Page 345 - High Power Laser Handbook

314 So l i d - S t at e La s e r s Ultrafast Solid-State Lasers 315

which has a precompressor, and a final compressor, in which the
beam is expanded and the final compression step is with chirped
mirrors.

12.4 Thermal Mitigation

Whether in a regenerative or a multipass amplifier, the first stage is
by far the most sensitive to the deleterious effects of thermal lensing,
thermal astigmatism, and spherical aberrations. This is because of the
small mode size and the large number of passes through the gain
material. Although it is possible to stabilize a first amplification stage
under ~20-W pump powers with conventional water or thermoelec-
tric cooling near room temperature, the system is then restricted to
operate only at a single power level (i.e., a single energy and repeti-
tion rate), which makes it very inflexible in operation. Cryogenic
cooling can extend this operation range to high average powers and
high energies, minimizing aberrations. In the case of near-room tem-
perature cooling, higher-order aberrations remain, drastically limiting
beam quality. Although spatial filtering can restore beam quality, it is
at the cost of laser efficiency and, therefore, of maximum operating
32
power. The thermal lens is given by Koechner as
dn 1
f therm −1 = P (12.10)
dT 2κ A

where f therm is the dioptric power, dn/dT is the refractive index change
with temperature, κ is the thermal conductivity at a given tempera-
ture, A is the area in which the power is deposited, and P is the total
power deposited. If we plug in some numbers for Ti:sapphire, we can
see a factor of 250 reduction in the thermal lens power and, thus, a
reduction in distortions in the pumped crystal as the temperature is
reduced from 300 K to 77 K due to the drop in dn/dT and the increase
in κ (Fig. 12.10).
If we look at the focal length of the thermal lens as a function of
pump power, we can see that it would be difficult to make multiple
passes through an amplifier at 100 W of pump, unless the crystal
were cooled to at least 100 K. Figure 12.10 also shows that the focal
length from 300 to 233 K only changes from 1 to 3 cm, which is far too
short for practical amplifiers.
We must worry not only about the thermal lens but also about the
thermal distortions. Because pumping is typically done with a gauss-
ian mode, only the central part of that mode looks like a parabolic
singlet lens. Therefore, spherical aberrations are present any time the
seed mode samples from outside this central pumped region. As a
2
rule, keeping the pump intensity below 7 kW/cm has been some-
what successful with ultrafast lasers in the range of 300 to 233 K. In
this case, spherical aberrations can be considered as a loss mechanism