Page 273 - High Power Laser Handbook

242 So l i d - S t at e La s e r s Thin-Disc Lasers 243

with P the absorbed pump power in the element and E the laser
V
r
power density inside the thin-disc, N the density of Yb ions, E
3+
r,
0
the laser power density inside the thin-disc, σ em,laser the emission
cross sections at the laser wavelength, τ the radiative lifetime, and
N ASE the difference between the number of emitted and the number
of absorbed ASE-photons in the finite element. A Monte Carlo ray
tracing method is used to calculate the absorbed pump power in
each element, following each photon from the source through the
complete system.
Calculation of the temperature distribution within the disc is
based on the steady-state heat conduction equation with the Stokes
Defect and the power transmitted through the HR coating as heat
sources. This partial differential equation is solved by a finite volume
method. Initial values for N and E are derived analytically (with
r
2
averaged crystal temperature and absorbed pump power density). In
an iterative procedure, the laser power density and the excitation
density are calculated.
To calculate DN ASE , a Monte Carlo ray tracing method is used. A
set of photons with a statistical distribution of wavelength, starting
coordinates, and propagation vectors are traced through the crystal.
Absorption and amplification are computed, as are reflection and
transmission at the crystal boundaries.
Simulations 30-32 show that scaling of the output power of a single
disc is only limited by ASE as the pump spot diameter becomes larger
and larger. Fortunately, the gain of low-doped Yb:YAG is rather small,
so ASE occurs only at very high pump power levels. With this numeri-
cal model, it was shown that an output power of more than 40 kW with
one disc is possible. 31
Figure 10.12 shows some scaling results to more than 10 kW out-
put power that result from changing the pumped diameter, thus
demonstrating the scalability by increasing the pumped area for
high-power operation.

10.5.9 Influence of ASE
As we have seen, the temperature and the thermally induced stress
are limitations which can be handled for the thin-disc design. The
remaining possible limit is the amplified spontaneous emission
(ASE). Increasing the output power of a thin-disc by increasing the
size of the active region and keeping the thickness constant will lead
to an increasing transversal gain. As consequence, this will lead to a
reduction of the possible excitation in the disc, reducing signal gain
and efficiency. To discuss this more in detail, we will look at the inter-
action of excitation, gain, pump absorption and ASE in more detail.
The quasi-static model is principally suitable to analyze the influ-
ence of ASE on the performance of a thin-disc laser. The calculation of
ASE with a Monte Carlo ray tracing is very flexible and can also handle