We investigated the two-photon-induced photoluminescence properties of single gold nanorods by scanning near-field spectroscopy. The process was found to be initiated by a sequential one-photon absorption for creating a pair of an electron and a hole in the sp and d bands. Photoluminescence is then radiated when the electron near the Fermi surface recombines with the hole near the X and L symmetry points. The polarization characteristics of emitted photons from the X and L regions were found to be different. These characteristics can be understood by the crystalline structure and the band structure of the gold nanorod. We found characteristic spatial oscillatory features along the long axis of the nanorods in photoluminescence excitation images. The images were well reproduced by density-of-states maps of the nanorods calculated with Green's dyadic method and were attributed to the spatial characteristics of the wave functions of the plasmon modes inside the nanorods.
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