We have enhanced the performance of near-field scanning optical microscopy (NSOM) in terms of the spatial resolution and the sensitivity in signal detection. A careful preparation of an aperture-NSOM probe provides us with a spatial resolution as high as 30 nm in fluorescence imaging spectroscopy. We have applied this technique to map out the center-of-mass wave functions of an exciton confined in a GaAs quantum dot (a monolayer-high island formed in a quantum well). The spatial profile of the exciton emission, which reflects the shape of the island, differs from that of biexciton emission, due to different distributions of the polarization field for the exciton and biexciton recombinations. A theoretical calculation of the spatial distribution of the polarization field quantitatively reproduced the experimental result. Furthermore, mapping of an excited state wave-function with a node structure is also demonstrated. The novel technique can be extensively applied to wave-function engineering in the design and fabrication of quantum devices.
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