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344   So l i d - S t at e   La s e r s     Ultrafast Lasers in Thin-Disk Geometry    345


                      Possibilities  for  overcoming  this  problem  and  for  achieving  pulse
                      energies in the 10 to 100 mJ regime are to reduce the nonlinearity in
                      the resonator by operating it in vacuum or in helium or to reduce the
                      intracavity pulse energy by increasing the laser cavity’s output cou-
                      pler transmission. Under helium atmosphere, pulse energies of up to
                                        60
                      11  mJ  were  obtained,   with  an  intracavity  pulse  energy  exceeding
                      100 mJ. The second approach requires an increased gain per cavity
                      roundtrip,  which  can  be  achieved  in  a  cavity  setup  with  multiple
                      passes through the gain medium. With this concept, pulse energies of
                      26 mJ and an output coupler of 78 percent, and thus an intracavity
                      pulse energy of only 34 mJ, were demonstrated in air atmosphere. 14
                         The available pulse energy for VECSELs is limited by the carrier
                      lifetime, which hinders operation at megahertz repetition rates for
                      CW pumping. As discussed in the previous section, the maximum
                      cavity length is limited by the onset of multiple pulsing instabilities
                                             93
                      or harmonic mode locking.  The highest pulse energies reported for
                      mode-locked  VECSELs  are  only  in  the  order  of  several  100  pJ, 38,68
                      which is orders of magnitude lower than in solid-state TDLs.


                      Pulse Duration
                      For both ultrafast TDLs and semiconductor disk lasers, the full poten-
                      tial  to  achieve  extremely  short  pulse  durations  has  not  yet  been
                      exploited. Currently, ultrafast TDLs are restricted to pulse durations
                      of more than 220 fs. To date, all ultrafast solid-state TDLs have been
                                                            3+
                                3+
                      based on Yb -doped gain materials. In the Yb  ion, the so-called lan-
                      thanide contraction leads to a lowered distance of the 5s and 5d shells
                      from the atom core. Therefore, the 4f shell, in which the optical transi-
                      tions take place, is less shielded from the surrounding crystal field
                      than is the case in other rare earth ions. This situation leads to a stron-
                      ger coupling to the host’s phonons and thus to broad absorption and
                      emission spectra, which have been shown to support the generation
                      of  pulse  durations  less  than  60  fs  in  longitudinally  pumped  low-
                                                    100
                      power bulk lasers (e.g., in Yb:glass,  Yb:LuVO ,  Yb:CaGdAlO ,
                                                               101
                                                                              102
                                                                             4
                                                              4
                      Yb:LaSc (BO ) ,  or Yb:NaY(WO )  104 ). Such short pulses require a
                                   103
                             3
                                                   4 2
                                 3 4
                      gain bandwidth Df  of about 20 nm in the spectral range of ~1 mm.
                                      g
                      However, the most common gain material for the solid-state TDL is
                      Yb:YAG,  which  was  chosen  for  its  beneficial  CW  properties,  even
                                                                              3+
                      though  its  gain  bandwidth  is  narrower  than  for  many  other Yb -
                      doped  gain  materials.  Consequently,  the  shortest  pulse  durations
                      obtained  with  Yb:YAG  TDLs  were  around  700  fs, 42,64   whereas
                      Yb:Lu O  TDLs enabled the generation of 535-fs and 329-fs pulses at
                             3
                           2
                                                                   67
                      63 W and 40 W of average output power, respectively.  Investigation
                      of new gain materials with even broader emission bandwidths has
                      enabled the generation of pulses as short as 240 fs at 22 W of average
                                                            62
                      output  power  with  Yb:KYW  (Yb:KY(WO ) )   and  227  fs  with  an
                                                          4 2
                      average output power of 7.2 W with Yb:LuScO .  The differences in
                                                               66
                                                              3
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