Ultra-high temporal and spatial resolutions using femtosecond and attosecond pulses

We show that ultra-high temporal Deltat and spatial Deltax optical resolutions can be provided simultaneously only by using a pulse with an ultra-short central wavelength of the wavepacket or/and decreasing the distance between the light source and sample. Such behaviour is the result of the existence of a cut-off frequency omega(co) in the Fourier time expansion of an electromagnetic wavepacket when we consider its transmission through an aperture. The phenomena could be important for achievement of femtosecond or attosecond temporal resolutions together with confinement of light to nanometre-scale transverse dimensions in near-field scanning optical microscopy and spectroscopy.