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250    So l i d - S t at e   La s e r s                                                                                              Thin-Disc Lasers     251


                         Besides the results on maximum power or efficiencies which are
                                                  35
                      presented in the mentioned paper , there is especially one important
                      feature in Eq. (10.32): the strong influence of the thermal load param-
                      eter C (cf. Sec. 10.5.1) and of the internal loss b inside the resonator.
                      This relation also holds for efficiency calculations.
                         Based  on  considerations  similar  to  the  ideas  presented  in  Sec.
                      10.5.10 and Fig. 10.13, a slightly different expression for the reduced
                      lifetime was found: 36
                                                    τ
                                τ ASE  ≈  exp(2 g +  gEi(2 gr h + ) 2  p /  ) 2 gEi(2 g)     (10.33)


                         This can be approximated by

                                               r      r 2  
                                        τ   ~  τ  p  exp −   p  g       (10.34)
                                         ASE   h       h   
                      With the lifetime reduction from Eq. (10.33), a similar dependence of
                      maximum output power from the internal loss and the thermal load
                      parameter  as  in  Eq.  (10.32)  can  be  derived.  The  results  are  clearly
                      beyond actually possible or planned thin-disc designs, but even more
                      than 20 MW from one disc seem feasible if the internal loss b inside
                      the  resonator  would  be  reduced  to  0.25  percent—but  requiring  a
                      pump spot diameter of ~5.5 m.
                         The achievable efficiencies are small (less than 10%), but follow-
                      ing both papers, 35,36  higher efficiencies are possible with a slightly dif-
                      ferent optimization. With an internal loss of 0.25 percent, 1 MW laser
                      power  will  be  possible  with  nearly  50  percent  optical-optical  effi-
                      ciency. Only a pump spot diameter of 20 cm will be required for this
                      laser power.


                 10.6  Thin-Disc Laser in Continuous-Wave Operation

                      10.6.1  High Average Power
                      Very high laser output power can be achieved from one single disc by
                      increasing the pump spot diameter while keeping the pump power
                      density constant. 37, 38  The highest output power reported for a single
                      disc is 6.5 kW. 39
                         Figure 10.18 shows one example for high output power with high
                      efficiency from a single disc (Trumpf Laser). More than 5.3 kW of
                      power has been achieved with a maximum optical efficiency of more
                      than 65 percent. This high efficiency of the thin-disc laser results in a
                      very high electrical efficiency for the total laser system—greater than
                      25 percent for industrial lasers with 8-kW output power and a beam
                      propagation factor M² of less than 24.
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