Page 375 - High Power Laser Handbook

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

Solid-state lasers can be operated at repetition rates that are sev-
eral orders of magnitude lower. The lower limit of the pulse repeti-
tion rate is usually set by the self-starting behavior. In the buildup
phase of CW mode locking, the intracavity pulse evolves from ran-
dom fluctuations of the CW operation, with much lower peak inten-
sities than the final pulse. As discussed in Refs. 94 and 95, the intensity
of these random fluctuations in the case of too-long resonators might
not be sufficient to ensure self-starting mode locking. So far, stable
mode locking has not yet been reported for repetition rates below
1 MHz; the lowest repetition rate from a mode-locked bulk solid-state
96
laser is 1.2 MHz, which corresponds to a cavity length of 121 m. A
sophisticated cavity design and several additional mirror bounces
were used to keep a reasonable footprint and a sufficient overall
mechanical stability. So far, the lowest repetition rate of ultrafast TDLs
97
60
has been 4 MHz when using the passive multipass cell concept or
2.93 MHz when using an active multipass cell with multiple passes
14
through the gain disk. In both cases, the operation was self starting,
the average output power was in the tens of watts range, and the
pulse energy exceeded 10 mJ.

Pulse Energy
The average output power of a mode-locked laser is the product of
the pulse energy and the repetition rate. Therefore, the typical higher-
average powers and lower repetition rates in solid-state TDLs result
in pulse energies about five orders of magnitude higher than in the
case of VECSELs (see Fig. 13.6).
Pulse-energy scaling of TDLs into the 100-mJ regime requires fur-
ther considerations, such as the nonlinearity of the atmosphere in the
resonator. In a typical mode-locked TDL, the nonlinearity in the cav-
61
ity is controlled by moving a few-millimeter-thick fused silica plate
that is inserted at Brewster’s angle along the axis of the diverging
beam near the output coupler. The amount of SPM scales inversely
proportionally to the cross section of the laser beam in the plate. The
first intuition one might have is that the nonlinearity of air (3 ×
10 –19 cm /W ) is negligible compared with the nonlinearity of fused
2
98
2
–16
99
silica (2.46 × 10 cm /W ), because air’s nonlinear coefficient is
roughly three orders of magnitude lower than silica’s. However, the
cavity length of a TDL with high pulse energies can be as large as several
tens of meters; therefore, the total SPM introduced by the air can easily
dominate over the SPM introduced by the thin fused silica plate.
Another challenging point for generating pulse energies exceed-
ing 10 mJ in the standard TDL configuration is the large amount of
dispersion needed to balance the total SPM introduced by the air
atmosphere in these very long cavities in order to obtain stable soliton
mode locking. Here, the dispersion needed becomes too large to be
balanced by a reasonable amount of bounces on dispersive mirrors.