Near-field diffraction of fs and sub-fs pulses: super-resolutions of NSOM in space and time

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.