  The near-field diffraction of fs and sub-fs light pulses by nm-size slit-type
apertures and its implication for near-field scanning optical microscopy (NSOM)
is analyzed. The amplitude distributions of the diffracted wave-packets having
the central wavelengths in the visible spectral region are found by using the
Neerhoff and Mur coupled integral equations, which are solved numerically for
each Fourier's component of the wave-packet. In the case of fs pulses, the
duration and transverse dimensions of the diffracted pulse remain practically
the same as that of the input pulse. This demonstrates feasibility of the NSOM
in which a fs pulse is used to provide the fs temporal resolution together with
nm-scale spatial resolution. In the sub-fs domain, the Fourier spectrum of the
transmitted pulse experiences a considerable narrowing that leads to the
increase of the pulse duration in a few times. This imposes a limit on the
simultaneous resolutions in time and space.
