In this letter, we theoretically investigate the coupling of far-infrared surface plasmon polaritons (SPPs) between spatially separated graphene sheets. By using the finite-difference frequency-domain method, we numerically illustrate the SPP propagation and modulation in the graphene sheets. The coupling of SPPs is employed to design zero insertion loss optical splitters, 1 × 2 digital optical spatial switches, and ultra-compact Mach-Zehnder interferometers with the arm length far below the diffraction limit. The study provides an effective way in designing graphene based high-speed and ultra-compact optoelectronic devices.

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The enhanced second-harmonic generation (SHG) from a monolayer WS2 coupled to a plasmonic nanocavity is experimentally and theoretically investigated. The nanocavity is comprised of monodispersed Ag nanocubes separated from an Ag film by a spacer Al2O3, namely, the nanoparticle on mirror (NPoM) system. When the surface plasmon polariton resonance (SPPR) wavelength of NPoM nanocavity overlaps well with the SHG wavelength of the monolayer WS2 (namely, harmonic resonance), a ∼300-fold SHG enhancement is achieved in experiment. For theoretical understanding, the quantum mechanical density matrix method has been used to develop a theory for SHG. It is found that the SHG intensity of nanohybrid is proportional to the square of the local-field intensity in NPoM nanocavity at SHG wavelength, which is ascribed to the dipole–quadrupole interaction between dipole, P SHG, in the monolayer WS2 and quadrupole, Q Ag, in Ag nanocavity. It is significantly different from that in metal nanoparticles under harmonic resonance, which is proportional to the local-field intensity. Therefore, it provides a novel mechanism for enhancing SHG signals from metal–semiconductor nanohybrids, which has potential applications in nonlinear devices and hybrid nonlinear metasurfaces.