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Since the beginning of the 90's, Titanium Sapphire has become the crystal of choice for the development of
ultrashort laser system producing very short and powerful pulses using the Chirped Pulse Amplification technique. In
parallel to these developments leading to commercial products, new laser crystals have been studied in order to reach
directly other wavelength range and to overcome the need to develop cw or pulsed green laser to pump the Titanium
Sapphire crystal. In order to be able to directly pump the crystals with very efficient and high power semiconductor
laser, new crystals doped with ytterbium ions have been developed. Actually, in the field of femtosecond lasers, an
intense interest has been shown for ytterbium-doped laser-crystals. These crystals are now well-known to be
particularly suitable for very efficient, directly-diode-pumped, solid state femtosecond oscillators. However, it has been
shown that the spectral properties of the Yb3+ dopant strongly depend on the matrix host and a lot of works have been
done to find the "ideal" matrix allowing both ultrashort-pulsed and high-power lasers. Firstly, in order to take advantage
of the very high-power laser diodes available to pump Yb-doped materials, ideal crystals need to be able to hold high
power pumping; so high thermal conductivity is required (\>5W/m/K, typically). Secondly, to generate very short
pulses (<100 fs) ideal crystals have to demonstrate very broad and smooth spectra. Among the numerous Yb-doped
crystals already studied, many failed with one of these two contradictory criteria (contradictory because broad spectra
are often synonymous of high disorder in the host lattice and the good thermal conductivity requires an ordered matrix
to allow good propagation of phonons). In this paper, we are relating the performance of a new Yb-doped crystal:
Yb:CaGdAlO4 (Yb:CALGO) and how it takes place in this quest of "ideal" crystal. Actually, this very new crystal
allowed, to our best knowledge, the shorter pulses ever produced with an Yb-doped crystal with the production of 47 fs
pulses. Moreover, compared to other crystals allowing the production of sub-100 fs pulses such as Yb:GdCOB,
Yb:BOYS and Yb:KGW, the atypical CALGO shows a thermal conductivity of 6.5W/m/K.
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