Page 362 - High Power Laser Handbook

330 So l i d - S t at e La s e r s Ultrafast Lasers in Thin-Disk Geometry 331

13.3 Thermal Management in Thin-Disk Geometry

3+
In Yb -based solid-state lasers, as well as in semiconductor lasers, the
performance is sensitive to an increase in the temperature of the gain
3+
17
material. Yb -doped lasers exhibit a quasi-three-level laser scheme,
with a thermal population of the lower laser level according to the
Boltzmann distribution. The lower laser level’s population increases
with rising temperature, which lowers the achievable gain for a given
pump intensity. A comparable behavior can be found in semiconductor
lasers, where the carrier distribution in the valence and conduction band
is described by the Fermi-Dirac distribution. In this case, a rising tem-
perature leads to a broader energy distribution of the carriers and,
consequently, a lower maximum occupation number, which also affects
18
the gain. In both cases, an elevated gain temperature requires a higher
density of excited states to achieve the same gain as is reached in a “cold”
laser and leads to a nonlinear increase of processes that are detrimental
for the laser performance. These processes mainly result from different
types of interactions between exited states. In solid-state lasers, this effect
is known as “quenching,” and the dominating processes are migration
3+
19
to impurities and upconversion (which is not present in Yb -doped
lasers due to the lack of suitable higher energy levels). The correspond-
20
ing processes in semiconductor lasers are Auger recombination and
thermally excited escape of the carriers over the confining potentials into
the barrier regions. It is also important to note that the semiconductor
band gap decreases with rising temperature, leading to a typical red shift
of the central emission wavelength of ~0.3 nm/K.
Furthermore, in both material classes, the index of refraction n and
the length l exhibit a dependency on temperature T. Whereas the dn/dT
causes the formation of a thermal lens with rising temperature, the
dl/dT causes stress in the laser material and can induce depolarization.
Both effects have a detrimental influence on beam quality, which dete-
riorates for strong temperature gradients in different directions.
The strong thermal sensitivity of laser performance and beam
3+
quality in Yb -based solid-state lasers and semiconductor lasers thus
require efficient heat removal for power scaling. The thin-disk geom-
etry is ideally suited for this task. The disks are usually mounted onto
an actively cooled heat sink with their backside HR coated. The thin
disk supports efficient heat removal due to the large ratio of cooled
surface to pumped volume. Solving the corresponding heat equa-
tions shows that more than 90 percent of the heat is extracted via the
back face of the cylinder-shaped pumped region for beam radii that
are about six times larger than the disk thickness. 21,22 Therefore, even
if it is not possible to totally avoid a temperature gradient in the disk,
the remaining gradient is mainly one dimensional and perpendicular
to the faces of the disk. This maintains good beam quality, because
the resulting thermal lens is isotropic and can be compensated by a
standard resonator design.