  By experimentally studying high-order harmonic beams generated in gases, we
show how the spatial characteristics of these ultrashort XUV beams can be
finely controlled under standard generation conditions. For the first time, we
demonstrate that these XUV beams can be emitted as converging beams and get
thereby focused after generation. We study this mirrorless focusing using a
spatially chirped beam that acts as a spatially localized probe located inside
the harmonic generation medium. We analyze the XUV beam evolution with an
analytical model providing the beam characteristics and obtain very good
agreement with experimental measurements. The XUV foci sizes and positions vary
strongly with the harmonic order and the XUV waist can be located at
arbitrarily large distances from the generating medium. We discuss how intense
XUV fields can be obtained with mirrorless focusing and how such
order-dependent XUV beam characteristics are compatible with broadband XUV
irradiation and attosecond science.
