1 3 O ct 2 00 3 Distortion - free tight confinement and step - like decay of fs pulses in free space

A method of formation of the tightly confined distortion-free fs pulses with the step-like decreasing of intensity under the finite-length propagation in free space is described. Such pulses are formed by the Fresnel source of a high refraction-index waveguide. The source reproduces in free space a propagation-invariant (distortion-free) pulse confined by the waveguide. Converse to the case of material waveg-uides, when the pulse goes out from the Fresnel (virtual) waveguide its shape is not changed, but the intensity immediately drops down to the near-zero level. Tight transverse confinement of a light wave in free space together with fast decreasing of its intensity after the finite-length propagation are required in many fields of optics, such as non-destroying light-matter interaction, control of light penetration-depth and surface processing. The effect is usually achieved by strong focusing a light beam by short-curvature-radius lenses or spherical mirrors. In the case of fs pulses, the control of the transverse and longitudinal intensity distributions is a particularly difficult problem, because the ultrashort pulses are distorted in the space and time domains by such optical elements (see, for example Refs. [1, 2, 3, 4, 5, 6]). Recently, it was shown that the tightly confined propagation-invariant (distortion-free) continuous waves with the fast decreasing of the intensity after the finite-length propagation in free space could be formed by the Fresnel source of 1