Polaritonic figure of merit of plane structures

Based on the ability of plane structures to simultaneously optimize the propagation, confinement, and energy of surface plasmon-polaritons or surface phonon-polaritons, we develop the polaritonic figure of merit Z = βRΛ²/δ, where βR, Λ and δ are the longitudinal wave vector, propagation length, and penetration depth, respectively. Explicit and analytical expressions of Z are derived for a single interface and a suspended thin film, as functions of the material permittivities and the film thickness. Higher Z are obtained for thinner films and smaller energy losses. The application of the obtained results for a SiC-air interface and a SiC thin film suspended in air shows that both structures are able to maximize the presence of polaritons at a frequency near to, but different than that at which the real part of the SiC permittivity exhibits a dip. Furthermore, using the temperature change of this dip, we show that the propagation length, confinement and energy of polaritons increases with its deepness, which provides an effective way to enhance the overall Z of polaritonic structures.