Page 266 - High Power Laser Handbook

234 So l i d - S t at e La s e r s Thin-Disc Lasers 235

α E
σ ≤ th elast (T −T ) (10.8)
f,max 1 − ν av cool
The tensile strength of YAG is 130 MPa, and the temperature
26
difference between the disc and the cooling can be calculated with
the effective thermal resistance derived above, but now neglecting
the heat sink. With an effective thermal resistance of 23 Kmm²/W, the
maximum heat density per area is 2.1 W/mm² (i.e., ~24 W/mm²
absorbed pump power density if we only take into account the quantum
defect as heat source).
The azimuthal stress inside the disc can be significantly reduced
by mounting the disc on a heat sink with adequate stiffness. A detailed
analysis of the stress inside the disc must also include the effects of
bending; this will be done in the next section based on finite element
analysis (see Sec. 10.5.4).
10.5.4 Deformation, Stress, and Thermal Lensing
A radially symmetric model of the disc mounted on the heat sink (or
alternative supporting structures) was generated using the commer-
cial finite element software COMSOL. Multiphysics and a uniform
heat source distribution was applied inside the pump spot. Figure 10.5
shows the calculated temperatures for the situation discussed in the
previous section though now for a large pump spot. The assumed
60-W/mm² absorbed pump power density and 7.5-mm pump spot
radius are equivalent to ~10 kW absorbed pump power, which is suf-
ficient for 6 kW laser power.
The main problem to be answered by finite element analysis
(FEA) calculations is the amount of tensile stress inside the disc. This
stress can be controlled even for high pump power densities by
choosing an appropriate mounting design. Figure 10.6 shows that
this stress is limited by the mounting on the CuW heat sink.

Temperature (°C)
200
180
160
140
120
100
80
60
40
20
Figure 10.5 Calculated temperature for a Yb:YAG thin-disc; thickness
180 µm, mounted on a CuW heat sink with thickness 1 mm, pump spot
radius 7.5 mm, and heat source per area 5.4 W/mm², equivalent to 60 W/mm²
absorbed power density.