Extraction efficiency of highly confined surface plasmon-polaritons to far-field radiation: an upper limit

We propose a unique method determining an upper limit of extraction efficiency of the surface plasmon-polaritons (SPPs), E(SP), which are highly confined on a corrugated metal surface. The method is based on measurement of the spectral bandwidth of a grating-induced absorption spectrum as a function of metal dielectric constant. After finding the fact that E(SP) exhibits an extremely linear relationship with the collision frequency Gamma of metal over a SPP band below the surface plasmon frequency, an upper limit of E(SP) can be determined by an asymptotic estimation as Gamma-->0 for total decay rates of the confined SPPs. Our method based on the bandwidth measurement is inherently free from the ambiguity and underestimation difficulties pertaining to the previous prism-coupling approaches for E(SP) estimation. It will also be quite applicable for evaluating SPP-mediated light-emitting diodes (LEDs) of which total external efficiency is dominantly restricted by the upper limit of E(SP). Especially for the case when SPP excitation probability approaches unity, the proposed method would excellently figure out the maximum realizable external efficiency of SPP-mediated LEDs.