Page 262 - High Power Laser Handbook

230 So l i d - S t at e La s e r s Thin-Disc Lasers 231

with R th disk = h/l being the heat resistance of the disc and T being
0
,
th
the temperature at the disc’s cooled face. In particular, the maximum
temperature will be
1
T max = T + 0 2 I heat R th disk (10.3)
,
and the average temperature will be

1
T = av T + 0 3 I heat R th disk (10.4)
,
For most thin-disc host materials, the thermal conductivity depends
on the doping concentration and the material temperature. For YAG,
–1
–1
a thermal conductivity of 6 Wm K is a good approximation for low
doping (~7 percent) and temperatures of ~100°C. For a disc of 180 mm
thickness, this will result in a thermal resistance R th disk = 30 Kmm 2 . Typ-
W
,
ically, the disc is not directly cooled. Instead, it is coated at the cooled
face with an HR coating and this coating is mounted on a heat sink.
The heat sink is then cooled with a cooling fluid of temperature T cool .
The thermal resistance of the HR coating is determined not only by
the materials used, but also by the quality of the coating and the coat-
ing process used. From experimental results and numerical calcula-
tions, a thermal resistance R th HR = 10 Kmm 2 seems reasonable. The heat
,
W
sink may consist of a large variety of materials, including a copper-
–1
tungsten (CuW) metal matrix material (l = 180 Wm K) or a
–1
th
–1
chemical vapor deposition (CVD) diamond (l ≈ 1000 Wm K),
−1
th
that have a typical thickness of 1 mm. The thermal resistance of the
“mounting” itself can either be nearly neglected (e.g., for a soldering
layer of 10 to 50 mm thickness, resulting in less than 1 Kmm²/W ther-
mal resistance) or it can have a strong influence on the performance,
as with glued discs, wherein the glue layer creates a thermal resis-
tance of about 10 Kmm²/W due to its poor thermal conductivity. The
heat transfer to the cooling fluid is also strongly design-dependent,
with the best cooling reached via a highly turbulent flow of the cool-
ing fluid. With water and a so-called impingement cooling, an effec-
tive thermal resistance of this transfer of 3 Kmm²/W was demonstrated.
The resulting total effective thermal resistance with respect to the
average temperature of the disc can therefore be expected to be about
30 to 35 Kmm²/W.
For high-purity Yb:YAG, the heat generation inside the disc is
only due to the quantum defect, given by
l
1
η =− p ≈ 8 7.% (10.5)
heat l l
We can expect an average temperature in the disc of about 200°C if
an absorbed pump power density of 60 W/mm² and a cooling fluid