Propagation of Gain Surface Plasmon Polaritons in AB-Stacked Bilayered Graphene
Surface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal ("surface plasmon") and electromagnetic waves in the air or dielectric ("polariton") [1]. Due to the short-lived nature of this inverted state, experimental evidence of active plasmons in graphene has so far been elusive. As a result of this ultrashort-lived transient state, a consequence of the absence of an electronic gap, the observation of optical gain (negative conductivity) associated with the inverted state has been elusive in experiments [2]. In this paper the existence of a resonant optical gain at frequencies around the energy gap due to a singularity in its joint optical density of states has been predicted theoretically. Thus, the task is to find the physical and COMSOL® modelling condition of graphene SPPs simulation with gain. Using the electric conductivity frequency dependence for AB-stacked bilayer graphene with a tunable electronic band gap up to 300 meV data taking from [2], the AB-stacked bilayer graphene thin layer has been designed in 2D COMSOL® model. We use the COMSOL Multiphysics® software with the Wave Optics Module to setup AB-stacked bilayer graphene model at THz frequency band. We took a 2D model structure as the initial model from Application Libraries site file - graphene_spp.mph. Our studied structure consists of two air layers and a thin AB-stacked bilayer graphene layer between of them. Using the dependence of real and imaginary part of electric conductivity of the bilayered graphene presented in [2] we have calculated the dispersion dependences of real and imaginary parts of wave number for graphene SPPs. It was obtained two gain regions (44-65 THz, 105-140 THz), where the real conductivity part is negative and the imaginary part of wave number is positive, and SPPs can be expected with gain in graphene. We have estimated SSPs propagation length for the gain regions and have obtained that the propagation length has more than zero module values, mainly, in the band of 103-114 THz approximately. Thus, the damping, undamping and gain SPPs can be exist in studied graphene only in this band.
Summary. The numerical COMSOL® simulation confirmed that GSPPs with gain were observed using 2D model for the AB-stacked bilayered graphene layer between air areas and there is a good agreement with the theoretical data. Conclusions. The obtained modelling evidence of the gain SPPs in graphene existence gives the opportunities to greatly increase the SPPs propagation length in graphene layers. It can be used in designing and fabricating nanostructures with desired optical properties.
