Manipulating electromagnetic local density of states by graphene plasmonics

Electromagnetic local density of states (ELDOS) counts the number of electromagnetic modes at a spatial point where a particle (atom, molecule, and quantum dot) spontaneously emits electromagnetic waves. ELDOS can be interpreted as a density of vacuum fluctuations of electromagnetic fields. Moreover, ELDOS is essential to control spontaneous decay rate (SDR) of particles; and thus plays a critical role in modern optical and quantum devices. Having a great degree of freedom to tune permittivity, graphene is an emerging building block to manipulate the ELDOS. In this work, we study SDR of a particle near a metallic split-ring resonator, which is embedded in a multilayered substrate incorporating a graphene layer. Analyzing ELDOS in such a complex multilayered system is not only computationally challenging but also highly important to practical devices. First, dispersion relations of graphene plasmonics and metallic plasmonics are comparatively studied. From our investigations, graphene offers several flexible tuning routes to control SDR, which highly depends on the chemical potential of graphene sheet and the position and polarization of particle. Then, considering graphene plasmonics is excited at infrared regime, we carefully design a metallic split-ring resonating around the same frequency range. Consequently, this design allows a mutual interaction between the graphene sheet and split-ring. To reduce the computational burden, boundary element method in conjugation with a multilayered medium Green's function is adopted. The multilayered medium Green's function automatically includes the information of the ultrathin graphene. Therefore, only the split-ring scatterer is meshed. Blue-shifted and splitting resonance peaks are theoretically observed, which suggests a strong mode coupling between the graphene and split-ring. Furthermore, the mode coupling has a switch on-off feature via electrostatically doping the graphene sheet. This work is fundamentally important to dynamically tune ELDOS and SDR in complex devices.