High Power Laser Science and Engineering, (2019), Vol. 7, e42, 7 pages.
© The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/
licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
doi:10.1017/hpl.2019.32
Modeling of the 3D spatio-temporal thermal profile of
joule-class Yb
3+
-based laser amplifiers
Issa Tamer
1,2
, Sebastian Keppler
1,2
, J
¨
org K
¨
orner
2
, Marco Hornung
1,2
, Marco Hellwing
2
, Frank Schorcht
1
,
Joachim Hein
1,2
, and Malte C. Kaluza
1,2
1
Helmholtz-Institute Jena, Fr
¨
obelstieg 3, 07743 Jena, Germany
2
Friedrich-Schiller-University Jena, Max-Wien Platz 1, 07743 Jena, Germany
(Received 8 March 2019; revised 4 May 2019; accepted 4 June 2019)
Abstract
Thermal profile modification of an active material in a laser amplifier via optical pumping results in a change in the
material’s refractive index, and causes thermal expansion and stress, eventually leading to spatial phase aberrations, or
even permanent material damage. For this purpose, knowledge of the 3D spatio-temporal thermal profile, which can
currently only be retrieved via numerical simulations, is critical for joule-class laser amplifiers to reveal potentially
dangerous thermal features within the pumped active materials. In this investigation, a detailed, spatio-temporal
numerical simulation was constructed and tested for accuracy against surface thermal measurements of various end-
pumped Yb
3+
-doped laser-active materials. The measurements and simulations show an excellent agreement and the
model was successfully applied to a joule-class Yb
3+
-based amplifier currently operating in the POLARIS laser system
at the Friedrich-Schiller-University and Helmholtz-Institute Jena in Germany.
Keywords: diode-pumped solid-state lasers; high intensity lasers; laser amplifiers; spatio-temporal thermal profile modeling; ytterbium
1. Introduction
Advances in relativistic laser plasma physics are reliant
on the optimization of state-of-the-art laser systems toward
higher peak and average powers. These laser pulses, when
focused to intensities in excess of 10
20
W/cm
2
, can acceler-
ate electrons
[1]
and ions
[2]
to relativistic velocities, as well
as generate X-rays
[3]
and high harmonics
[4]
. Attaining and
increasing such laser intensities requires the proper design,
characterization, and optimization of the final multi-pass
amplifier stages to amplify the seed laser pulse well into the
multi-joule regime while maintaining its spatial and temporal
fidelity.
Within these final multi-pass amplifier setups, large beam
diameters are necessary to reduce the fluence of the laser
pulse below the laser-induced damage threshold (LIDT) of
the active materials. Consequently, these large beam profiles
are particularly susceptible to effects leading to wavefront
aberrations, the ramifications of which are prominent due
to the long propagation distances typically found in non-
imaging joule-level multi-pass amplifiers. Such wavefront
aberrations occur in part due to the quantum defect, in which
a portion of the pump laser energy is transferred to the active
Correspondence to: I. Tamer, Helmholtz-Institute Jena, Fr
¨
obelstieg 3,
07743 Jena, Germany. Email: issa.tamer@uni-jena.de
material in the form of heat, resulting in a change in the
temperature profile that forms within the timescale of the
pump pulse. This pump-induced temperature change causes
a modification of the refractive index
[5]
, leads to thermal
expansion and stress, and alters the emission and absorption
spectra
[6]
of the laser material.
To mitigate the impact of these effects, narrowband diode-
pumped Yb
3+
-doped active materials can be employed,
which can provide a significantly lower quantum defect
of 9%
[6]
when compared to other dopants, such as Nd
3+
(24%
[7]
) or Ti
3+
(33%
[8]
). Present-day high-power Yb-
based laser systems have used this advantage to achieve
pulse energies higher than 50 J
[9]
and 100 J
[10]
within
pulse durations of 100 fs and 10 ns, respectively. De-
spite the reduced heat load within Yb
3+
-doped materials,
significant detrimental effects can still occur due to the
pump-induced thermal profile. The influence of strong ther-
mally induced
[5]
wavefront aberrations – in conjunction
with electronic contributions
[11]
– may heavily distort
[12]
the
amplified beam profile upon propagation. Additionally, the
spatially varying depolarization of the amplified seed beam
due to thermal stress
[5]
induced by the thermal gradient in
a multi-hundred-joule pumped active material can directly
lead to energy loss and possible spatial profile deformations
1
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