scattered by
conjoined semicircles, we outline the fundamental physics behind these
phenomena, associated with broadband adiabatic focusing of surface plasmons at
the nanoscale. We are able to justify the apparent paradox of finite
absorption/gain in the limit of infinitesimally small material loss/gain, and
we explore the potential of these phenomena in nonlinear optics, spasing,
energy-harvesting and sensing.
