Page 264 - High Power Laser Handbook

232 So l i d - S t at e La s e r s Thin-Disc Lasers 233

at the system’s “energy balance”, roughly 9 percent of the pump
power is transformed to heat, and, for the highly efficient thin-disc
laser, about 60 percent is transformed to laser power. The remaining
31 percent is emitted as fluorescence radiation. We can expect that all
fluorescence that is emitted at angles smaller than the critical angle
will leave the disc through the AR-coated front face, either directly or
after one reflection at the HR-coated face. For YAG the refractive index
is 1.83, and the critical angle is therefore about 33°; therefore about
16 percent of the fluorescence will leave the disc through the AR face.
If we sum these results, about 26 percent of the absorbed pump power
will be transformed to fluorescence that is “captured” inside the disc.
Neglecting any further interactions of this fluorescence with the
disc material, the HR coating design will determine whether this fluo-
rescence is emitted or transformed to heat. A coating that is highly
reflective at all angles and wavelengths will simply guide the fluores-
cence to the disc’s lateral surface, where it will be reflected, scattered,
“extracted”, or perhaps transformed to heat. Neither back reflection
nor back scattering is favorable due to the problems of amplified spon-
taneous emission (ASE) discussed later; in addition, extraction of
several kilowatts of power at the lateral surface is technologically
challenging. The contrary possibility is a coating which is highly trans-
parent at all wavelengths and all angles larger than the critical angle,
including a layer between the coating and the glue or solder (for mount-
ing), which is highly absorbing. With this coating, nearly all “captured”
fluorescence will be transformed to heat that must pass through the
heat sink. Because the combination of heat sink, solder/glue and cool-
ing has an effective thermal resistance of ~10 Kmm²/W, the 60 W/mm²
absorbed pump power discussed above would create an additional
temperature rise of 150°C.
A compromise between the reduction of fluorescence reaching
the lateral surface and heat generation would be a partially transpar-
ent coating; such a coating design would also be closer to designs that
are technically possible. For simplicity, assuming a transparency of
25 percent for all angles larger than the critical angle, the absorbed
fluorescence would create an additional temperature rise of only
40°C. This additional heat generation would also reduce the limita-
tion of absorbed pump power density to avoid boiling of the cooling
fluid to about 175 W/mm².
The additional temperature rise due to fluorescence absorption
would be much bigger if there were no lasing; in this case ~76 percent of
the absorbed pump power would be transformed to “captured” fluo-
rescence. With 25 percent transparency, the additional temperature rise
would be ~110°C, and the “boiling limit” would be 95 W/mm².
Figure 10.4 shows the results for different values of the absorbed
pump power. All these results are calculated without any heat spread-
ing. In the disc, the heat spreading will have only a very small influence