Effects of Confinement and Optical Response of Ultrathin Plasmonic Films

We study theoretically confinement related effects in the optical response of ultrathin plasmonic films of finite thickness[1]. We start with the Coulomb interaction potential in the confined planar geometry to obtain the conditions for in-plane collective electron (plasma) motion. We show that, while being constant for relatively thick films, the plasma frequency acquires spatial dispersion typical of 2D materials, gradually shifting to the red with the film thickness reduction. The complex-valued dynamical response function shows the red shift of its epsilon-near-zero point, accordingly, with the dissipative loss decreasing at any fixed frequency and rising up at the plasma frequency. This explains recent experiments done on TiN films[2], offering ways to tune spatial dispersion (and so magnetic permeability[3]) and magneto-optical properties of plasmonic films and metasurfaces — not only by varying their material composition but also by controlling their thickness and choosing substrate and superstrate materials appropriately. -- [1]I.V.Bondarev & V.M.Shalaev, Opt. Mater. Expr. 7, 3731 (2017); [2]D.Shah, et al., Adv. Opt. Mater. 1700065 (2017); [3]L.D.Landau & E.M.Lifshitz, Electrodynamics of Cont. Media, NY, 1984.