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346   So l i d - S t at e   La s e r s     Ultrafast Lasers in Thin-Disk Geometry    347


                    2.0                 Yb: YAG     2.0      ∆T:  0 K 30 K 60 K  Gain
                   Gain cross section (10 −21  cm 2 )  1.5  Yb: LuScO 3  Gain (a.u.)  1.5
                                        Yb: Lu O
                                            2 3
                                                                      Field enhancement
                                        β = 0.15
                                                    1.0
                    1.0
                                                    0.5
                    0.5
                    0.0                             0.0
                      1020   1040   1060   1080         940    960    980   1000
                              Wavelength (nm)                 Wavelength (nm)
                                  (a)                             (b)

                 Figure 13.8  (a) Gain spectra of Yb:YAG, Yb:Lu O , and Yb:LuScO  for an inversion
                                                      3
                                                    2
                                                                  3
                 level β of 0.15. (b) Field enhancement and resulting gain spectra for a typical
                 VECSEL structure at different temperatures.  DT represents the temperature
                                                  91
                 difference to the designated operation temperature.
                      used for Fig. 13.8 uses seven QW layers in successive maxima of the
                      standing wave pattern ). However, the generation of transform-lim-
                                         91
                      ited  pulses  in  the  femtosecond  regime,  which  exploit  a  significant
                      fraction of the bandwidth, is challenging. Most SESAM mode-locked
                      VECSELs operate at few-picosecond pulse durations, with an optical
                      bandwidth below 1 nm in the slow saturable absorber regime.
                                                                  70
                         The first subpicosecond pulses from a VECSEL  were obtained
                                                                 108
                      with a special SESAM, utilizing the AC Stark effect.  In this device,
                      the strong electromagnetic field during the pulse leads to a blue shift
                      of  the  absorption.  Hence,  for  wavelengths  longer  than  the  peak
                      absorption wavelength, the absorption decreases. Because no carriers
                      are involved in this process, the recovery time is comparable to the
                      pulse duration and is much faster than in conventional SESAMs. To
                      further  decrease  the  SESAM’s  recovery  time,  the  single  QW  was
                      placed near the surface to enable fast recombination for carriers by
                      tunneling into surface states. By applying such an AC Stark SESAM,
                      pulses as short as 477 fs with 100-mW average output power at a
                      repetition rate of 1.21 GHz were realized as early as 2002.  Six years
                                                                      70
                      later,  an  improved AC  Stark  SESAM  and  a  carefully  tailored  gain
                      spectrum  of  the  VECSEL  resulted  in  260-fs  pulses  with  25  mW  of
                                         69
                      average output power.
                         Even shorter pulses of only 190 fs could be obtained by optimiz-
                      ing  the  spectral  position  of  the  SESAM’s  absorption  maximum  in
                      relation to the VECSEL’s gain maximum by varying the temperature
                      of both devices. However, in this sensitive operation regime, band-
                      width-limited pulses could be observed only in a temperature range
                      of about 10°C, which limited the applicable pump power. Therefore,
                      the  average  output  power  did  not  exceed  5  mW  for  the  shortest
                                    109
                      observed pulses.  A recent breakthrough was the demonstration of
                      a mode-locked VECSEL with only 60-fs pulses; however, the output
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