Fig. 1. Schematic views and SEM images of structures possessing plasmonic band structures:　(a), (b) Metal films with periodic arrays of sub-wavelength holes^[61]; (c), (d) periodic arrays of metal particles^[62]; (e), (f) metallic substrate coated with dielectric photonic crystal^[63]; (g), (h) metallic substrate coated with self-assembled dielectric spheres^[64].

Fig. 2. Field distributions of (a) SPP, (b) localized SPP and (c) spoof SPP^[65].

Fig. 3. (a) Plasmonic band structure of flat metallic substrates coated with two-dimensional dielectric photonic crystal layer^[63]. (b) Left panel: transmission spectra of Ag grating coated symmetrically with dielectric layers; right panel: folded dispersion of guided (solid lines) and SPP (dashed lines) modes of Ag grating coated symmetrically with dielectric layers^[67].

Fig. 4. Band structure of metal nanoparticle chain^[69].

Fig. 5. Properties of band which inside light cone including BIC, time and spatial coherence^[62,63].

Fig. 6. Topological nature of BICs^[63].

Fig. 7. Properties of plasmonic bands inside the light cone:　(a) Wave guiding^[93]; (b) complete band gap^[95]; (c) Dirac point^[97,98]; (d) negative refraction^[96]; (e) topological edge state^[46]; (f) spoof SPP waveguide^[99].

Fig. 8. Applications of plasmonics:　(a) Extraordinary optical transmission^[104]; (b) beaming light with a bull’s eye structure^[105]; (c) structural colors^[106]; (d) infrared perfect absorber^[108]; (e) distributed feedback laser based on silver particle array^[110]; (f) hydrogen sensor based on metallic photonic crystal slabs^[112]; (g) sensor based on hybrid plasmonic-photonic crystal^[64]; (h) coherent fluorescence emission by hybrid photonic-plasmonic crystals^[113]; (i) enhance Raman spectroscopy by using metal nanoparticles^[114].

Fig. 9. (a) Dispersion of graphene-based plasmons^[125]; (b) dispersion of graphene ribbon based plasmons^[129]; (c) TM band structure for monolayer graphene sheet array^[126]; (d) band structure for graphene ribbon array^[130]; (e) band structure for graphene-based plasmonic crystal^[128]; (f) band structure for one-dimensional dielectric grating coated with monolayer grapheme sheet^[125].

Fig. 10. Applications of graphene-based plasmonic: (a) Cherenkov terahertz radiation viagraphene plasmons^[133]; (b) complete absorption by periodic array of graphene nanodisks^[134]; (c) slow and release light based on graphene plasmons^[136]; (d) beam splitting and direction control of light based on monolayer graphene sheet array^[137].