  The observation and electrical manipulation of infrared surface plasmons in
graphene have triggered a search for similar photonic capabilities in other
atomically thin materials that enable electrical modulation of light at visible
and near-infrared frequencies, as well as strong interaction with optical
quantum emitters. Here, we present a simple analytical description of the
optical response of such kinds of structures, which we exploit to investigate
their application to light modulation and quantum optics. Specifically, we show
that plasmons in one-atom-thick noble-metal layers can be used both to produce
complete tunable optical absorption and to reach the strong-coupling regime in
the interaction with neighboring quantum emitters. Our methods are applicable
to any plasmon-supporting thin materials, and in particular, we provide
parameters that allow us to readily calculate the response of silver, gold, and
graphene islands. Besides their interest for nanoscale electro-optics, the
present study emphasizes the great potential of these structures for the design
of quantum nanophotonics devices.
