Negative Effective Mass in Plasmonic Systems II: Elucidating the Optical and Acoustical Branches of Vibrations and the Possibility of Anti-Resonance Propagation

We report the negative effective mass metamaterials based on the electro-mechanical coupling exploiting plasma oscillations of free electron gas. The negative mass appears as a result of the vibration of a metallic particle with a frequency ω which is close to the frequency of the plasma oscillations of the electron gas [Formula: see text] , relative to the ionic lattice [Formula: see text]. The plasma oscillations are represented with the elastic spring constant [Formula: see text] , where [Formula: see text] is the plasma frequency. Thus, the metallic particle vibrating with the external frequency ω is described by the effective mass [Formula: see text] , which is negative when the frequency [Formula: see text] approaches [Formula: see text] from above. The idea is exemplified with two conducting metals, namely Au and Li embedded in various matrices. We treated a one-dimensional lattice built from the metallic micro-elements [Formula: see text] connected by ideal springs with the elastic constant [Formula: see text] representing various media such as polydimethylsiloxane and soda-lime glass. The optical and acoustical branches of longitudinal modes propagating through the lattice are elucidated for various ratios [Formula: see text] , where [Formula: see text] and [Formula: see text] represents the elastic properties of the medium. The 1D lattice, built from the thin metallic wires giving rise to low frequency plasmons, is treated. The possibility of the anti-resonant propagation, strengthening the effect of the negative mass occurring under ω = ω(p) = ω(1), is addressed.