Higher Heat Generation Density, Stronger Thermal Effects?

Posted on 2007-07-25 as a part of the Photonics Spotlight.

Permanent link: http://www.rp-photonics.com/spotlight_2007_07_25.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: encyclopedia articles on thin-disk lasers and thermal lensing

It is common wisdom (and seems pretty plausible) that the density of dissipated power in a laser crystal should be kept low enough to avoid excessive thermal effects, such as thermal lensing. In this light, it may appear unlikely that the concentration of the dissipated power in a rather thin disk of crystal material, as used in a thin-disk laser, is a good idea.

It is worth to consider what happens when e.g. the thickness of such a disk (made e.g. of Yb:YAG) is reduced to one half the original value, while leaving the total dissipated power unchanged:

• The density of dissipated power is doubled.
• The temperature gradient near the cooled surface of the disk stays unchanged, since the total heat flow (in watts per square millimeter) stays constant.
• Assuming a constant density of heat generation, the magnitude of the temperature gradient is linearly decreasing when moving toward the uncooled surface of the disk. At that surface, it becomes zero.
• As a consequence, the temperature difference between both surfaces is reduced to one half.
• The average temperature rise of the crystal with respect to the cooling finger is also reduced, but by less than a factor of 2, since the thermal impedance of the transition from crystal to heat sink (through the dielectric mirror) stays unchanged.

So in total we have reduced temperature rises, and consequently also reduced transverse temperature gradients and thermal lensing, even though we have doubled the density of heat generation.

In conclusion, one should be a bit careful concerning the link between power density and thermal effects; geometry has an important influence.