We have investigated second harmonic generation (SHG) from Ag-coated LiNbO 3 (LN) core-shell nanocuboids and found that giant SHG can occur via deliberately designed double plasmonic resonances. By controlling the aspect ratio, we can tune fundamental wave (FW) and SHG signal to match the longitudinal and transverse plasmonic modes simultaneously, and achieve giant enhancement of SHG by 3×10 5 in comparison to a bare LN nanocuboid and by about one order of magnitude to the case adopting only single plasmonic resonance. The underlying key physics is that the double-resonance nanoparticle enables greatly enhanced trapping and harvesting of incident FW energy, efficient internal transfer of optical energy from FW to SHW, and much improved power to transport the SHG energy from the nanoparticle to the far-field region. In this work we will address this problem by insightful design. The most important thing is to look for a nanoparticle with double SPR modes. For this purpose, we turn to nanoparticles of anisotropic geometry, among which nanorods have attracted great attention due to their dimension induced wavelength tunability and polarization sensitivity [11][12][13]. One can control the aspect ratio of nanorods easily and obtain double SPR modes simultaneously, which are associated with the longitudinal and transverse SPR modes [14,15]. Moreover, the optical cross-sections of nanorods are much higher than those of nanospheres, and this has attributed nanorods promising features in wide applications like low-threshold surface plasmon amplification [16,17] and ultrafast optical devices [18]. The two SPR modes can be designed to enable their wavelengths matched to the absorption bands and emission bands of fluorescent molecules absorbed in gold nanorods [19] for enhancing their fluorescence intensity. It would be expected that this double-resonance mechanism should also play a very good role in enhancing SHG intensity of nanostructured materials.To illustrate and confirm this hypothesis, we propose and design an anisotropic nanoparticle, an Ag-coated LiNbO 3 (LN) core-shell nanocuboid [Ag-LN in Fig. 1(a) [23,24]. This approach is efficient equally for nonlinear optical problem solutions.Assume a plane wave FW at the frequency of ω 1 is incident upon a nonlinear particle. The FW electric field 1
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