Upper Bound on the Modal Material Loss Rate in Plasmonic and Metamaterial Systems

A better understanding of optical loss in plasmonic and metamaterial systems is of increasing importance for both basic and applied research in a broad range of topics including sensors, antennas, optical interconnects, and photovoltaics. In this Letter, we use a photonic band formalism for plasmonics to exactly derive a fundamental upper bound on the nonradiative material loss rate of modes in plasmonic, polaritonic, and metamaterial systems. This bound is purely defined by material properties and cannot be overcome by device design. Moreover it is frequency dependent in the presence of multiple Lorentz poles. We numerically verify this bound through direct calculations for a range of plasmonic systems, including optical antennas where the bound places fundamental performance constraints.