We propose graphene plasmonic crystals (GPCs) with a Kagome lattice, and investigate the properties of the flat band (FB) in the plasmonic system. By modulating the arrangement of the chemical potentials, a FB is obtained. Furthermore, the authenticity of the FB is confirmed by comparing the band structures and the eigen field distributions obtained from using the tight-binding modeled Hamiltonian with numerical calculations. The proposed Kagome-type GPCs could be of great significance for the study of novel effects in strong interaction systems in the field of plasmonics.

Fast light which demonstrates negative group velocity, is achieved by the anomalous dispersion or photon tunneling. However, many applications based on the fast light are limited due to the disadvantages of inferior tunability or nonlinear dispersion relationship of the fast light-carrying medium. In this paper, we propose the graphene plasmonic crystal waveguides whose guiding and claddings are composed of the graphene plasmonic metamaterials, where the backward propagating plasmonic modes corresponding to negative group velocity are observed. The dispersion relation and the group velocity of three types of graphene plasmonic crystal waveguides are investigated by varying the materials and the geometrical parameters of the graphene plasmonic crystal waveguides. Numerical experiments are designed to verify the authenticity of a fast plasmon in the graphene plasmonic crystal waveguides. Our proposed graphene plasmonic crystal waveguides might find significant applications in the fields of nanophotonics, on-chip electromagnetic field manipulation in deep nanoscale, and the technique of high density plasmonic integrated plasmonic circuit in the future.

The valley degree of freedom, like the spin degree of freedom in spintronics, is regarded as a new information carrier, promoting the emerging valley photonics. Although there exist topologically protected valley edge states which are immune to optical backscattering caused by defects and sharp edges at the inverse valley Hall phase interfaces composed of ordinary optical dielectric materials, the dispersion and the frequency range of the edge states cannot be tuned once the geometrical parameters of the materials are determined. In this paper, we propose a chirped valley graphene plasmonic metamaterial waveguide composed of the valley graphene plasmonic metamaterials (VGPMs) with regularly varying chemical potentials while keeping the geometrical parameters constant. Due to the excellent tunability of graphene, the proposed waveguide supports group velocity modulation and zero group velocity of the edge states, where the light field of different frequencies focuses at different specific locations. The proposed structures may find significant applications in the fields of slow light, micro–nano-optics, topological plasmonics, and on-chip light manipulation.

In this article, three categories of the edge states in the honeycomb lattice are investigated theoretically by using the effective tight binding Hamiltonian. The edge-bulk corresponding dispersions of zigzag, bearded, and armchair edge states analytically. The actual edge-bulk corresponding and the light field distribution of the graphene plasmonic crystals are obtained by solving Maxwell equations with boundary conditions, which are in good agreement with the analytical results. The proposed plasmonic structures provide guidance for designing the frequency range dependent property of topological structures, and show the potential applications in topological robust devices.

In this paper, the axial plasmonic Talbot effect is investigated with a graphene monolayer sheet with different chemical potential distribution. The Talbot distance of axial self-imaging effect is discussed by controlling the chemical potential of graphene and the frequency. The Talbot distance is in inverse proportion to the frequency, and decreases when the chemical potential of graphene increases. Moreover, the full width at half maximum (FWHM) of Talbot image is also studied by varying the frequency and the chemical potential of graphene. The result shows that the FWHM follows an upward curve with the increase of chemical potential and frequency. The proposed structure might find applications in the fields of deep sub-wavelength imaging and nano-lithography.