Graphene plasmonics for tuning photon decay rate near metallic split-ring resonator in a multilayered substrate

Study of photon decay rate is essential to various optical devices, where graphene is an emerging building block due to its electrical tunability. In this paper, we study photon decay rate of a quantum emitter near a metallic split-ring resonator, which is embedded in a multilayered substrate incorporating a graphene layer. Analyzing photon decay rate in such a complex multilayered system is not only computationally challenging but also highly important to experimentally realizable devices. First, the dispersion relation of graphene plasmonics supported at a dieletric/graphene/dielectric structure is investigated systematically. Meanwhile, the dispersion relation of metallic plasmonics supported at a dielectric/metal structure is studied comparatively. According to our investigation, graphene offers several flexible tuning routes for manipulating photon decay rate, including tunable chemical potential and the emitter's position and polarization. Next, considering plasmonic waves in a graphene sheet occur in the infrared regime, we carefully design a metallic split ring resonating around the same frequency range. Consequently, this design enables a mutual interaction between graphene plasmonics and metallic plasmonics. The boundary element method with a multilayered medium Green's function is adopted in the numerical simulation. Blue-shifted and splitting resonance peaks are theoretically observed, which suggests a strong mode coupling. Moreover, the mode coupling has a switch on-off feature via electrostatically doping the graphene sheet. This work is helpful to dynamically manipulate photon decay rate in complex optical devices.