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342    So l i d - S t at e   La s e r s                                                                       Ultrafast Lasers in Thin-Disk Geometry    343


                      spectral  filtering  due  to  the  gain  bandwidth,  stabilizes  additional
                                                                 87
                      pulse  generation  against  Q-switching  instabilities.   The  basic  idea
                      for the additional stabilization in the femtosecond region is as fol-
                      lows: If the energy of a pulse increases by relaxation oscillations, the
                      spectrum  of  the  pulse  is  broadened  by  SPM. A  broader  spectrum,
                      however,  will  experience  a  smaller  average  gain  due  to  the  laser
                      material’s finite bandwidth. This effect has a much smaller influence
                      on  picosecond  lasers,  because  SPM  is  much  weaker.  In  addition,
                      inverse saturable absorption of the absorber further reduces the QML
                      threshold. 88,89  Again, the basic idea is simple: An inverse saturable
                      absorption  causes  a  rollover  in  the  nonlinear  reflectivity,  which
                      increases  the  losses  for  pulses  with  higher  energy,  thus  damping
                      relaxation oscillations. Therefore, SESAMs are ideal for mode-locking
                      diode-pumped  solid-state  lasers,  because  semiconductor  saturable
                      absorbers  inherently  have  a  large  absorption  cross  section  (a  low
                      absorber saturation energy), and their nonlinear reflectivity dynam-
                      ics can be designed over a wide parameter range. In contrast, the low-
                      gain  saturation  energy  of  VECSELs  makes  them  immune  to  such
                      Q-switching  instabilities,  moreover  their  short  upper-state  lifetime
                      (typically in the nanosecond regime) tends to restrict the pulse repeti-
                      tion rate to the gigahertz range for stable CW mode locking. High-
                      power TDLs typically operate in the 1- to 100-MHz regime, because
                      at much higher pulse repetition rates, QML instabilities become more
                      severe. This is, however, not a problem for most applications, because
                      the  larger  pulse  energy  at  lower  pulse  repetition  rates  is  advanta-
                      geous for many applications, such as precision micromachining.
                         Stable  mode-locked  operation  with  dynamic  gain  saturation
                      requires the absorber to saturate at lower intracavity energy than the
                      gain in order to obtain stable pulse formation. For mode-locked VEC-
                      SELs, the active region typically consists of the same material as the
                      absorber. Therefore, a large ratio between the mode areas on the gain
                      and on the absorber material is necessary to achieve saturation of the
                      absorber before the gain saturates. In this case (see Fig. 13.7a), geo-
                      metrical issues for the laser cavity give an upper limit for the repeti-
                      tion  rate  of  a  fundamentally  mode-locked  VECSEL.  One  way  to
                      overcome these issues is mode locking with similar mode areas on
                      the gain and the absorber (see Fig. 13.7b), which is referred to as 1:1
                      mode locking. In this case, SESAMs with low saturation fluence are
                      required, which can be achieved using quantum dot (QD) SESAMs
                      instead of conventional quantum well (QW) SESAMs. In QW-SES-
                      AMs, the product of the saturation fluence F  and the modulation
                                                            sat
                      depth DR is proportional to the energy needed to completely saturate
                      the absorber. This means that these two parameters cannot be adapted
                      independently. However, for 1:1 mode locking with ultrahigh repeti-
                      tion rates and very low pulse energies, a low F  and DR are required,
                                                            sat
                      according to the QML criterion. This problem could be overcome by
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