Investigation Of The Graphene-based Nanocavity Supporting Plasmonic Whispering Gallery Modes

The surface plasmon polaritons（SPPs）-guided whispering gallery mode（WGM） resonant cavity supports WGMs withhigh quality factor（Q factor） and small mode volume（V_m）. And the size of the resonant cavity could be further reduced to subwavelength size, which overcoming the diffraction limit.The noble metals, such as Au and Ag, have been popular plasmonic materials. However, once the geometries are fixed, the plasmonic devices based on metals suffer from non-tunability, and the ohmic loss of metals is great, which would limit the developments of the plasmonic devices based on metals. Graphene with positive imaginary part of conductivity would support the transverse magnetic（TM） SPPs. Graphene has been theoretically and experimentally proved high confinement capability, low loss and regulatory. Hence, the SPPs-guided WGM resonant cavity based on graphene will be one of the key component for a series of practical applications, for example, low threshold lasers, high sensitive sensors, nonlinear optics and high efficiency single photon source. The conductivity of graphene depends on the chemical potential which could be controlled by chemical doping or static electric field. We can tune the conductivity of graphene locally and inhomogeneously. In this thesis, we numerically investigate the mode characteristics of SPPs-guided WGM resonant cavity based graphene, and analyze its physical mechanisms.Firstly, we numerically studied the tunable graphene equilateral triangle nanocavity. And the relation between mode characteristics and the size of cavity R₁, frequency, relaxation time and chemical potential of graphene are investigatedwith the finite element method. The results show the Q factor does not change obviously with the variation of R₁ in the near infrared spectrumwhen other parameters are stable, but the change of frequency, relaxation time and chemical potential can influence the Q factor. A high-order plasmonic WGM with a Q factor of 147.93 and an ultra-small mode volume of 10^-7（λ₀/2n）³-is obtained in our nanocavity with a wavelength of around 1.415μm in free space, with a corresponding Purcell factor as high as 10^-8.Then the mode characteristics and output characteristics of graphene-based deformed equilateral triangle nanocavity which is connected to vertex output waveguide with geometrical parameters and material parameters of graphene are analyzed by the finite element method. When the chemical potential μ_c1 and μ_c2 are set as 0.9eV and 0.59 eV, the Purcell Factor of the integrated plasmonic device with cavity size of 30 nm and waveguide width of 5nm can reach 7¹0, and the corresponding output efficiency is 20.2%.Finally, the coupling characteristics of graphene nanodisks are also numerically investigated with the finite element method. As the inter-disks gap g decreases, the behavior of modes splitting occurs in the twin coupled graphene nanodisks. And the coupling of the fundamental mode TM_8,1 and first-order mode TM_5,2 also exist in the twin coupled nanodisks. The size difference of two graphene nanodisks also influences the mode coupling characteristics. In addition, the geometry of trimer plasmonic molecules is another key factor for the coupling characteristics. The results show the geometry of the structure has an effect on the mode electric field Ez distribution, the corresponding frequency and the Q factor. The Q factor of one coupled mode could reach 510 when the α=135°.