On the validity of the local Fourier analysis

Local Fourier analysis (LFA) is a useful tool in predicting the convergence factors of geometric multigrid methods (GMG). As is well known, on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such methods. In this work, using the Fourier method, we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems

Hot-Electron Intraband Luminescence from GaAs Nanospheres Mediated by Magnetic Dipole Resonances

Significantly enhanced electric field in plasmonic hot spots can dramatically increase the linear and nonlinear absorption of light, leading to a high-temperature electron gas which radiates, through mainly intraband transition, a broadband luminescence quite similar to blackbody radiation. Here, we demonstrate that such hot-electron intraband luminescence (HEIL) can also be achieved by exploiting the significantly enhanced electric field at the magnetic dipole resonances of gallium arsenide (GaAs) nanospheres (NSs). We show that monocrystalline GaAs NSs with distinct electric and magnetic dipole (ED and MD) resonances can be obtained by using femtosecond laser ablation and annealing. Significantly enhanced second harmonic generation and broadband HEIL are observed when the MD resonances of such GaAs NSs are resonantly excited. The lifetime of the HEIL is found to be as short as ∼82 ps, indicating a significant enhancement in radiative intraband transition rate. We reveal that the slope extracted from the dependence of the HEIL intensity on the irradiance is linearly proportional to the energy of the emitted photon. The existence of distinct ED and MD resonances in combination with a direct bandgap makes GaAs NSs an attractive candidate for constructing novel all-dielectric metamaterials and active photonic devices