▎ 摘　　要

Although graphene's particularly strong third-order susceptibility has drawn intensive attention in theoretical and experimental studies, its low bulk nonlinear response heavily emphasizes the nanostructure's design for a sufficient magnitude of third-harmonic generation (THG). Meanwhile, currently few tools are available for accurate theoretical analyses of graphene's nonlinear performance within a relatively complex structure, which renders the design of graphene-based nonlinear optoelectronic devices even more challenging. In this work, a high-accuracy self-consistent numerical solver based on the boundary-integral spectral element method is first proposed for the THG problem. Starting from the coupled vector wave equations, the proposed solver solves for the fundamental frequency field and third-harmonic field together iteratively, and it covers the optical/electro-optic Kerr effects ignored by most previous THG studies. After validating the proposed method with the comparison between numerical results and experimental data, we extend our study to the THG enhancement strategy with ultrastrong localized surface plasmon resonances (LSPRs) and Kerr effects. For both optical and electro-optic Kerr effects, the systematic simulation is performed for graphene's THG within the incident spectra of 400-1000 nm. Compared with the THG of floating single-atom-layer graphene, numerical results show that under specific LSPR engineering, graphene's THG backward emission is enhanced by 4.4 x 10(5) times. Simultaneously applying the electro-optic Kerr process can further boost the THG emission. However, its contribution is only secondary compared with LSPR. This study is also extended to bilayer and trilayer graphene models under strong LSPR. (C) 2016 Optical Society of America