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322    So l i d - S t at e   La s e r s                                                                                  Ultrafast Solid-State Lasers     323


                      physics, electronics, and lasers. However, one region of the EM spec-
                      trum has been relatively underutilized to date: the extreme ultravio-
                      let (EUV) and soft x-ray range, corresponding to wavelengths 10 to
                      100 times shorter than visible light and with photon energies in the
                      range of tens to hundreds of electron volts. EUV light is both useful
                      and difficult to exploit for the same reason—that is, it is ionizing radi-
                      ation  that  interacts  strongly  with  matter.  This  strong  interaction
                      makes EUV light difficult to generate and severely restricts the types
                      of optics that can be used. However, the development of EUV optical
                      technologies has strong motivation. With EUV light, it is possible to
                      make microscopes that can resolve smaller features than is possible
                      using visible light. In addition, with EUV lithography, it is possible to
                      write  smaller  patterns.  Furthermore,  these  wavelengths  are  well
                      matched to the primary atomic resonances of most elements, making
                      possible  many  element-  and  chemical-specific  spectroscopies  and
                      spectromicroscopies.
                         The compelling scientific applications of EUV light have led to
                      the development of several dozen large-scale synchrotron radiation
                      sources, with more than 10,000 users worldwide. However, synchro-
                      tron light sources have major disadvantages, especially when uses for
                      EUV light move from the research lab into manufacturing or analyti-
                      cal applications. The most obvious disadvantage is the large size and
                      cost of these sources. Experiments must be constructed at the facility
                      itself, and any samples must be brought to the facility. Furthermore, a
                      number of emerging applications of EUV and soft x rays, such as soft
                      x-ray holography, require coherent light. This need has prompted the
                      development of large-scale “fourth generation” free-electron lasers.
                      However, these sources are even larger and often more costly than
                      synchrotron  light  sources.  The  need  for  small-scale  coherent  light
                      sources has motivated research in both x-ray lasers and upconversion
                      of coherent light from a laser to very short wavelengths. During the
                      past decade, both types of light sources have been successfully used
                      for a variety of application experiments, such as nanoscale imaging
                      and studies of molecular dynamics.
                         In  particular,  the  process  of  high-order  harmonic  generation
                      (HHG) has proven to be a very useful coherent tabletop x-ray laser
                      source  that  can  be  used  for  a  variety  of  applications  in  basic  and
                      applied science (Fig. 12.16). 46,47  In HHG, a very intense femtosecond
                      laser focused into an atomic gas is upconverted into the EUV or soft
                      x-ray regions of the spectrum. The HHG process results from a com-
                      plex laser-atom interaction, in which the light from an incident intense
                      laser pulse first pulls an electron from an atom through a process of
                      field ionization and then drives this electron back into its parent
                      ion. The resulting recollision process coherently emits a short-wave-
                      length photon whose energy is given by

                                          E   =  I +  . 32 U              (12.11)
                                           max   p     p
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