A universal macroscopic theory of surface plasma waves and their losses

Abstract

Recently, we have revealed an intrinsic instability of metals due to surface plasma waves (SPWs) and raised the prospect of using it to create lossless SPWs. The counter-intuitive nature of this finding prompts one to ask, why had not this instability been disclosed before, given the long history of this subject? If this instability does exist, how far is it from reality? The present work is devoted to answering these questions. To this end, we derive a unified macroscopic theory of SPWs that applies to any type of electron dynamics, be they local or non-local, classical or quantum-mechanical. In light of this theory, we analyze the behaviors of SPWs according to several electron dynamics models, including the widely used local dielectric model, the hydrodynamic model and the specular reflection model, in addition to the less common semi-classical model. We find that, in order to unveil the instability, one must (i) self-consistently treat surface effects without any of the usually imposed auxiliary conditions and (ii) include translation symmetry breaking effects in electron dynamics. As far as we are concerned, none existing work had fulfilled both (i) and (ii). To assess the possibility of realizing the instability, we analyze two very important factors: the dielectric interfacing the metal and inter-band transitions, which both were ignored in our recent work. Whereas inter-band absorption-together with Landau damping-is shown adverse to the instability, a dielectric brings it closer to occurrence. One may even attain it in common plasmonic materials such as silver under not so tough conditions.

A theory of electrodynamic response for bounded metals: Surface capacitive effects

“…It is to the latter that the SPWs contribute. We find that under ABCs the surface contribution would be totally lost and hence no SPWs would exist, in agreement with our recent work 92 showing that the apparent SPW solution admitted in ABC-based HDM is incompatible with that of the DM.…”

“…It leads to lossless SPWs at the critical point 93 , a highly desirable attribute in plasmonics. This finding defies conventional wisdom 95 but is consistent with empirical facts and agrees with our previous work 92,[96][97][98] , where it was shown that the decay rate of SPWs is not simply a sum of the thermal collision rate, Landau damping rate and other loss rates such as inter-band absorption rates, but should be from these deducted by a positive-definite term, which is guaranteed by the principle of physical causality.…”

“…As shown in Refs. 92,96,97 , the resulting equation admits of two types of solutions representing VPWs and SPWs, respectively. Those of VPWs satisfy S (k, ω) ≡ 0, and then the VPW frequencies are obtained as solutions to the secular equation H −ω 2 = 0.…”

“…As shown in Refs. 92,96,97 , the SPW dispersion relation is determined by the equation that s (k, ω) = 0. Further discussions of this equation and the properties of SPWs are presented in Ref.…”

Electrostatic responses of anisotropic dielectric films

“…As a result, boundary conditions are done away with in totality. It should be mentioned that this macroscopic description of surfaces has recently been employed in the study of surface plasma waves, [2][3][4] i.e. electron density ripples propagating on the surface of conductors.…”