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The spatial localization of the electromagnetic field (EMF) on periodic and aperiodic structures has been studied by SNFOM. The influence of the polarization of the probing optical radiation on the image obtained by SNFOM in the "reflection" working mode has been studied. The spatial distribution of EMF near the periodic structures has been studied by the numerical method based on the direct solution of the Maxwell equations. The calculations have been compared with the experimental data. The three-dimensional EMF distribution near the sublong-wave hole in the metallic film has been studied.