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Thulium (Tm3+) is an excellent candidate for
infrared laser applications thanks to its broad emission spectrum at around 1.8
micron, which makes it very appealing for several applications from precise cut
and ablation of biological tissues to sensing applications (Hanna et al. 1988, Jackson and Lauto 2002, Allain, Monerie, and Poignant 1989, Scholle et al. 2010, Dobler et al. 2013, Godard 2007). Furthermore,
Tm3+ has a significant property, which is cross-relaxation process (3H4,
3H6  3F4, 3F4)
where two ions are promoted in the upper level of laser by every single pumping photon. This
process significantly improves pumping quantum efficiency
and lasing at 1.8 ?m. Yet most of laser simulations do not consider, or do not
directly measure, the reverse cross-relaxation process (3F4,3F4,?3H6,3H4)
that reduces the efficacy of cross-relaxation process.

Various glasses
including silica, fluoride, germanate and tellurite have been used as laser
host material (Jha, Shen, and Naftaly 2000, Yamamoto, Miyajima,
and Komukai 1994, Huang
et al. 2010, Richards
et al. 2008, Peterka
et al. 2004).

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Amongst of all oxide glasses, tellurite glasses have the lowest phonon energies
(~750 cm?1) and provide high rare earth ions solubility.

Independently from the type of glass, laser development and design optimization
rely on the accurate modeling and comparison of different doping levels (Jackson and King 1999, Evans et al. 2009).

While lifetimes and cross-sections are well known, the ion-ion related
parameters, namely cross-relaxation and the reverse transfer process (Jackson and King 1999, Evans et al. 2009, Taher et al. 2011, Cornacchia et al. 2002, Simpson et al. 2006, Gebavi et al. 2010) are
more difficult to obtain. In particular, these usually are not available as
parameters validated over a large interval of doping level and therefore
suitable for doping level optimization. In previous papers (Albalawi, Varas, Chiasera,
Gebavi, Albalawi, et al. 2017, Albalawi, Varas, Chiasera, Gebavi, Balda, et al. 2017), we numerically investigate the
reverse transfer process in Tm-doped tellurite glasses and compare it with
experiment with accuracy measurements
and best set-up validated by fitting experimental fluorescence decay curves of
both 3H4 and 3F4 levels.

We demonstrate that we are able to fit a set of samples with doping level
variations by a factor of 30 (0.36 mol% to 10 mol%) using the same parameters
for all samples. We also demonstrated information can be obtained on the
reverse cross-relaxation process parameter. This was an alternative approach to
the one based on Kushida as in Ref (Kushida 1973) . It defined
a as the ratio between reverse and cross
relaxation process and calculated it as of 0.03 (P22 = a  P41), i.e. a was equal 3% in Ref. (Albalawi, Varas, Chiasera,
Gebavi, Albalawi, et al. 2017) .

In this paper we evaluate and assess the impact of the
reverse cross relaxation parameter
on the amount of pump power
required to achieve a given population inversion. It shows also that a good
choose of glass depend on the value of the reverse cross relaxation process  

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